Testimony

A Lean 4 library for machine-checkable models of biblical arguments.

Testimony formalises Christian arguments from Scripture — that Jesus of Nazareth is the promised Messiah, that salvation is by grace through faith — with every textual, linguistic, historical, hermeneutical and theological premise made explicit, sourced, and contestable.

What this project is — and is not

Lean verifies that conclusions follow from encoded premises. It cannot, by itself, establish that an interpretation of an ancient Hebrew text is correct, that a historical event occurred, or that a theological premise is true.

So Testimony is not a "computer proves Christianity" system. It is a machine-checked testimony: the argument's structure laid bare, its assumptions enumerated, its verdict left to the reader. A sceptic can see exactly which premises are assumed; a believer can see precisely how the argument hangs together; a scholar can swap in a rival interpretation and watch the derivation diverge.

What it produces

Three kinds of result, all machine-checked:

An argument is valid. Given a named, cited premise package, the conclusion follows over every valuation.

theorem reformed_establishes : Establishes reformed

A rival package does not establish the conclusion. Not a failure to find a proof — a countermodel is named, and it is the rival's reading written down.

theorem tridentine_not_establishes : ¬ Establishes tridentine

A premise is, or is not, load-bearing. Remove it, retain everything else, and see whether the argument survives.

theorem worksOfLaw_not_load_bearing : Establishes reformedWithoutWorksOfLaw
theorem lexical_premises_jointly_load_bearing :
    ¬ Establishes reformedWithoutEveryStrandsPremise

That last pair is the most useful thing the library does. Sola fide runs on three independent strands — Paul's ἔργα νόμου, Jesus' "your faith has saved you" at Luke 7:50, and Peter's refusal of the law's yoke at Acts 15:10 — so no strand's disputed premise carries it alone. An opponent must defeat all three. The virgin-birth argument began with a single strand, where defeating עַלְמָה defeated it outright; it now runs on four, and no single interpretive hinge is load-bearing — only all four jointly.

Which argument has which shape is a fact about the encodings rather than a matter of emphasis, and the roadmap lists every result the library claims, generated from the Lean source by lake exe statusgen.

Each argument also has a page of its own — Sola scriptura is the longest — generated by lake exe argdoc from the Lean files themselves: the module docstrings as prose, every position and objection as typeset notation over one numbered legend of claims, and every result with the axioms it rests on. Nothing on those pages is written twice.

Getting started

lake exe cache get   # fetch prebuilt Mathlib — do this first
lake build

Requires elan. The toolchain is pinned to Lean v4.33.1 by the Foundation dependency.

License

Two licences, split by what the file is:

• Code — Lean sources, scripts/, build tooling: Apache License 2.0.
• Documentation and data — this site, the encoded premises, citations and generated prose: Creative Commons Attribution 4.0 International.

Scripture and the commentary literature are quoted for citation and criticism; those works remain under their own terms, recorded per entry in the bibliography.

Rationale

The problem with arguing in prose

Christian arguments from Scripture are old, well developed, and almost always delivered as prose. A case that Jesus fulfils the messianic prophecies runs through dozens of texts, each requiring a reading, each reading resting on lexical, historical and hermeneutical assumptions that the argument rarely stops to enumerate.

This has three consequences, and they damage the argument's defenders more than its critics.

Premises hide. An argument that Micah 5:2 predicts the Messiah's birthplace assumes that Micah 5:2 is forward-looking prophecy rather than an oracle about a contemporary Judaean ruler. That assumption is doing real work. In prose it appears as a clause, or as nothing at all.

Disagreement diffuses. When two scholars disagree about sola fide, where exactly do they part company? Both accept that Paul wrote Romans 3:28. Both accept the text. Somewhere in a hundred pages of argument there is a step one grants and the other denies, and locating it is itself a research project.

Nobody can audit the whole. A cumulative case over twelve prophecies has a shape no reader holds in their head at once. Which conclusions depend on which premises? If one premise falls, what else falls with it? Prose cannot answer this, and neither can its author.

What formalisation changes

Encoding an argument in Lean does not make it true. It makes it inspectable, in four specific ways.

Premises become enumerable. Every atomic claim in a Testimony argument carries a citation, enforced by the type system: the function from atoms to their sources is total, so an uncited claim does not compile. The assumption manifest is then generated from the premises rather than maintained beside them, and cannot drift out of step with the argument it describes.

Validity becomes mechanical. Whether the conclusion follows is settled by a proof term, produced by backward chaining over the premises and checked by Lean's kernel; where it does not follow, a named countermodel says so. This is the least interesting guarantee the library offers, and it is worth having anyway: it means no disagreement about an argument is ever a disagreement about whether it is valid.

Disagreement becomes locatable. This is the real payoff. Encode the Reformed reading of justification, encode the New Perspective alongside it, and the library will tell you that the two packages differ in exactly one premise — whether Paul's ἔργα νόμου means works in general or Jewish covenant boundary markers — and then tell you what that premise is worth. It turns out not to be worth the argument: worksOfLaw_not_load_bearing holds, because the dominical strand at Luke 7:50 carries the conclusion without it, and the New Perspective package establishes the conclusion too. What is load-bearing is a disjunction: Paul's two disputed readings of Galatians 2:16 — ἔργα νόμου and πίστις Χριστοῦ — or Jesus' σῴζω at Luke 7:50, or Peter's yoke at Acts 15:10.

That result is not Protestant or Catholic. It is a description of the disagreement that both sides can accept — including the part neither side expected, that the famous dispute is not where the argument's weight rests — and it is the kind of thing prose almost never delivers.

Circularity becomes visible. A premise grounded only in Scripture is epistemically different from one grounded in scholarship, and the library types the difference. Source.isScriptureOnly computes it, and every argument reports its scripture-only atoms. An argument from Scripture that reads Scripture a particular way and cites only Scripture for that reading is assuming part of what it sets out to show. That is sometimes fine. It should never be invisible.

Why this is the stronger position, not the weaker one

It might look like a concession to publish every assumption an argument makes. It is the opposite.

An argument whose premises are all declared is harder to dismiss than one that claims more than it can deliver. The sceptic's usual move — you are assuming what you set out to prove — is answerable here by pointing at the manifest and asking which premise they reject, and on what grounds. The conversation moves from suspicion to a specific, arguable claim.

The library is also, deliberately, useful to people who reject its conclusions. A critical scholar who thinks Isaiah 7:14 is a near-term sign to Ahaz can encode that reading with the same machinery, and the library will confirm that the Christian conclusion does not follow from it. Both encodings live in the same repository. That is not neutrality for its own sake; it is what makes the Christian encodings worth taking seriously.

Prior art

Machine-checked theology is not new. The clearest precedent is Benzmüller and Woltzenlogel Paleo's formalisation of Gödel's ontological argument, which verified the proof in higher-order logic and found, in the process, that Gödel's axioms collapse modal distinctions — a result about a famous argument that a century of prose commentary had not established.

That is the pattern this project expects to repeat: formalisation rarely settles whether a conclusion is true, and frequently discovers something about the argument's structure that nobody had noticed.

See the bibliography for the citation.

Why a community

Two kinds of expertise are needed and almost nobody has both.

Formalising an argument requires knowing Lean. Judging whether a formalisation faithfully represents the argument it claims to represent requires knowing biblical studies, the history of interpretation, and the secondary literature. A subtly wrong encoding is worse than no encoding, because it launders a bad argument through a proof assistant and comes out looking rigorous.

So the review that matters most here is not a Lean review. It is a theologian or biblical scholar reading an encoding and saying that is not what the argument says. The project is set up to make that contribution possible without writing any Lean: see Contributing.

Scope and limits

This chapter states what the library does not do. It is here near the front, before the claims, on purpose.

What Lean settles

Exactly one thing: whether a conclusion follows from the premises as encoded. Where it does, establish produces an ordinary proof term and Lean's kernel checks it; where it does not, a named valuation satisfies every premise while falsifying the conclusion, and the kernel checks that. Nothing else is verified by the machine.

What Lean does not settle

Whether the premises are true. That Micah 5:2 is a forward-looking prediction is an interpretive claim held by some traditions and denied by others. The library records who holds it, with what confidence, and on what authority. It does not adjudicate the claim.

Whether the confidence ratings are right. A rating records how firmly a source holds a claim, and elsewhere it is information for a reader. In a dispute it is more: which position defeats which depends on the ratings, so a dispute's outcome is conditional on them in exactly the way a result is conditional on its premises. Lean checks what follows from the ratings. Whether a rating is fair to its source is a judgement it cannot make, and the Isaiah 7:14 dispute names the ratings it rests on.

Whether the encoding is faithful. That a Lean formula represents the argument a commentary actually makes is a human judgement. No proof assistant can check it, and it is the most common way a formalisation goes wrong. This is why encodings need review by people who know the literature, and why a subtly wrong formalisation is worse than none.

Whether the atoms carve the argument correctly. Choosing which atomic claims carve sola fide is already an interpretive act. A different carving might make a different premise load-bearing. The atoms are visible and arguable, and that is the best the method offers.

Whether the argument is the best one available. The library encodes particular arguments from particular sources. A better argument for the same conclusion may exist and simply not be encoded yet.

Circularity, specifically

An argument that Scripture predicts X, which reads Scripture as predicting X, and cites only Scripture for that reading, is assuming part of what it sets out to establish.

The library does not forbid this. Sometimes a text really is plain, and demanding external corroboration for every reading would be its own distortion. What the library does is make it computable: Source.isScriptureOnly is true exactly when a premise appeals to Scripture with no scholarly support, and ArgumentPackage.scriptureOnlyAtoms lists them.

In the Bethlehem argument, jesusBornInBethlehem is such a premise: the historicity of the Bethlehem birth is disputed in critical scholarship, and the argument assumes it on the authority of the texts whose reading is in question. That is stated in the module, and it is visible in the manifest.

The trust base

Results depend on Lean's kernel and on three axioms: propext, Classical.choice, and Quot.sound. Nothing else.

This is enforced rather than asserted. lake exe axiom-audit inspects the kernel environment — not the source text — and fails CI if any declaration depends on anything outside that allowlist. It catches sorry (which appears as sorryAx), native_decide (which adds Lean.ofReduceBool), and any hand-rolled axiom arriving through an import.

native_decide is prohibited outright. A project whose entire claim is that every assumption is declared cannot rest results on an undeclared one.

This gate has already earned its place. During development a decide proof failed silently and fell back to sorryAx; the axiom audit caught it, and the underlying API was removed.

What is deliberately out of scope for now

• Probabilistic and evidential reasoning. Cumulative-case arguments update on evidence; that is a different formal apparatus and will live in a separate namespace, never conflated with deduction.
• Corpus grounding. Passage values are references, not text. They do not yet resolve against real manuscript data.
• Modal logic. Needed for divine-attribute arguments. Not part of Foundation, contrary to what this page said until recently: it is a sibling package in the same family, depending on Foundation and sharing its interfaces, so reaching it means adding a dependency rather than changing substrate. See the roadmap.
• Quantification. Every argument here is propositional, so a claim whose force depends on scope — this holds of doctrine but not of practice — is carried by atom design and by prose rather than by the logic. Foundation's first-order fragment would close this and is already a dependency; it is unused, not unavailable.

Reading the logic

Contributing says you can review an encoding without knowing Lean, and that the review this project most needs is the one only a theologian or biblical scholar can do: does this formal statement faithfully represent the argument it claims to represent?

This page is the minimum you need to answer that. It is not a logic course, and it deliberately teaches nothing you will not use. Links to real courses are at the end.

The library borrows its logic rather than inventing it

One thing worth knowing before the four ideas, because it is the reason you can trust the rest.

This project does not define what "follows from" means. That definition comes from Foundation, a general-purpose formal-logic library, and this project uses it as written — the same relation a logician would recognise, with the same name. What is local here is only the cataloguing: which claims, whose, cited to what.

That division is deliberate and it is the whole basis of the guarantee. A library that wrote its own definition of entailment could get that definition subtly wrong, and every result in the catalogue would inherit the mistake without any of them looking wrong. Borrowing a definition that thousands of other theorems already depend on removes that failure mode. When you read Entails here, you are reading Foundation's logical consequence relation, narrowed to this project's premise lists.

The same goes in the other direction: because the relation is Foundation's, facts Foundation has already proved about it hold here for free — that adding premises never destroys an entailment, that a premise is entailed by the set it belongs to, and more besides. None of those had to be re-proved, so none of them could be re-proved wrongly.

Four ideas, and then you can read anything here

(A fifth, further down, is needed only for the replies that settle nothing; come back to it when you meet one.)

An atom is a claim, quoted

An atom is one indivisible claim, written down once and given a name. The logic never looks inside it. scriptureIsSufficient is an atom; so is magisteriumIsInfallible. Each carries a label, a classification, and a source saying who holds it and where.

Because the logic never looks inside, everything interesting about an atom is in its label and its citation — which is precisely the part you can check and the machine cannot.

A package is a position

A package is one position's premises, its conclusion, and a citation for every premise. tridentine is the Tridentine position; orthodox is the Orthodox one. Rival positions get their own packages, with their own sources.

A package is not a claim that the position is true. It is a claim that this is what the position assumes.

Entailment is "no way out"

The premises entail the conclusion when there is no way of assigning true and false to the atoms that makes every premise true and the conclusion false. Not "the conclusion is true" — "you cannot have the premises without it."

So a result like protestant_establishes says: grant these premises and you are stuck with this conclusion. It says nothing about whether you should grant them. Every result in this library is conditional in exactly this way, and that is not modesty, it is the only thing a proof assistant can check.

A countermodel is the rival's reading, written down

To show the premises do not entail the conclusion, you exhibit a way for all the premises to hold while the conclusion fails. That assignment is a countermodel, and in this library it is always given a name and a docstring, because it is not a technical device — it is a position.

tridentineReading says: everything else stands, and scripture is not the sole infallible rule. That is Trent's reading, in the only form a machine can check. tridentine_not_establishes is the result that it holds.

Two things that go wrong, and what the library does about them

An argument can be valid and worthless

If a package's premises contradict each other, then there is no way to make them all true — so there is trivially no way to make them all true with the conclusion false. The premises entail the conclusion, and they entail its opposite, and they entail anything at all.

Such a result would be proved, machine-checked, free of hidden assumptions, and completely empty. So every package that claims to establish its conclusion must also exhibit a model: an assignment on which all its premises hold together. reformed_is_satisfiable is one. Rule L11 fails the build without it.

A model is the mirror image of a countermodel: where a countermodel is the rival's reading, a model is the position's own world — what things look like if it is right.

A reply can defeat an objection and prove nothing

A common move in these disputes is to grant an objection's point and deny that it discriminates: yes, that is circular — so is yours. It works, in the sense that the objection no longer goes through. It also establishes nothing, because conceding a charge is not answering it.

The library states both halves. compatibility_does_not_establish_criterion is the result recording that a reply of this kind is purely defensive. When you see a pair like that, the second half is not a hedge; it is the price.

A fifth idea, for the replies that settle nothing

Independence: the premises settle nothing either way

Sometimes the two halves above are not two facts. Take a set of premises and one disputed claim. Three things can be true of them:

• the premises entail the claim — grant them and you are stuck with it;
• the premises entail its denial — grant them and you are stuck without it;
• the premises do neither. There is a way of reading them on which the claim holds, and another way, equally faithful to every premise, on which it does not.

The third is independence: the premises settle nothing either way. It is shown by exhibiting both readings — two of them rather than one, each satisfying every premise, one with the disputed claim true and one with it false.

They need not agree about anything else, and usually do not. Each is a whole position, not the other with one atom flipped: Kruger's reading refuses that identifying the canon requires an infallible authority, while the reading that concedes his point and still denies the sole rule refuses something else entirely. What independence asks of the pair is only that both satisfy every premise and that they disagree about the claim in dispute.

This is exactly what a parity reply produces. "It blocks the objection" means the denial does not follow; "it establishes nothing" means the claim does not follow either. Together they say the reply leaves the question open, and parity_leaves_the_canon_open says it in one result instead of two.

A pair of results can hide a mistake that a single result cannot, and this is not hypothetical. One of the three parity replies in the sola scriptura argument was written as a pair whose halves were about different claims over the same premises, while being presented as complements. Restating the pattern as independence forced the claim to be named once, and the mismatch was immediate.

Reading an independence result, your job is the same as ever and now doubled: are both readings ones someone would actually hold? A reading nobody occupies proves the premises settle nothing only in a sense nobody cares about.

A sixth idea, for when positions meet

A dispute asks who prevails, not what follows

Everything above asks one question of one position: do these premises force that conclusion? A dispute asks a different question of several positions at once: given who defeats whom, which positions can be held, and which can hold their ground against every attacker?

Entailment cannot answer that, for a structural reason. Adding a premise never takes a conclusion away — whatever follows from some premises still follows when you add more. So in the entailment results a reply can only be encoded by removing something from the objection. That is right for a reply that declines to grant a premise. It cannot express a reply that answers an objection by contradicting it and wins.

A dispute can. Positions become the nodes of a graph, an arrow from one to another means the first defeats the second, and the question is which sets of nodes survive together. This is Dung's theory of argumentation (1995), and the library proves its main results rather than assuming them.

Attack, refusal and defeat

One position attacks another when its premises entail the negation of one of the other's premises, or of its conclusion. It is a fact about entailment, so it is proved, and so is its absence — by naming a world in which both positions hold.

A reply that merely refuses a premise — I do not grant that — attacks nothing. It is a different move, and the entailment results already handle it. Kruger's parity reply on the canon is a refusal; Berry's objection on Isaiah 7:14 is an attack, because it asserts the negation of what the critic assumes.

An attack is a defeat unless what it attacks is strictly better supported. Every atom in the library carries a cited confidence, from disputed to consensus, and a position is judged by its weakest link: it is no stronger than the least supported thing it assumes. That includes its inferences. A step from observations to a conclusion is rated on its own, and it is disputed when someone grants the observations and denies the conclusion. Without that comparison, attacks between positions built from premises come in pairs — if you contradict what I assume, I contradict what you conclude — and nobody ever prevails.

This is the one place where a confidence rating decides a result. Elsewhere a rating tells you how firmly a premise is held. In a dispute it can decide who wins, and contesting the rating is contesting the result.

A note on vocabulary: several older results say a reply "defeats" an objection — compatibility_defeats_lexical_objection is one. There the word means the objection no longer reaches its conclusion once the reply is granted, an entailment fact. In a dispute, defeat is the relation just described.

Grounded and preferred: two ways to say who survives

• The grounded extension is what the dispute forces: the positions left standing if you accept only what cannot be resisted. When two sides defeat each other, it takes neither.
• A preferred extension is one way the dispute can be resolved: a set of positions that do not defeat one another and answer every defeat on any of them, made as large as it can be. A dispute can have several.

The Isaiah 7:14 dispute shows both. Against the scriptural reading alone, nothing is forced: the critic and the scriptural reading each rest on something rated disputed, so each defeats the other, and the grounded extension is empty. Add the replies. Each defeats the critic, by denying a premise the critic's case turns on. The critic defeats two of them back, because their inferences are as contested as its premises; it cannot defeat Postell's two counterexamples, whose inference no cited source contests. So those two stand unanswered, and they defend everything else the critic attacked: the grounded extension is the scriptural reading with all the replies. The replies have not proved the predictive reading. They have answered the objection to it, which is what a reply is for.

Reading a dispute, check the two things the machine cannot: is each position one someone holds, and is each rating one its source would stand behind?

What to look for when you review

The machine checks that the reasoning is valid. Everything that makes the encoding honest is outside what it checks, and that is your part:

• Is the rival's premise set one its holders would recognise? A package that attributes to Orthodoxy a premise only Rome holds is a strawman, however valid the reasoning from it. This has happened here and was caught in review.
• Is the citation the right one? An atom sourced to a critic's summary of a position rather than to someone who holds it is the same failure, one step removed.
• Is one atom doing two jobs? If a label would be read differently by the two sides, the encoding has hidden the dispute instead of showing it.
• Is a premise missing? Especially one the argument needs and its author would rather not state.
• Is a confidence rating deciding a dispute? In a dispute the ratings are premises. A rating nobody would defend can hand a position a win it has not earned.
• Does the prose match the theorems? Generated tables cannot drift, but a paragraph that names a result correctly and describes it wrongly will pass every check in this repository.

You do not need to read Lean to do any of that. You need to read the labels, the citations, and the module's own prose.

Further reading

For the logic itself, in increasing order of commitment:

• forall x — a free introductory logic textbook, and the gentlest of these. The chapters on truth tables cover everything this library's propositional fragment does.
• The Open Logic Project — a free, open graduate-level text, for going further.
• Stanford Encyclopedia of Philosophy: Propositional Logic, Classical Logic, and Modal Logic — reference articles rather than tutorials, but authoritative and free.

For disputes, the Stanford Encyclopedia's Argument and Argumentation introduces Dung's frameworks, and Defeasible Reasoning covers the grounded and preferred semantics this library uses.

Modal logic is listed because arguments about what cannot be otherwise need it, and the library does not yet have it.

For how the encoding works rather than how to read it, see Encoding arguments. For what the library does and does not claim, see Scope and limits.

Architecture

Testimony models arguments in layers. The guiding rule: formal validity and truth of premises are different things, and the library's job is to keep that boundary visible at all times.

Principles

1. Conditional analysis. Every theorem has the shape given premise package P, conclusion C follows. No premise is smuggled in.
2. Rival interpretations are first-class. Divergent conclusions are a feature. An argument module encoding a Christian reading without at least one rival package is incomplete.
3. Relation types are not collapsed. Quotation ≠ allusion ≠ typology ≠ prediction ≠ retrospective interpretation. Much of the messianic-prophecy debate is precisely about which of these a given link is.
4. Provenance everywhere. Enforced by the elaborator, not by review: see Citations.
5. Assumption manifests are generated, never maintained.
6. Canon is a parameter. Results are relative to a declared canon.

The layers

The library, and the packages built on it

The library is the machinery for representing and checking arguments: the logic, the provenance types, the vocabulary and its ontology, the solver, the checks and the generators. Everything an argument needs from it is public, and a package built on it uses that and nothing else: it requires the library as a Lake dependency, imports it, and keeps its own works, unfold sets, checks and documents.

There are two. TestimonyArguments, in arguments/, holds the worked arguments this documentation presents: their claims, sources, packages, disputes and verdicts, what each claim means, the articles examined against them, the works they cite beyond the library's, their unfold sets, and the library's checks run over them. Its generators write the generated files below into the repository's docs/. TestimonyExamples, in examples/, holds a case from outside theology (see Beyond theology), with a document of its own that is not in this book's index.

Each package requires the library by path, shares its downloaded dependencies, and is built and checked in CI after it, through the same gates. The library knows nothing of either: it imports neither, and names no argument. An argument module's own path is arguments/TestimonyArguments/<Argument>, and its namespace is TestimonyArguments.<Argument>.

Two structural enforcements

The library's central rule — nothing is asserted bare — is enforced twice, at two levels, by making the bad state unrepresentable rather than by checking for it.

Source.primary is a single required Reference, not a possibly-empty list. An uncited Source cannot be written down. There is no free-text escape hatch, because an escape hatch would be used.

ArgumentPackage.cite is a total function from atoms to their metadata. An atomic proposition without a citation does not compile.

Neither of these requires a linter, a review checklist, or a proof obligation at the use site. They are consequences of the types.

The documentation is generated from the library

Four executables of the arguments package write files that live in the repository, and each has a --check mode CI runs, so a committed copy that has fallen behind the source fails the build rather than misleading a reader. They run in arguments/, and each is a few lines over a library module that any package could call (Testimony.Tools.Site, Status, Bibliography, and latexDocument in Pages).

argdoc and argtex are the two that read the prose. An argument module is written as a literate document — a module docstring saying what the dispute is, /-! ### … -/ blocks marking its sections, a docstring on every package, line and result — and Testimony.Tools.Pages walks the environment for all of it, in source order, interleaving the module docstrings with the declarations they introduce. What a reader meets, on the site or in the PDF, is the file typeset: the same paragraphs, with the formulas set as notation and the atoms numbered against one legend for the whole argument.

The two tools share that harvest rather than each doing their own, so the page and the PDF are two settings of one text. Only the setting differs: Markdown tables and MathJax on the site, longtable and \cite in print. Print also links each variable in a formula to its row in the legend, and puts a derivation's premises, what each step would give and the conclusion at issue into the legend's words; the site sets the variables plain, for now.

That is why there is no hand-written page describing an argument. There is nothing to keep in step, because there is no second copy — the docstring is the documentation, and --check fails if what is committed is not what the source now says.

Dependencies

The library depends on FormalizedFormalLogic/Foundation for its propositional syntax and semantics, and transitively on Mathlib, doc-gen4 and axiom-audit. Foundation pins Lean v4.33.1.

Foundation supplies the formula type, the Hilbert systems, the Boolean and Kripke semantics, and the metatheory; Testimony reimplements none of it. What Testimony adds is the provenance layer over the formulas, lines of reason, and the establish/refute_with/satisfied_by/leaves_open/granted tactics that settle entailment, refutation, satisfiability and independence — explained in Encoding arguments.

Encoding arguments

This page assumes you are writing an encoding. If you are here to review one — which is the contribution this project most needs, and needs no Lean — start with Reading the logic instead.

If you are writing, the Pedagogy rule applies to everything below: assume a reader who knows the theology and not the logic, and elucidate or link rather than leaving a notion to be inferred.

How entailment is settled

An argument is a list of premises and a conclusion, both formulas over cited atoms. Two questions get asked of it, and they are answered by different means.

Does the conclusion follow? Once a package is unfolded, what is left is almost always a Horn problem: facts, and inference steps from a conjunction of literals to an atom or a conjunction of atoms. Horn entailment is decidable in linear time (Dowling and Gallier, 1984), and backward chaining over Horn clauses — SLD resolution, Prolog's procedure — is what establish runs, as Lean's solve_by_elim, after currying each step with and_imp, splitting conjunctive heads with imp_and, and currying a negated conjunction with not_and — the shape of a goal that rebuts a conjunctive conclusion, which the sola fide dispute needs. If that leaves the goal open, establish fails rather than silently searching; establish_by_search runs Mathlib's tauto, a general classical search whose cost is exponential in the number of inference steps, for a step that genuinely cannot be Horn. No result in the library needs it. Both produce ordinary proof terms, so the trust base is unchanged.

Entails is a thin local wrapper; the relation it names is not this library's. It is Foundation's logical consequence, T ⊨[M] φ, at this library's premise lists:

def premiseSet (prems : List (Formula α)) : Set (Formula α) := {φ | φ ∈ prems}

def Entails (prems : List (Formula α)) (concl : Formula α) : Prop :=
  premiseSet prems ⊨[Valuation α] concl

Why two shapes. Consequence is about a set of premises — order and repetition make no difference to it, and Foundation states it over Set F accordingly. A package's premises are a list, because manifest is computed by walking them and Set F is F → Prop, which cannot be walked. The generated assumption manifest, the atom legend and the numbered derivation on every argument page all depend on that walk. premiseSet is the one step between the two, and entails_iff states the relation back in the ∀ φ ∈ prems form every result is written in.

Borrowing rather than restating is what makes Foundation's own results available: monotonicity, the relation between consequence and satisfiability, and compactness are inherited rather than re-proved. A definition of entailment written locally could be subtly wrong, and every result in the catalogue would inherit the error while each one still looked correct.

Does it fail to follow? Name a countermodel — a valuation satisfying every premise while falsifying the conclusion:

theorem not_entails_of_countermodel
    (w : Valuation α)
    (hsat : ∀ φ ∈ prems, w ⊧ φ)
    (hfail : ¬ w ⊧ concl) : ¬ Entails prems concl

Checking a named valuation is linear. Searching for one is not, which is why the library asks the author to supply it.

That turns out to be a feature rather than a chore. "A countermodel exists" tells a reader nothing; a named valuation is the rival's reading, written down. So countermodels here carry the rival's name — nppReading, tridentineReading, criticalReading — and a reader can inspect what the opposing position actually commits to.

There is no atom budget

An earlier version decided entailment by exhaustive truth table, which cost 2^n and forced a twelve-atom cap on every argument. Both are gone. An argument tracing a theme across the canon may use as many atoms as it needs.

What was rejected, and why

bv_decide, Lean's SAT-solver tactic, is fast and unusable here. It emits a per-theorem native axiom:

'bvtest' depends on axioms: [propext, Classical.choice, Quot.sound,
                             bvtest._native.bv_decide.ax_1_5]

That is an external solver's certificate entering the trust base. For a library whose claim is that every assumption is declared, it is not a trade worth making, and axiom-audit would reject it.

Foundation's proof calculi supply soundness and completeness metatheorems for the Tait calculus, but no executable decision procedure, so they cannot discharge a goal.

A hand-rolled pruning search was written and then deleted once tauto proved to handle the same goals with less machinery and no new proof obligations.

tauto alone was the recipe until the arguments outgrew it. It case-splits on every implication in the context, so each inference step added to a case multiplies its cost however simple the step is: splitting SolaFide's closing step in three took reformed_establishes to twenty times the default heartbeat budget, and the argument was carried with two closing steps until the recipe changed; it now has the three, and reformed_establishes takes about two thousand heartbeats. On four SolaFide goals with no heartbeat limit, tauto, simp_all and aesop each failed to finish in fifteen minutes; Mathlib's itauto (Dyckhoff's G4ip, J. Symbolic Logic 57(3), 1992), complete for intuitionistic logic, took six. The Horn path takes four seconds — about two thousand heartbeats a goal where tauto took about four million — because it is the procedure the goals' shape calls for. It is also constructive where tauto is classical, so every Establishes result now rests on propext and Quot.sound alone; Classical.choice remains in the trust base only for the dispute results, which come from the Dung semantics.

Why a faster recipe cannot have made a result wrong

Speed is not correctness, so the change of recipe was checked, not assumed. The argument rests on how Lean is built, and each part of it was then verified on the library itself.

The recipe is not in the trust base. Lean follows the LCF architecture: a tactic does not certify anything, it constructs a proof term, and the kernel checks that term against the theorem's statement. A tactic can fail to find a proof; it cannot make the kernel accept a false one. What establish proves is Establishes pkg, which unfolds to Foundation's semantic consequence — every valuation satisfying the premises satisfies the conclusion — so a successful establish is a kernel-checked proof of exactly that, whatever algorithm found it. What is trusted is the kernel, the axioms each result reports, and the statements themselves. The three checks below cover what is not already covered by the kernel.

Every statement is unchanged. The change touched no argument module: in Testimony/Logic it rewrote the tactic macros and two comments. To make that mechanical rather than argued, the commit before the change (5cb6bc0, still on tauto) and the commit after were both built, and every Testimony declaration was printed with its fully elaborated type — and, for definitions, its value — under pp.all, so that no notation could hide a difference. Of the 2,429 declarations that existed before, all 2,429 are identical. The only differences are four additions: the syntax of establish_by_search, establish_unfold and horn_close, and the sanity theorem establish_by_search_proves_cases. So every result states what it stated before, over the same definitions; only proof terms changed.

The kernel re-checks every proof. scripts/kernel-replay.sh runs leanchecker, which replays every declaration of all 53 Testimony modules through the kernel, into the environment as it stood before each module, independently of the elaborator and of every tactic. It passes, and runs in CI after the axiom audit. The audit itself reports every Establishes result resting on propext and Quot.sound at most — no sorryAx, no Classical.choice.

It proves nothing the library refutes. For every result of the form ¬ Establishes pkg, establish is run on pkg with its argument's unfold set, and must fail with horn_close's message. The set is the one the refutation's own proof unfolds — refute_with evaluates the countermodel on every premise, which it cannot do through a folded definition — so a failure is the entailment failing and not a definition left folded. This was a manual check; it is now #check_refutations (Testimony.Checks.Refutations), which finds the refutations itself; the arguments package runs it over every argument in its lake build, so CI runs it on every change. Tactic.lean pins the same check on affirming the consequent, the canonical invalid inference.

What the change does not claim is completeness beyond Horn: SLD resolution is complete for Horn clauses, and establish fails — it does not silently succeed or fall back — on anything else. A failure is never read as a refutation; that is what countermodels are for.

Rendering an argument as logic

lake exe argtex, run in arguments/ as every generator below is, writes docs/latex/arguments.tex: every package set the way a logic paper would set it — a legend of numbered propositional variables with each one's claim, classification and source, then the premises and conclusion in ordinary notation.

cd arguments && lake exe argtex
cd ../docs/latex && tectonic arguments.tex    # or xelatex / lualatex

A Unicode engine is required: the claims contain Greek and Hebrew. Citations render as live \cite commands against the generated references.bib.

Atoms are numbered rather than named, which is the usual convention and the point of rendering at all. It separates an argument's shape from its content. So that the reader need not turn back to the legend at every row, each variable links to its row there, and a derivation puts its claims into the legend's words: a premise that is a claim, which the position holds; a step, by what it would give — unless that is the conclusion — whether or not the position holds what the step needs; and the turnstile row, by the conclusion at issue, whether or not the premises reach it. A claim met only inside a step is left to its link.

(17)  (P₂ ∧ P₃ ∧ P₈ ∧ P₇ ∧ P₆) → P₂₅  — would give: Justification is by faith alone
(18)  (P₁₇ ∧ P₁₈ ∧ P₁₉) → P₂₆  — would give: Faith is sufficient: whoever believes
      is saved
(19)  (P₉ ∧ P₁₀) → P₂₆  — would give: Faith is sufficient: whoever believes is saved
(20)  (P₂₀ ∧ P₂₁) → P₂₂  — would give: James 2:24 is compatible with Paul, using
      ‘justify’ in a different sense
(21)  (P₁ ∧ P₄ ∧ P₅) → P₂₇  — would give: Salvation is by grace, a gift and not
      wages owed
(22)  (P₁ ∧ P₄ ∧ P₅ ∧ P₂₂ ∧ P₂₄) → P₂₈  — would give: Salvation is not by works:
      no work is its ground
(23)  P₂₅ → P₂₆  — would give: Faith is sufficient: whoever believes is saved
(24)  (P₂₆ ∧ P₁) → P₂₉  — would give: Salvation is received through faith
  ⊢   P₂₇ ∧ P₂₈ ∧ P₂₉  — at issue: P₂₇ Salvation is by grace, a gift and not wages
      owed; P₂₈ Salvation is not by works: no work is its ground; P₂₉ Salvation
      is received through faith

That is sola fide. Three strands reach the sufficiency of faith (P₂₆): Paul, by way of P₆ and P₇ (Paul's ἔργα νόμου, and πίστις Χριστοῦ read as faith in Christ) to justification by faith alone (17), and from there to P₂₆ (23); Jesus' words at Luke 7:50, by way of P₁₈ and P₁₉ (σῴζω there, and 7:47 read as love evidencing forgiveness) (18); and Peter at Acts 15, by way of P₁₀ (the yoke of 15:10) (19). That redundancy — the reason no strand's disputed premise carries the argument on its own (lexical_premises_jointly_load_bearing) — is visible on the page before you read a word of the legend. So is the split in the conclusion, one step per part: (21) reaches grace (P₂₇) from the texts alone; (22) reaches "not by works" (P₂₈) from the same texts, the answer to James (P₂₂) and scripture's consistency (P₂₄); only (24), "through faith" (P₂₉), needs a strand (P₂₆).

The marks are there because the words are read as sentences. Unmarked, a step's words in a rival's package would read as the rival conceding them, and the turnstile's words under a refuted package as the conclusion reached. Nor is the conclusion always a position's aim: the positions an argument sets side by side are often asked about one thesis, which a rival may deny. Whether a package reaches its conclusion is what its results say.

Publishing what the library claims

lake exe statusgen writes the roadmap's status table from the environment: every @[headline] declaration, with its statement as Lean states it and the first sentence of its docstring, grouped by argument in source order.

lake exe statusgen           # rewrite the generated block in docs/src/roadmap.md
lake exe statusgen --check   # CI: fail if the committed block is stale

Nothing selects the rows. @[headline] already marks the results the library claims rather than the lemmas supporting them, so the table is the tag's contents; an argument whose results change moves the table, and one whose namespace is new fails the build until it is given a heading in sections. The prose around the block is written by hand, because why an argument is worth making does not follow from its statements — and rule L9 checks that the names that prose cites still exist.

Publishing the argument itself

lake exe argdoc writes one page per argument under docs/src/arguments/, and that page is the Lean file read back out: every module docstring in source order, every /-! ### … -/ section where the source puts it, and after each docstring the declaration it introduces — a package as premises above a turnstile, a line of reason as grounds and step, a result as Lean states it with the axioms it rests on, a countermodel as the function it is.

lake exe argdoc            # rewrite docs/src/arguments/ and the SUMMARY block
lake exe argdoc --check    # CI: fail if a committed page is stale

lake exe argtex writes the same document for print, from the same harvest:

lake exe argtex                             # rewrite docs/latex/arguments.tex
cd ../docs/latex && tectonic arguments.tex  # ... and render it

The atoms are numbered once for the whole argument rather than per package, so \(P_{9}\) means the same claim in the Protestant position and in the Tridentine one and a reader can compare them. Only the setting differs between the two: Markdown tables and MathJax on the site, longtable and live \cite commands in the PDF. The formulas themselves are rendered once, by Testimony.Logic.Latex, because what TeX wants is what MathJax reads. The PDF adds what a reader of a printed page cannot do without: each variable in a formula links to its row in the legend, and a derivation puts its claims into the legend's words (above). The site sets the variables plain, for now.

The practical consequence is for how you write docstrings. They are not commentary for the next contributor; they are the page. A module docstring that says what the dispute is not about, or which of two answers to an objection the position takes, is read by whoever opens the argument on the site, and it is the only prose about that argument anywhere — there is no hand-written page to fall out of step with it.

Lines of reason

An argument is not a heap of premises. It is a small number of lines of reason, each resting on its own grounds, each licensed by its own inference step, converging on a shared conclusion. BornOfAVirgin runs on four strands; SolaFide on three.

A Line makes that structure a value rather than a remark in a docstring:

structure Line (α : Type) where
  name     : String
  grounds  : List (Formula α)   -- what this line contributes of its own
  step     : Formula α          -- the inference licensing what it delivers
  delivers : Formula α

and caseOf lines shared closing assembles a premise list from them — every line's grounds, then the premises the lines hold in common, then every line's step, then the steps that close the argument. Grounds before steps, so that the material the case rests on comes first and the inferences that move it come last.

This buys four things.

Variants become differences. "The scriptural reading minus the lexical premise" is one line with one ground dropped, written as isaianicLine.onGrounds [...], instead of twenty premises retyped with one missing — where a reader cannot see which one went and a slip in the other nineteen is invisible. Every load-bearing result in the library needs such a variant, so this is most of what the packages do.

A line can be checked alone. Line.asPackage turns one into an ArgumentPackage, so Establishes applies to a single strand.

A large argument survives being split. Because the strands are values, they can live in their own module: over about five hundred lines an argument becomes a directory of Atoms, Sources, Lines, Packages and Results.

Independent lines matter without being counted. A case on three lines is not three times as strong, and the library never says it is: three citations of one premise are one premise, and a tally of allies is a popularity axis. What independent lines change is what an opponent has to give up. OpponentsBurden (Testimony.Logic.Burden) states it: the minimal sets of readings — line steps, with every line's grounds still granted — whose rejection overturns the case. It proves three things of the list, each decided by the engine and checked by the kernel:

• each set overturns the case: reject its readings and the conclusion fails;
• each set is minimal: keep any one of its readings and the conclusion holds;
• there is no other way: every rejection that overturns the case contains one of the listed sets.

The last is what makes it a burden rather than a selection. It is checked over every subset of the readings, which is exponential in the number of lines — a handful — and never in the number of atoms.

Name the burdens, too. The certificate is for the logician; the reader of the page is a theologian, who learns from "Paul's reading is not load-bearing" stated as a result of its own, with a package they can read. So an argument keeps its specific burdens as named variants, built with ArgumentPackage.rejecting — the operation the certificate quantifies over — and proves each from the certificate:

• establishes_rejecting: a named variant that leaves a reading of every set standing still holds (paul_not_load_bearing);
• not_establishes_rejecting, or refute_with and a named countermodel: a named variant that rejects a whole set fails (works_witnesses_jointly_load_bearing, where the countermodel is the world that opponent stands in);
• rejecting_satisfiable: every named variant has a model.

A named burden is then an instance of the computed one and cannot drift from it, and the computed one guarantees that the named ones are not a flattering selection. Name the readings too (Reading.paul), so the certificate's statement reads as the corpora it concerns, and check each name against its line. The page renders the sets with each reading's rating, so a reader sees at once when overturning a case means rejecting a reading its rival itself makes. CanonicalWitness is the worked example: canonical_burden finds exactly two ways to overturn faith alone, and one of them runs through a reading Trent affirms.

Sharing scripture between arguments

Arguments overlap in the texts they read. Testimony.Scripture names the passages once and collects the groups that travel together — the two infancy narratives, the pair of Genesis verses calling Rebekah both עַלְמָה and בְּתוּלָה, the Assyrian timeline of Isaiah 8–10 — as List ScriptureCitation bundles. A bundle is a clique in the citation graph, and naming it means an argument cites the evidence rather than assembling it:

| .maryConceivedAsVirgin =>
  { label := "Mary conceived Jesus while a virgin"
  , kind := .historical
  , source :=
      { primary := .scripture virginConceptionNarratives
      , tradition := .christianHistoricalGrammatical
      , confidence := .disputed } }

The module also holds the Source shapes several arguments build — calvinHolds, na28Apparatus, scriptureWithCalvin — so that a premise cites a claim and not a re-spelled citation.

Writing an argument

An argument module has five parts.

1. An atom type, one constructor per atomic claim, each documented with what it asserts:

inductive Claim
  /-- Romans 3:28 teaches justification by faith apart from works of the law. -/
  | romans3_28
  /-- Paul's ἔργα νόμου denotes human works in general. **The disputed
  premise.** -/
  | worksOfLawMeansWorksGenerally
  ...
deriving DecidableEq, Repr

2. A total citation function. Because it is total, an uncited atom does not compile:

def cite : Claim → AtomMeta
  | .romans3_28 =>
    { label := "Romans 3:28 teaches justification by faith apart from works of the law"
    , kind := .textual
    , source := { primary := .scripture [{ ref := .verse ⟨.romans, 3, 28⟩ }]
                , supporting := [.work calvinInstitutes (.sectionRef "III.xi.19")]
                , tradition := .reformedProtestant
                , confidence := .wellSupported } }
  ...

3. Packages — rivals first. Writing the rival before proving anything keeps the encoding honest; it is much easier to build a strawman after you have a proof you like.

4. Theorems, tagged @[headline] and followed by #print axioms. To establish, name the argument's unfold set:

@[headline]
theorem reformed_establishes : Establishes reformed := by
  establish [solaFideDefs]

To refute, name the rival's reading and check it:

def tridentineReading : Valuation Claim := fun a =>
  match a with
  | .salvationNotByWorks => False
  | .justificationIsForensicOnly => False
  | _ => True

@[headline]
theorem tridentine_not_establishes : ¬ Establishes tridentine := by
  refute_with tridentineReading [solaFideDefs]

To record that a premise set settles a question neither way — which is what a parity reply does — name both readings:

@[headline]
theorem parity_leaves_the_canon_open :
    Independent canonUnderParity.premises (p .scriptureIsSoleInfallibleRule) := by
  leaves_open parityEstablishesNothingReading krugerParityReading
    [solaScripturaDefs]

Independent prems φ is ¬ Entails prems φ ∧ ¬ Entails prems ∼φ, the semantic counterpart of Foundation's proof-theoretic Independent. Use it in place of a pair of ¬ Establishes results over the same premises: one result cannot be about two different propositions, and a pair can.

The bracketed set is only what to unfold. Each argument has one, declared in arguments/TestimonyArguments/Attr.lean, and a definition joins it where it is written — @[solaFideDefs] def reformed ... — so a new definition is tagged once rather than added to every proof that passes through it. An untagged one stays folded, and establish reports the premises as not Horn. The generic half of the recipe — caseOf, Line.onGrounds, p, notP, the list-membership lemmas that turn ∀ φ ∈ prems into a conjunction, and Foundation's truth lemmas for the connectives — lives inside the tactics, in Testimony.Logic.Tactic.

That is not tidiness. A hand-written proof has to name the semantics, and the semantics used to be named by unfolding Formula.Boolean.val. Formula is an abbreviation in Testimony.Logic as well as a structure in Foundation, so a proof written inside an argument module resolved the wrong one, simp did nothing, and the proof term fell back to sorryAx — with a successful build.

Formulas are now written in Foundation's own notation — ➝, ⋏, ⋎, ∼, and ⋀ for the conjunction of a list — so the recipe reaches for Foundation's own @[simp] truth lemmas, one per connective, rather than reconstructing them by unfolding the definition of the semantics. Those lemmas live in Foundation's namespaces and have no ambiguous siblings here: name one wrongly and it is an unknown identifier, not a silent no-op. refute_with also takes an identifier rather than a term, so a countermodel must be a named definition.

5. The load-bearing results, where there is a disputed premise. Drop the premise from the line that contributes it:

def reformedWithoutSozo : ArgumentPackage Claim :=
  { reformed with
    name := "Reformed, minus the dominical lexical premise"
    premises :=
      caseOf [paulineLine, dominicalLine.onGrounds [p .luke7_47LoveIsEvidence], apostolicLine]
        sharedGrounds closingSteps }

Then ask whether the argument survives. Where an argument has independent strands, as sola fide has three, no strand's disputed premise is load-bearing alone — only their disjunction is, and that is the more interesting result.

Disputes

Every result above is about one package. A dispute is about several: which of them defeats which, and which survive together. Testimony.Logic.Framework is Dung's abstract argumentation, over any relation; Testimony.Logic.Dispute makes the nodes argument packages and derives the relation from entailment. Arguments/BornOfAVirgin/Dispute.lean is the worked example.

Nothing about the relation is stipulated. One package attacks another when its premises entail the negation of one of the other's premises (UnderminesOn), of its conclusion (Rebuts), or of a claim one of its steps delivers (RebutsStep). The third is a derived attack, and it is gated twice: the denied claim must be the head of one of the attacked package's own steps, and that package must entail it. A package answers for what it assumes, what it concludes and what it derives on the way — not for every consequence of what it holds, which would make every attack mutual. An attack is a defeat unless the cited confidences block it: a position's strength is its weakest link — the lowest rank among its premises, inference steps included — and an attack fails only when what it attacks is strictly stronger. A denied atom ranks disputed, because the citation rates the claim, not its denial. A step ranks at the citation in its line's inference field, and Dispute refuses a node without one: rate a step disputed when a cited source grants its grounds and denies its conclusion. Leaving steps unrated would let the placement of a contested move — atom or step — decide who prevails.

What a party holds includes what its claims mean. Every attack is decided over a package's premises and its argument's meaning postulates (ArgumentPackage.held; computed ratings). Two claims the atom type keeps apart, but whose meanings exclude each other, cannot be held together by either party. In the James dispute, the Reformed harmony ("James 2:24 is compatible with Paul") and the renewal reading ("James's δικαιόω is Paul's") defeat each other for that reason alone. The postulates are the same for every party and are not ranked, so they cannot favour a side or change a strength. A node must hold together with them. establish does not use them: they could only add entailments, and Testimony.Checks.Postulates shows that no non-entailment the library states — no ¬ Establishes, ¬ Entails or Independent result — is undone by them.

Why confidence at all: without it, premise attacks between classical arguments are always mutual, and Dung's semantics reduce to a consistency check (Cayrol, 1995). The consequence is that ratings become premises of every dispute that uses them, and a rating change can reverse a result. Say so in the module docstring, and say which rating decides the outcome.

Encoding a dispute has three steps.

1. Every node is an argument. Dispute requires each node's premises to be satisfiable and to establish its conclusion — a node with contradictory premises would attack everything. A reply written with Line.onGrounds keeps the objection's conclusion and so is not a node; write the reply as its own Line, with what it concludes as delivers.

2. State the table, and let the engine check it. Write down who defeats whom as a table over the parties, give each party's strength, and prove the dispute's relation equal to the table. Every cell is computed from the premises and checked by the kernel — the defeats and the absences alike:

theorem isaiahDispute_defeats : ∀ i j, isaiahDispute.defeats i j ↔ partyDefeats i j := by
  intro i j
  refine Horn.defeats_iff_of_certified (partyNode_strength i) (partyNode_strength j) ?_
  cases i <;> cases j <;> horn_certify

Horn.defeats? (Testimony.Logic.Horn) decides each pair by asking whether formulas can all hold together: a undermines b on φ exactly when a's premises and φ cannot, rebuts it exactly when a's premises and b's conclusion cannot, and rebuts it on the step p ➝ ψ exactly when b's premises and ψ's negation cannot, nor a's premises and ψ. A rebuttal on a step is weighed as a rebuttal of the conclusion is, against the attacked package's weakest link: a claim a package derives on the way is no better protected than the claim it derives at the end. Weighing it against the step's own rating instead would let a well-rated inference shield a poorly-rated premise it needs — as it once shielded both Trent's definition and Campbell's deliverance, and with them the sola fide verdicts that rested on the gap. It translates the premises to clauses — atoms, denied atoms, and steps from a conjunction of literals to an atom, a conjunction or a contradiction — and decides them by unit propagation. Each answer carries its evidence: satisfiable only once a candidate model has been checked against every clause, unsatisfiable only when a clause is violated by atoms every model must have. So the procedure can fail to decide — a formula with a disjunction has no clauses, and it answers unknown — but it cannot decide wrongly, and its correctness theorems do not depend on it being complete. decide +kernel runs it inside the kernel and adds no axiom, unlike the banned native_decide.

The kernel need not run the search itself, and in a table it does not. horn_certify (Testimony.Logic.Certificate) runs the same propagation at elaboration time and hands the kernel what it found, a certificate for each question: a model, which the kernel checks against every clause once, or the clauses that fired, in order, which it replays once and checks that they end in a violated clause. Checking is far cheaper than searching, pass after pass, to a fixed point. The certificate is not trusted: the kernel checks it, a wrong one can only make the proof fail, and Horn.defeats_iff_of_certified states exactly what Horn.defeats_iff_of_defeats? does. decide +kernel on Horn.defeats? still proves any cell, searching.

A single defeat worth naming is one line, from the same computation:

theorem berry_defeats_critical : Defeats berryObjection criticalDenial :=
  Horn.defeats_of_certified berryObjection_strength criticalDenial_strength
    (by horn_certify)

Strengths are computed by decide, and are worth stating as results of their own, because they are what a reader contests. They are also why the engine takes them as arguments: a strength looks up every atom's citation, the most expensive part of a decision, and a dispute proves each party's once.

Say why an absence is not a counter. A computed absence names no reason, and the reason is often the point: the critic is not answered by Postell's step, because a critic can date Isaiah 9 and 11 later. Grants a φ states that some reading holds everything a holds and φ too; it is proved with satisfied_by and a named reading, and gives ¬ UnderminesOn a b φ when φ is b's premise and ¬ Rebuts a b when it is b's conclusion:

/-- The critic's world, with Isaiah 9 and 11 taken off the Assyrian timeline … -/
def laterOraclesReading : Valuation Claim := …

theorem critic_grants_postells_step_by_dating_the_oracles_later :
    Grants criticalDenial parityDefeatsNearTermExclusion := by
  satisfied_by laterOraclesReading [Grants, bornOfAVirginDefs]

One reading, one premise, one line: nothing depends on it, adding a premise elsewhere cannot break it, and its docstring carries the explanation into the generated page. Write one wherever the absence of a counter is something a reader would ask about.

Parties that can all hold at once stand together, and that is still worth stating with a named world — replies_stand_with_the_scriptural_reading is the reading on which none of five positions has to give way — though the table no longer needs it.

What it costs. One pair takes the kernel between a tenth and a quarter of a second. The sola fide table, now 121 pairs, checks as one theorem within the default heartbeat budget; at sixty-four pairs its module built in 24 seconds where the hand-written table took 31; the born-of-a-virgin disputes, thirty-six pairs and nine, build as fast as they did.

If the engine answers unknown — a premise it cannot write as clauses — prove that cell by hand: a defeat from the attack and the comparison of strengths, an absence with not_defeats_of_models or not_defeats_of_outweighed, one named world per premise.

3. State what survives, with its reason. Describe the dispute once in solver form (Testimony.Logic.Solver): every party listed, and the table as a Boolean. Then declare each verdict as a Verdict (Testimony.Logic.Verdict). It holds the verdict's claim and its witness, a small statement of why it holds. A checker proved sound once against Testimony.Logic.Framework confirms the witness (Testimony.Logic.Witness), and the result follows from Verdict.holds:

def isaiahFinite : Solver.Finite isaiahDispute.defeats where
  parties := [.scriptural, .critical, .berry, .postell, .motyer, .micah]
  complete i := by cases i <;> decide
  defeats i j := decide (partyDefeats i j)
  spec i j := by rw [isaiahDispute_defeats]; simp

/-- Why the critical denial cannot be defended: Postell attacks it, and nothing
answers Postell. -/
def criticAnsweredByPostell : Verdict isaiahDispute where
  finite := isaiahFinite
  claim := .indefensible .critical [(.critical, .postell)]
  checked := by decide +kernel

theorem critical_denial_indefensible (S : Set Party)
    (hS : Admissible isaiahDispute.defeats S) : Party.critical ∉ S :=
  criticAnsweredByPostell.holds S hS

A wrong witness fails to check, so it cannot prove a wrong verdict. And the page does not take the docstring's word for the reason. It renders the reason from the witness itself, naming each defeat by the two parties' packages:

Critical denial of the predictive reading of Isaiah 7:14 cannot be defended: no admissible position holds it.

• Postell's parity argument against the near-term exclusion defeats Critical denial of the predictive reading of Isaiah 7:14, and nothing defeats Postell's parity argument against the near-term exclusion.

Under the reasons, the page says what they rest on: how many cells of the defeat table they state (defeats named, and the absences of defeat that "nothing defeats c" quantifies over), and every party those cells involve at its weakest link, each premise with its citation. Those are the readings to contest to contest the verdict. Two limits, stated in the module docstring: that the verdict holds of any table agreeing on those cells is stated but not yet proved, and denying one reading need not overturn the verdict, which may stand by another route.

So a docstring that drifts from its witness is visible: the generated list beneath it says otherwise, and changing the witness changes the page, which argdoc --check catches. A defeat that a Because on the same page explains links to it. Each page also names the defeat table's theorem, where every defeat mentioned is proved.

To find a witness, ask the untrusted finder — #eval Witness.findSkeptical F a, findIndefensible, findDefeaters, findStages, findUnanswered — and copy what it returns into the file. Checking a witness is polynomial. The sceptical witness is a sufficient condition, not a characterisation: where no witness of that shape exists, the solver's whole-set enumeration (skeptically_accepted, preferred_eq, not_mem_admissible and the rest) decides the verdict instead, at a cost exponential in the parties — some such cost is unavoidable in the worst case, since sceptical acceptance under the preferred semantics is Π₂ᵖ-complete (the module docstring of Testimony.Logic.Solver gives the results and their sources).

Dispute.restrict hears only some of the parties, and Finite.restrict gives the checkers the same hearing; Witness.Table.sub and Witness.listSub write a hearing's witnesses in the parties' own names. That is how a result says what one party is worth: take it away and see what survives. A verdict re-checks itself when a party is added, and a witness that no longer holds fails to check.

Draw the dispute. An ArgumentMap (Testimony.Logic.Map) is the dispute's graph as one declaration: the defeat table the solver uses, and two tables of how parties stand together (Testimony.Logic.Support).

• Support. One party supports another when its conclusion entails a claim the other rests on. Only a claim counts, an atom or a denied atom, never an inference step. A conclusion can entail a step vacuously, by denying its antecedent. Or it can entail the step by concluding what the step concludes, which is agreement, not support. Both happen in the library's disputes.
• Part of. One party's case is part of another's when every premise of the first follows from the second's premises. The Pauline strand derives its ἔργα νόμου premise from the critics' line, which denies covenantal nomism, instead of assuming it. So the critics' case is part of Paul's, and Sanders meets Paul on the history of Second Temple Judaism, where the literature has the dispute.

Both tables are proved like the defeat table, cell by cell, by supports? or partOf? and decide +kernel:

theorem solaFideDispute_partOf : ∀ i j, solaFideDispute.partOf i j ↔ partyPartOf i j := by
  intro i j
  refine partOf_iff_of_partOf? ?_
  cases i <;> cases j <;> decide +kernel

The page draws the graph, lists the parties by number, and tabulates every edge. With the defeats, supports and parts it lists the attacks they imply. A supported attack is one where a supports a party that defeats c. A secondary attack is one where a defeats a party that supports c. An attack on a part is one where a defeats a party whose case is part of c's. These are reported alongside the defeats and never added to them, so no verdict depends on them. Each is marked by whether it is already a defeat, and the page counts those that are not: questions the dispute leaves open.

A derived attack that is not already a defeat is a modelling question, not a vote. Either the attacked case claims more than its sources do, or the attack is real and a verdict must move — and which, the encoding cannot decide for you. Sola fide is the worked example. When rebuttals on steps entered the relation, the apocalyptic reading attacked Luke's case and Peter's: both were encoded as deriving justification by faith alone, which Campbell denies. But Luke 7:50 says "your faith has saved you", not "faith alone"; Acts 15 says the gentiles are saved without the yoke. So the strands were re-encoded to deliver what their texts say, faithIsSufficient, and the attack disappeared with the over-claim — leaving the dispute between Campbell and the Reformed reading where the literature has it, between Campbell and Paul, over the genitive. Check the derived attacks before a dispute is merged: every rebuttal on a step should already be a defeat, or the difference should be the point.

4. Say why a position stands against a rival. A verdict says who survives; a reader also asks why. Because P R (Testimony.Logic.Because) answers for one pair, as one checked object. It names a crux, one of P's premises, and proves:

• P's premises have a model and establish its conclusion;
• where the crux sits: P's premises are before ++ crux :: after;
• a core of R's premises cannot be held with the crux, together with any granted grounds of P the break needs, stated rather than hidden;
• the core is minimal: drop any one of its premises and the rest hold with the crux, so the core is exactly where R breaks;
• the core and the granted grounds hold together without the crux, so the crux does the breaking, not the grounds;
• R's premises have a model: it falls to the crux, not to itself;
• the crux's role. It derives when P's conclusion does not follow without it, so it is part of P's case. It answers when the conclusion follows anyway, so the crux is held only as P's answer to R.

The role is proved, not chosen. The dominical case for sola fide turns out to hold the Reformed distinction between justification and sanctification only as its answer to Trent: its conclusion follows from its other premises. Luther's step from Galatians is part of his case against Aquinas.

def whyLutherAnswersAquinas : Because lutherOnGalatians thomistOnJohn :=
  Because.ofChecks lutherLine.step lutherLine.grounds [] lutherLine.grounds
    [p .johannineBelievingIsFormedByCharity] .derives
    luther_answers_aquinas_from_galatians lutherOnGalatians_is_satisfiable
    (by simp [lutherOnGalatians, Line.asPackage, Line.premises])
    (fun φ hφ => by simp [lutherOnGalatians, Line.asPackage, Line.premises, hφ])
    (by simp [solaFideDefs, caseOf, Line.onGrounds])
    (by decide +kernel)

Because.ofChecks takes the engine's check as one decide +kernel: the break, its minimality, the crux being needed, the rival standing and the role. It also takes the facts the engine cannot decide. P holds, and its premises have a model; both are theorems the argument already has. The split and the two membership claims are proved by unfolding. The split has to be declared, because equality on Formula does not reduce in the kernel. Declaring it is also the honest form, since it names the occurrence of the crux that is meant.

From a Because follow not_together, that the two positions cannot be held at once, and undermines, that a one-premise core with nothing granted is an attack in the dispute's own sense.

What it claims, and what it does not. It is conditional on its crux: if the crux holds, P stands and R cannot be held, and this is the premise of R that fails. It says nothing about whether the crux is true. The rendered explanation therefore ends with what it rests on: the crux and the granted grounds, each with its rating and citation. When the crux is a step rather than a claim, the step's own rating is listed too. A Because in an argument's module is harvested into its page and the PDF like any other result, and its docstring is the prose above the explanation.

5. Answer every reading of an ambiguous claim. A rival's premise can be read more than one way, and the readings can meet different objections. Trent defines justification as "the sanctification and renewal of the inward man". Read as a claim about what Paul's word δικαιόω means, it is a lexical claim. Read as a claim about what God does in justifying, no lexical argument touches it. An argument that answers only one reading has answered a rival of its own choosing.

Dilemma R (Testimony.Logic.Dilemma) makes that impossible to dodge. It names one of R's premises, the claim, and a list of horns, at least two. Each horn carries:

• a reading: what the claim commits R to under it, who reads it that way, with a rating, and any grounds R rests the reading on. R.readAs claim r is R with those grounds and the step claim ➝ r.commits added, and the reading's citation among its inferences. The reading is a named difference, like every variant here: R's own premises are untouched. Trent's reading of Paul's word rests on Augustine's gloss, "being justified" as "being made righteous", and the dilemma checks where that ground breaks too;
• a proof that the reading is fair: R read that way still has a model, so no horn is a strawman that falls to itself;
• its fates, never empty. Each fate is set against a named position P. Either the reading falls, carried by a Because P (R.readAs claim r) that names the crux, or it is not reached: P holds, and P's premises can be held with R read that way.

A reading enters only as part of a horn, with its fates, so a dilemma cannot list a reading and leave it unanswered (Dilemma.answered).

def whatTrentsDefinitionClaims : Dilemma tridentineCase where
  claim := p .justificationIncludesSanctification
  horns :=
    [ { reading := trentOnPaulsWord
      , fair := tridentineOnPaulsWord_is_satisfiable
      , fates :=
          [ .falls lexicalCase whereTrentsWordReadingFalls
          , .falls lexicalCase whereTheLatinReadingFalls ]
      , answered := by simp }
    , { reading := trentOnWhatGodDoes
      , fair := tridentineOnWhatGodDoes_is_satisfiable
      , fates :=
          [ .unreached lexicalCase lexicalCase_establishes
              lexical_case_does_not_reach_what_god_does
          , .falls galatianGospel whereTrentsGraceReadingFalls
          , .falls romansFourCase whereRomansFourMeetsWhatGodDoes ]
      , answered := by simp } ]
  claim_mem := by simp [solaFideDefs, tridentinePremises, Line.premises]
  two := by simp

What it claims, and what it does not. It does not claim that the readings are the only ones; it is a dilemma over the readings it names, each cited. A reader with a third reading has a third horn to add, and the certificate will not build until that horn is answered too. Nor does it say which reading the rival means. What it shows is what each reading costs: where it cannot be held, against what, at which crux, rated how — and where nothing reaches it. A reading that cannot be held against a position at a disputed crux has not been refuted: whoever grants the crux rejects the reading, and whoever denies it need not. The rendering says "cannot be held", not "refuted", for that reason. The rendering sets the horns side by side, each with its explanations, so a reader can see when the choice of reading is a choice of which crux to defend.

No razor enters the solver. The dilemma above turns on the rule of least meaning: a word contributes the least meaning its context requires (Joos; Silva), and one occurrence does not carry the whole doctrine (Barr's "illegitimate totality transfer"). It is tempting to build such a principle into the semantics as a preference. That would decide cases without ever appearing on a page — an uncited premise inside the machinery. So the rule enters as a premise, leastMeaning, cited and rated like any other, and contestable in the same way.

Manifests

Generated from the premises, never maintained beside them:

def ArgumentPackage.manifest           : List AtomMeta
def ArgumentPackage.scriptureOnlyAtoms : List AtomMeta

manifest is every atom the premises rest on, deduplicated and mapped through cite. scriptureOnlyAtoms filters it to those appealing to Scripture with no scholarly support — the circularity surface described in Scope and limits.

Citations

Every claim in this library carries a citation, and the citation is a typed value rather than a string. The point is that a reader can check it.

The binding rule

No bibliographic identifier is ever written from memory.

Verify every ISBN, DOI, edition statement, publisher and page range against a public catalogue before committing it. If a field cannot be verified, leave it none.

An entry with no identifier renders in the bibliography as (no public identifier). That is the rule working, not failing: five of the fourteen seed entries carry no identifier, because none could be tied to a specific printing. A plausible-looking wrong ISBN is far worse than an honest gap, because it survives review — it looks exactly like a right one.

Useful catalogues: Open Library (/search.json, /isbn/{isbn}.json) and Crossref for DOIs.

Entry types

Two distinctions that are easy to get wrong:

criticalEdition versus book. A critical edition has editors rather than authors, and is cited by siglum (NA28) and apparatus location rather than by page. If you would cite it as "NA28 at Matt 1:23", it is a criticalEdition.

ancientWork versus its modern edition. Scholarly practice cites Josephus, Ant. 18.63, in a named Loeb volume. Encode the ancient work with editionUsed pointing at the modern edition's key; the registry checks the reference resolves.

Adding an entry

1. Verify against a public catalogue. Leave unverifiable fields none.

2. Add a tagged definition to the Works.lean of the package that cites it: arguments/TestimonyArguments/Works.lean for a work an argument cites, Testimony/Bib/Works.lean only for one the library itself cites. The tag is what puts it in the registry; an untagged entry is invisible to bibgen and linter rule L4 rejects it.

   /-- Why this work is cited here. -/
   @[bib_entry] def mooRomans : BibEntry := .book
     { core :=
         { key := "moo-romans-2018"
         , contributors := { authors := [.person "Douglas J." "Moo"] }
         , title := "The Letter to the Romans"
         , year := some { value := 2018 }
         , identifiers := [.isbn "9780802871268"] }
     , publisher := "Wm. B. Eerdmans"
     , place := some "Grand Rapids"
     , edition := some "2nd edition"
     , series := some "New International Commentary on the New Testament" }
   

   Citation keys are family-shorttitle-year, lowercase, hyphen-separated. Rule L7 and a compile-time #guard both check the format. The key is also the entry's anchor in the generated bibliography, so it is what every citation on an argument page links to — bibliography.md#moo-romans-2018 lands a reader on the entry.

3. Cite it from a Source, with a pinpoint:

   source :=
     { primary := .work mooRomans (.adLoc ⟨.romans, 3, 28⟩)
     , tradition := .reformedProtestant
     , confidence := .wellSupported }
   

4. Regenerate and commit both generated files:

   cd arguments && lake exe bibgen
   git add ../references.bib ../docs/src/bibliography.md
   

   CI runs lake exe bibgen --check, in arguments/, and fails if they are stale. The two files list the library's works and the arguments' together.

Pinpoints

Locus says where in a work:

(sectionRef rather than section, because section is a Lean keyword.)

Scripture is not a bibliography entry

Scripture citations use a separate Reference constructor over typed passages:

primary := .scripture
  [ { ref := .verse ⟨.matthew, 2, 1⟩ }
  , { ref := .range ⟨.luke, 2, 4, 2, 7⟩ } ]

This is not a stylistic choice. It makes citations traversable — "what cites Isaiah 7:14?" is answerable — and it makes Source.isScriptureOnly computable, which is how the library surfaces circularity. See Scope and limits.

Generated outputs

lake exe bibgen writes two files from the Lean source, both committed:

• references.bib — biblatex-flavoured, for Zotero, pandoc and LaTeX
• docs/src/bibliography.md — the bibliography chapter of this book, each entry carrying an anchor named after its cite key

Neither is edited by hand. lake exe bibgen --check verifies they match.

Entry types map onto BibTeX as follows. If you add a variant to BibEntry, extend Testimony/Bib/Render.lean and add a golden test for it.

Style guide

Conventions, and the command that enforces each one. A rule that lives only in prose is a rule that gets broken by someone in a hurry, human or agent, and nobody notices for months.

The four tiers

Run them in this order. Each catches what the previous one cannot.

Plus lake exe bibgen --check, lake exe argtex --check, lake exe statusgen --check and lake exe argdoc --check for generated-file drift. The library and each package built on it are held to the tiers in their own directories: the arguments in arguments/, where those four tools are.

lake build passing is not "it builds". Three further gates exist, and tier 3 in particular catches things nothing else will — a decide proof that silently fails and falls back to sorryAx produces a successful build.

Naming

• lowerCamelCase for definitions, snake_case for theorem names, after mathlib convention.
• Lines of reason are named <strand>Line: isaianicLine, paulineLine.
• Scripture-reference defs are the one exception: micah5_2, isaiah7_14, matthew1_23. The underscores are meaningful — they are chapter and verse. These carry @[nolint defsWithUnderscore], so the exception is declared rather than silent.
• Atom constructors read as passage + claim: romans3_28, worksOfLawMeansWorksGenerally, timothy3_16GodBreathed.
• Citation keys are family-shorttitle-year: france-matthew-2007, na28-2012.

Docstrings

Required on every declaration — enforced by linter.missingDocs at build time and docBlame/docBlameThm in lake lint. docBlameThm is disabled by default in Batteries and deliberately enabled here.

This is not decoration. A docstring in this library states what a premise asserts and who holds it, so an undocumented premise is very nearly an uncited one, and a theorem asserting a theological result must say what it claims.

• Atoms and premises: what is asserted, and which tradition asserts it.
• Packages: which position it encodes.
• Headline theorems: what it does and does not establish.
• Module docstrings: the layer, the purpose, and — for argument modules — a prose statement of the dispute. BornOfAVirgin.lean is the model.

The one exception is Book, where missingDocs is disabled for that declaration alone with the reason recorded inline: a constructor named genesis is documented by its name.

Pedagogy

Write for a reader who knows the theology and not the logic.

Contributing says the review this project most needs is the one only a theologian or biblical scholar can do, and that it requires no Lean. That promise is only kept if the encoding explains itself. A proof that nobody competent to judge the theology can read has not been reviewed; it has only been checked.

So: assume no logical training, and never leave a technical notion to be inferred.

• Elucidate where you use it, or link an explainer. The primer is Reading the logic. Prefer linking it to re-explaining the basics; extend it when an argument needs a notion it does not cover.
• A countermodel's docstring says what the reading is. Not "the valuation refuting X" — the position, in the words its holders would use. tridentineReading is "everything else stands, and scripture is not the sole infallible rule", which a reader can evaluate. A valuation described as a valuation tells them nothing.
• A model's docstring says whose world it is. Same rule, opposite sign: the way things look if the position is right.
• Gloss logical vocabulary exactly as you gloss Greek and Hebrew. This library already explains ἔργα νόμου and עַלְמָה where they appear, because it does not assume its reader is a Semitist. "Independent", "satisfiable", "countermodel" and "vacuous" get the same courtesy, for the same reason.
• A notion the primer cannot carry is a reason to reconsider the encoding, not a reason to shrug. If an argument can only be stated in a fragment whose countermodels are unreadable, say so in the module docstring and explain them in prose beside the Lean.

This one is not enforced by a command

Every other rule on this page names the check that catches it. This one cannot: you can lint that a docstring exists — missingDocs and docBlame already do — but not whether it explains anything. It is enforced in review, and it is the rule most easily lost in a hurry, which is why it is written down at this length.

Encoding

• Rivals are not optional. An argument module encoding a Christian reading without at least one rival package is incomplete, not merely unpolished. Write the rival before proving anything. Rule L5 enforces this.
• There is no atom budget. Entailment is settled by backward chaining and refuted by named countermodels, neither of which enumerates valuations.
• Keep inference steps Horn. A step is a conjunction of literals implying an atom or a conjunction of atoms. Then establish proves by SLD resolution, whose cost grows with the length of the chain rather than the number of steps. A step with a disjunction anywhere, or an implication inside an antecedent, makes establish fail; establish_by_search would prove it with tauto, whose cost is exponential in the number of steps. Encode alternatives as separate lines instead.
• Write formulas in Foundation's notation. ➝, ⋏, ⋎, ∼, and ⋀ for the conjunction of a list — not the raw constructors .imp, .and, .or. They build the same terms, but only the notation is what Foundation's @[simp] truth lemmas are indexed under, and those lemmas are where the proof recipes get their semantics. p and notP stay: a reader of a rival's premise list should not have to decode the encoding of negation. Implication is written ➝, an alias for Foundation's 🡒 — see Typing the connectives.
• Compose arguments from lines of reason. A strand is a Line — its own grounds, its own inference step, what it delivers — and a package is caseOf lines shared closing. A variant package is then a named difference (Line.onGrounds) rather than a retyped premise list.
• State reduced packages explicitly; do not filter premises out of an existing package. List.filter over a derived DecidableEq (Formula α) does not reduce in the kernel, and Line.onGrounds says the same thing better.
• Name your countermodels after the position they encode. A countermodel is the rival's reading written down, and a reader should be able to see what it commits to.
• Never native_decide, never sorry. This also rules out bv_decide, which adds a per-theorem native axiom.
• Use establish and refute_with, never the hand-written simp only recipe. See Proof tactics below.

Proof tactics

Testimony.Logic.Tactic provides five, and they are not conveniences.

theorem christian_establishes : Establishes christian := by
  establish [bornOfAVirginDefs]

theorem critical_not_establishes : ¬ Establishes critical := by
  refute_with criticalReading [bornOfAVirginDefs]

theorem christian_is_satisfiable : Satisfiable christian.premises := by
  satisfied_by christianOwnReading [bornOfAVirginDefs]

theorem parity_leaves_the_canon_open :
    Independent canonUnderParity.premises (p .scriptureIsSoleInfallibleRule) := by
  leaves_open parityEstablishesNothingReading krugerParityReading
    [solaScripturaDefs]

theorem circle_parity_concedes_the_charge :
    Establishes circleParityConcedingTheCharge := by
  granted [solaScripturaDefs]

granted is not a faster establish. establish would close the same goal, by searching for a proof of something that is sitting in the premise list. The two say different things — that the conclusion follows, against that it was granted — and where a reply concedes the charge it answers, which it is matters more than that the goal closes.

The bracketed set names what to unfold: the argument's unfold set, declared in arguments/TestimonyArguments/Attr.lean, which holds its packages, lines and inference steps. A definition joins it where it is written, @[bornOfAVirginDefs] def christian ..., rather than being added to the proofs that pass through it. Everything generic — caseOf, Line.onGrounds, p, notP, the list-membership lemmas, and the semantics — is supplied by the tactic.

This closes a silent-failure hole. Formula is an abbreviation in Testimony.Logic as well as a structure in Foundation, so inside an argument module the short name Formula.Boolean.val used to resolve to the wrong namespace. The semantics then never unfold, simp leaves the hypothesis alone, and the proof term rests on sorryAx — with a successful build. Only tier 3 catches it, and only afterwards. Written once inside a macro quotation, where identifiers resolve at the definition site rather than the call site, the mistake is no longer available to make.

This is the same move as Source.primary being a required field rather than a review rule: make the bad state unrepresentable instead of checking for it.

refute_with takes an identifier, not a term, so a countermodel must be a named definition. That enforces the rule above it — a countermodel is the rival's reading written down, and an inline valuation would satisfy the checker while telling a reader nothing. leaves_open takes two, in the order of Independent's two halves: first the reading on which the proposition fails, then the reading on which it holds.

Prefer Independent to a pair of refutations. When a reply is recorded as "it blocks the objection" and "it establishes nothing" over the same premise set, those are the two halves of one independence claim and should be stated as one. Written as a pair, nothing checks that the two halves are about the same proposition, and a pair whose halves were not has already reached main. The primer's entry is Independence.

Two premise sets asked two different questions are not this pattern — compatibility_defeats_lexical_objection and compatibility_does_not_establish_criterion range over different premise sets, and forcing Independent onto them would be false.

Typing the connectives

Write implication as ➝ (U+279D, TRIANGLE-HEADED RIGHTWARDS ARROW). The other connectives are Foundation's as written: ⋏, ⋎, ∼, and ⋀ for the conjunction of a list.

➝ is an alias, not a divergence. Foundation binds implication to 🡒 — U+1F852, in the Supplemental Arrows-C block — and that is the only token it declares. Testimony.Logic.Notation adds a second notation for the same class:

scoped infixr:60 " ➝ " => FFL.HArrow.hArrow
macro_rules | `($x ➝ $y) => `(binop% FFL.HArrow.hArrow $x $y)

Both parse to FFL.HArrow.hArrow, Foundation's own class, with the same binop% elaborator, so nothing about the encoding diverges from Foundation except the character on the page. It is scoped, so it applies where Testimony.Logic is open — every module here — and nowhere else. ➝ occurs nowhere in Mathlib, Foundation, Batteries or any other dependency, so it shadows nothing.

Why bother. Foundation's 🡒 is a poor character to build a corpus on, for two reasons that compound:

• Almost nothing renders it. Supplemental Arrows-C is covered by Symbola, Unifont and PragmataPro, and not by Fira Code, JetBrains Mono, Iosevka, Cascadia Code or DejaVu Sans Mono. A Nerd Font patch does not help — Nerd Fonts add glyphs in the Private Use Area, not in this block. It shows as an empty box in GitHub, in pull-request diffs, and in most editors.
• Nothing types it. The Lean 4 extension has no abbreviation producing U+1F852; \to and \r both give → (U+2192), which is Lean's function arrow and will not elaborate as Foundation's implication.

A catalogue whose whole claim is that anyone can read and contest it should not be written in a character most readers cannot see and no contributor can type.

Typing ➝. It has no built-in abbreviation either, so add one:

// settings.json
"lean4.input.customTranslations": { "fimp": "➝" }

which makes \fimp produce it — f for formula, since the arrow this library writes is the one between formulas rather than Lean's own.

Do not bind \imp. It is already taken: \imp is one of six abbreviations for → (U+2192), alongside \to, \r, \r-, \-> and \rightarrow, and a custom translation shadows the built-in one. \fimp, \impl, \Imp and \fto are all free and share a prefix with nothing.

The dev container ships this translation under customizations.vscode.settings, so in .devcontainer/ it is already there and nothing needs configuring; outside it, add the line to your own settings.json. See Editor setup, which also records why the font half cannot be shipped — editor.fontFamily is resolved on the contributor's own machine, so no container setting reaches it.

None of this reaches a reader of the site. The generated argument pages render formulas through Logic.Markdown and Logic.Latex as \rightarrow, so every published page shows an ordinary arrow whichever glyph the source uses. This is an authoring concern only — which is exactly why it was worth fixing cheaply.

Layout

Line width at most 100 columns; no trailing whitespace.

An argument is one module until it approaches ~500 lines, at which point it becomes a directory: Atoms, Sources, Lines, Packages, Results, with the root module reduced to imports and the module docstring. Dependencies run one way, so there are no import cycles. BornOfAVirgin/ and SolaFide/ are the worked examples; BornInBethlehem and SolaScriptura are small enough to stay single files, and the structure is not mandatory below that size.

Material shared across arguments goes further out: passages and citation bundles in Testimony.Scripture, Person values in Testimony.People.

Domain linter rules

scripts/testimony_lint.py, tier 4. Every rule has a test that must trip it and a test that must not — a linter that silently stops firing is worse than no linter.

Run its own tests with python3 scripts/test_testimony_lint.py.

What L12 exempts, and the one thing it does not

L8 has held Lean to 100 columns all along. L12 is its counterpart for prose, which is at least as much of the deliverable: a reviewer who does not read Lean reads the primer, the style guide and the roadmap. It counts characters rather than bytes, so a line of Hebrew is as long as it looks.

Four things are exempt.

• Generated pages. docs/src/bibliography.md and docs/src/arguments/*.md belong to bibgen and argdoc, and their --check runs already guard them.
• Generated blocks inside hand-written pages. The roadmap's status table sits between <!-- BEGIN GENERATED: lake exe statusgen --> markers and SUMMARY.md's argument list between argdoc's. The rule reads the markers, not the path, so the prose on either side of a block is still held to the width — excluding the file would have exempted the page along with the table.
• Table rows. A newline ends a markdown table row, so a wide row cannot be wrapped at all. A row counts as one either by its leading | or by sitting in a block opened by a delimiter row, since markdown allows both | a | b | and a bare a | b.
• YAML frontmatter. A skill's description: is one scalar the loader reads whole. A folded scalar would wrap it while preserving the string, but only if the loader is a real YAML parser, and finding that out by breaking a skill is a poor trade. The block has to be closed: a page that opens with --- and never repeats it has a thematic break, not frontmatter.

Long links are not exempt, deliberately. An inline link cannot be broken across lines, which sounds like the argument the table rows win on — but unlike a table row a link has a second form that fits: [text][ref], with the URL defined elsewhere in the file. So a link that will not fit becomes a reference link; the roadmap's issue links and the Independence link above are both written that way. Code fences are not exempt either: a sample too wide for 100 columns is too wide for the rendered page. They are still tracked, so that the other exemptions stop at the fence — a | in a sample is code rather than a table row, and a page that fences a sample of a BEGIN GENERATED marker opens no exemption over the prose that follows it.

Documentation moves with the argument

A change under arguments/TestimonyArguments/ is not finished when it compiles. The pages that carry results — README.md, Introduction, Encoding arguments, Rationale, Scope and limits, Roadmap — and the module docstring of the argument itself state what the library claims, and a page asserting the opposite of a proven theorem is the failure this project exists to rule out. It has happened: the roadmap spent two commits saying the virgin-birth argument was single-stranded and that its lexical premise was load-bearing, after the theorem saying so had been replaced.

Two mechanisms hold the line, and between them they cover different halves of the problem.

What can be generated is generated. The roadmap's status table is emitted from the @[headline] results by lake exe statusgen, the way bibgen emits the bibliography and argtex the rendered arguments. Rename a theorem, restate it, delete it, or add one, and the table moves on the next run; lake exe statusgen --check fails CI if the committed copy has not. The block between the two <!-- ... statusgen --> markers in docs/src/roadmap.md is generated: do not edit it by hand.

The argument pages under docs/src/arguments/ go further: lake exe argdoc writes each one whole, from the module docstrings and the declarations of the argument's own files, and lake exe argtex sets the same material for print. A docstring is therefore documentation in the ordinary sense — write it for a reader, because a reader will meet it on the site and in the PDF — and there is nothing to keep in step, because there is no second copy. Do not edit those pages, docs/latex/arguments.tex, or the <!-- ... argdoc --> block in docs/src/SUMMARY.md, by hand.

What cannot be generated is checked. Prose about why an argument matters is not derivable from theorem statements, so it stays hand-written. Rule L9 then reads every result name the prose cites, in backticks or declared in a Lean code block, and fails if the library no longer declares it. That is the specific way the roadmap went wrong, and it is now a linter finding rather than a matter of someone happening to reread the page.

A docstring counts as prose. L9 reads the /-- … -/ and /-! … -/ blocks in the Lean sources as well as the pages, because argdoc and argtex publish them verbatim — a module docstring naming a deleted result reaches the site and the PDF exactly as a stale page would, and once did. Ordinary /- … -/ and -- comments are left alone: they are notes to whoever opens the file, not something this project publishes.

A name the library imports counts as existing. Prose may cite Foundation's own results — of_mem, models_imply — and the rule reads Foundation's declarations alongside this library's so that it does not report them missing. Before it did, the rule pushed documentation towards describing a lemma rather than naming it, which is the opposite of what it is for.

The generated pages under docs/src/arguments/ are deliberately not read. A stale name there comes from a docstring, which is now checked at its source, and lake exe argdoc --check catches a page that has drifted from one. Reading both would report a single defect twice and invite someone to edit a generated file.

What is left over is judgement: whether a paragraph's description of a result still describes it. Say what the encoding now does, in the same commit that changes it.

@[headline]

Marks a result the library actually claims, as against a supporting lemma. It makes "what does this library assert?" a greppable question, and rule L6 requires every headline result to display its trust base with #print axioms — documentation in the source for a reader of the argument, where the axiom audit is the gate for CI.

Meanings and articles (draft)

A design note, with a working draft. Nothing here changes what any argument proves. The modules it describes sit outside the arguments, and no argument's verdict reads them.

The library checks arguments it has encoded itself. This note is about checking an argument someone else has published — an article, a tract, a chapter that claims a position is unbiblical or fallacious — and saying, as the library's own commentary, whether its claim can be defended. Such an article does not come as a premise list. It quotes, attributes, asserts and infers, and it can be careful in one paragraph and careless in the next. To check it fairly is to check each of those acts for what it is, and then to weigh what it claims against everything the library already holds.

That needs three things the library did not have: a way to say what a claim means, so that two claims can be compared; a way to model what an article does, move by move; and a way to hear an article's claim as a position in a dispute, so that whether it can be defended is computed, like every other verdict here.

Where the parts live

Nothing in the generic layer names an argument. Every argument has an instance: sola fide is analysed; sola scriptura, the virgin birth, Spirit baptism and the canonical witness in part, the claims whose meanings bear on a join — and, in the virgin birth, the claims about the words of Isaiah 7:14 and its versions, the woman it describes and the birth it is read to promise; and born in Bethlehem, looked at and found to have no joins, is registered with its citations' labels and marked unanalysed. Each is counted from the start (each module's coverage_now). Testimony.Checks.Meanings fails the build for an argument with no instance, so a new argument is registered when it is added. It also fails the build for an argument whose joins are not listed and pinned, or whose meaning postulates come from anywhere but those lists (computed ratings).

What a claim means

Every argument names its atomic claims in a type of its own. dikaioIsForensic is a name with a docstring; to the library it is opaque. So it cannot answer the questions a reader asks of the whole collection — every claim about δικαιόω, every passage read two ways, the same claim in two arguments — and it cannot see an article move from one passage to another under one word.

A meaning is a term built from the shared vocabulary. Its parts were each added because a claim in the library needed them:

Three distinctions in it do most of the work.

• The word and what it means are kept apart. A textual claim is stated with the words as they stand; what a word denotes is a separate claim, means. Romans 3:28 says a person is justified by faith apart from works of the law; what those words mean in Paul is three further claims, each disputed. This is Barr's distinction between the word and the concept, which the sola fide argument already turns on.
• says is not teaches. What a passage says, in its own words, is textual. What it teaches, read rightly, is a reading, which a rival may read otherwise. Luke 7:47 says her sins are forgiven, for she loved much; that her love is the evidence of forgiveness and not its ground is what the Reformed say it teaches. The two are never the same claim, as quotation is never prediction.
• A sense can be the same, or not, at two places. sameSense states that a word means the same in two texts. Every contradiction between two texts depends on it, for every word they share, and most arguments never say so.

The atoms are not replaced. An argument keeps its own claim type and its proofs are untouched; its instance says what each atom means, as cite says who holds it. Ninety-five of the hundred and seven sola fide atoms are analysed; twelve — the stories of the thief and the tax collector, a curse, a command, a disjunction, and the claims about texts and their translations — are marked unanalysed and counted, not forced.

What the meanings already make computable, from the meanings alone, for any argument:

• The contested readings are found, not listed. For sola fide: δικαιόω in Paul, the believing of John 6:29, doing the will in Matthew 7, keeping the commandments in Matthew 19, the water of John 3:5 four ways, the fire of Matthew 3:11 three ways (contested_length). Nothing else turns up.
• Every claim about a word. Thirteen sola fide claims turn on δικαιόω (about_dikaioo).
• The same claim in two places. An article's quotation of James 2:24 means exactly what the library's atom for the verse means (jamesSays_is_the_library's), so the two are one claim. Once a second argument is analysed, the same holds between arguments.

The ontology, derived in articles

Two claims join — one excludes or entails the other — when a reader who holds the one is bound to deny, or to hold, the other. That depends on what their words commit a reader to, and the words are the vocabulary's. "Faith is the only means of justification" and "baptism is a means of justification" contradict each other only because of what only means.

So a meaning is read for what its words mean (Testimony.Semantics.Ontology). It is taken apart into the facts it affirms and denies, and closed under definitions: what the vocabulary's own words mean, each with a source, as a premise has one. Doctrine — what is held to be so — is taken apart; what a passage says, what it teaches, what it is written against and what a voice held are kept whole, because a text may say a thing without saying all that follows from it.

The definitions are not a list kept beside the vocabulary. Each is derived in an article (Testimony.Ontology), which names no argument and does two things, both checked:

1. Define. What the words mean, with a source. A definition is what a word means, which no reader disputes; what one tradition holds of a word and another denies is a premise of a position, and the article leaves it apart and says why.
2. Show each definition at work on two statements of its own, built from the vocabulary alone: they exclude each other with the definition, and not without it.

What the definitions do in the arguments is computed, for every argument the library has, by Testimony.Checks.Ontology, from the generic queries of Testimony.Ontology.Search. It finds the arguments itself and pins, for each, how many of its joins are found with no definition at all, how many claims use each defined word as doctrine or of a text or voice, and the joins each definition contributes: those found with it and not with it taken out. It fails the build if any meaning contradicts itself.

The first article, Testimony.Ontology.Relations, writes out three definitions the vocabulary already gave in words: "not a ground" is the denial of "a ground"; the only means of a thing is a means of it, and nothing else is; the whole ground of a thing is a ground of it, and nothing else is. One join follows from them, in sola fide — faith alone against Trent's baptism as the instrumental cause of justification (the_only_means_at_work) — and one more was found by reading the meanings more carefully: "forensic only" against Trent's "justification includes sanctification", whose denial was always in the Reformed claim's own meaning (a_denial_inside_needs_no_definition). No dispute's table and no verdict moves; the named readings of sola fide take a side on both pairs.

Testimony.Ontology.Usage is about senses rather than relation words. A word's usage as a whole is the senses its passages give it, so a sense a word has in one passage of a text is a sense it has in that text's usage (a_sense_in_a_usage_at_work). That is all it does. It says nothing about any single passage, and it does not count a word used of a virgin as evidence that the word means "virgin". What a word means at a passage stays a premise, cited and rated, and the context it is read from is the premise's evidence. What it can show false is a claim that a usage lacked a sense, wherever a passage of it is held to have that sense. In the virgin birth argument it joins the laws of the Greek Pentateuch, and the status reading of Genesis 34:3, to the Septuagint's Greek: their sense "virgin" makes "virgin" one of the word's senses in the Septuagint, which is the claim encoded for Rico and Gentry, and excludes Wegner's "not yet 'virgin'". It says nothing of which sense the word has at Isaiah 7:14.

What the search found, not yet fixed

The search was run over every argument's meanings before any article was written. Besides the two joins, it found five things a stricter vocabulary has to answer, each the subject of an article to come.

• Paul's texts are stated in doctrinal words, James's "by works" is not. What Romans 3:28 says is encoded with "the means of" and "not a ground of"; what James 2:24 says, with saidBy, the word kept for a "by" that leaves open whether it is a ground, a means or the evidence. A text's own connective should be stated in a textual word for both, and what it denotes argued as a reading for both.
• One concept does two jobs. The vocabulary's baptism is water baptism. Spirit baptism's readings of 1 Corinthians 12:13 say what "the baptism" of that verse is, using the same concept, so that read literally they say what water baptism is. Whether Paul's word and Luke's name one baptism is the question the argument says is not yet encoded.
• isA does three jobs: a kind ("Scripture is a rule of faith"), a property ("Scripture is infallible"), and the identity of an event ("the baptism of 1 Corinthians 12:13 is Christ's baptizing in the Spirit"). Disjointness and subsumption cannot be stated over it until they are told apart.
• Faith alone is analysed two ways. Sola fide states it as "faith is the only means of justification"; the canonical witness, as faith necessary, faith sufficient and works not the ground. And the canonical witness's labels for the first two parts say saved, while its module, and its meanings, say justified.
• Senses and concepts overlap, and voices repeat the traditions. salvation and worksOfFaith are both a sense and a concept; the kinds of faith a word can mean — trust, faith formed by charity, bare assent — are senses of πίστις but not kinds of faith. And the vocabulary's voices name again what Tradition already names: the Reformed, Rome, Second Temple Judaism.

Testimony.Semantics.Discourse models an article as a list of moves. Each move records who makes it, the article's own words, verbatim, and the act they perform: an assertion, a quotation, an attribution, or an inference from premises to a conclusion.

The first check is the one that needs the grammar. An inference that sets one text against another — or a text against a doctrine — assumes, for every word they share, that it means the same in both. Move.unstated computes, from the move alone, the senses it needs and does not state; Move.meets finds the claims of any argument that deny them. A move with unstated senses is not thereby fallacious. It is conditional, on exactly those senses.

Commentary: whether an article's claim can be defended

The library's verdicts already say, of a position, whether it can be defended. A position is indefensible when no admissible set holds it: something defeats it, and nothing the dispute can hold answers that defeat. Trent's definition, read as a claim about what Paul's word means, is indefensible in the sola fide dispute (trent_on_pauls_word_indefensible). That is the library's own judgment, checked, and an article that argued the same would meet the same verdict, for the same stated reason.

So an article's claim is judged the same way, in four steps:

1. Model the move, verbatim.
2. Make its unstated assumptions explicit as premises, from Move.unstated. A position is answerable for what it needs, not only for what it says.
3. Hear it as a party in the argument's dispute, alongside every existing party.
4. Report what the solver computes: indefensible, defensible but not forced, or forced — whichever way it goes, and with the defeats that decide it.

This is commentary, not reproduction: the verdict is the library's, and it is a checked result about the article's claim, not a summary of the article.

Whether a dispute makes sense

A premise is rated disputed when a cited source grants its grounds and denies its conclusion. That is a fact about the literature: someone denies it. Whether the denial, stated as a position and weighed against everything else, can still be defended is a further fact, and Testimony.Logic.Contest makes it a computed one.

• A claim is contested in a dispute (Contested) when one party holds it, another denies it, and each can be defended. The rating disputed is then what the weighing finds.
• A claim's denial is answered (DenialAnswered) when every party that denies it is indefensible. The claim is disputed in the literature, and the denial does not survive the weighing; a page should say both.

The weighing takes the cited ratings as its input, so a contest result does not make ratings out of nothing. It says what the ratings already in the library imply once the positions that hold and deny a claim are heard together. A rating still moves only with a new, cited argument.

A worked example

Kenneth Howell, "Aren't We Saved by Faith Alone?", Catholic Answers Magazine, 2003, is a dialogue between a Protestant objector and a Catholic. TestimonyArguments.Articles.Howell2003 models four of its moves, quoted from the publisher's page, and hears one of them.

The argument about works. "If Paul and James mean the same thing by works, then they contradict one another. Since you and I both believe that the Bible cannot contradict itself, we must agree that Paul and James mean two different things by the word works." Romans 4:2–5 and James 2:24 share three words, not one — works, justify and faith — and their clash needs all three the same. The Bible's consistency rules out only that all three agree; it does not choose works (consistency_does_not_choose_works, refuted by the reading on which James uses "justify" otherwise, as Moo and Calvin read him). The article does give a reason for its choice — Paul's "works of the law" — and that reason is weighed where the library weighs ἔργα νόμου.

The argument from the phrase. "The phrase 'faith alone' does occur in the New Testament: one time, in James 2:24. There the inspired apostle denies that justification is from faith alone." To deny sola fide by this, James's "faith" and "justify" must be the ones the Reformers' formula uses of Paul. The move does not say so (faithAlone_unstated), and those are exactly the two senses one claim in the library denies, james2_24Compatible (faithAlone_meets_the_library).

Heard in the dispute, it cannot be defended. Stated as a position, with the senses it needs made explicit, and heard with every party to the sola fide dispute and with James's own words about faith, the move falls (howell_indefensible). James calls the faith he denies justifies dead (2:17, 2:26); Trent reads it so (Session VI, ch. 7); the Reformers' confession calls the faith that alone justifies "no dead faith" (Westminster XI.2). The denial the move needs does not survive the weighing (faithDenialAnswered). The article's other case from James — that works "actually justify" — is the Catholic reading of James's "by works", weighed in TestimonyArguments.SolaFide.James: as a claim about James's word it cannot be defended (trent_on_james_word_indefensible); as a claim about what works do before God it can, and is not forced (trent_on_works_defensible).

The same check, on the other side. The objector's reply — James 2:14 "is dealing with the problem of those who claim faith but who don't show it by their works" — takes "faith" in 2:14 for "faith" in 2:24 without saying so (deadFaith_unstated). That is the Reformed reading's own condition, and the claim that carries it, james2TargetsDeadFaith, is rated disputed too.

What each position rests on

Testimony.Logic.Warrant answers a reader's question about any position: where does this rest on someone's word alone? Each cited work has a role — a text or lexicon, argued scholarship, a binding decree or confession, or a theologian's own teaching — and a premise's warrant is the best of its references: Scripture, evidence, authority alone, or the library's own assertion. A claim about what someone holds is proved by their own text, so it rests on evidence.

The warrant is reported beside the verdicts and never weighed in them. A rule that discounted authority inside the solver — "Scripture first, by default" — would decide the sola scriptura dispute by fiat, since whether a council's or a confession's word binds is what that dispute is about. And it applies to every side: in the James dispute (james_warrants) Trent's readings rest on Trent's word, and the readings of the Greek on Pius XII's and Westminster's at "the original outweighs any translation". The Reformed harmony rested on Westminster's word at "works are fruit, not ground" until it was given the Assembly's own proof texts as a step (fruitLine); it rests on Scripture now, and the step is still disputed, because Trent grants the texts and calls the fruit merit.

The same check answers whether Rome contradicts itself over Trent's Latin texts (TestimonyArguments.SolaFide.Vulgate). Read as what the inspired authors wrote, Trent's "as it is written" at Revelation 22:11 cannot be held with Pius XII's teaching that the original outweighs any translation (trent_as_the_inspired_text_contradicts_pius). Read as Pius XII reads Trent's decree — the Vulgate juridically authentic and free from error in faith — Rome is consistent (pius_reading_is_consistent), and the two texts then rest on the Church's word (pius_reading_rests_on_authority), which Pius XII asks to be confirmed from the originals; at these verses the originals do not confirm it (pius_finds_no_confirmation).

Computed ratings

A rating today is asserted, with a citation: disputed when a cited source grants a step's grounds and denies its conclusion. That records that someone dissents, not whether the dissent is an argument or only "I disagree". Computed ratings sets out the design for telling them apart — five checks a dissent must pass to count as credible, under a stated standard of evidence — and its first phase is built. It finds that Howell's move is a disagreement, not a critique (howell_asserts_his_denial). Trent's denial that works are fruit, not ground, rests at one claim on the council's word, so that step stands under the evidence standard and is disputed under the tradition standard (fruit_turns_on_the_standard). And what James's δικαιόω denotes turns on the standard in the same way (james_word_turns_on_the_standard). Contested and DenialAnswered remain the checks of whether a dissent survives the weighing: the Howell hearing shows one that does not (faithDenialAnswered), the James dispute one that does (worksContested).

What it would take to decide James

The library says a reading is right in one sense only: the dispute forces it. A reading is forced when it is in the grounded extension — every rival reading is indefensible, given premises that are cited and rated. Paul's word is forced in that sense (only_pauls_word_prevails), because the lexical case rests on links rated above disputed and nothing that attacks it is as strong. For James, four things are missing.

1. The dispute now exists (TestimonyArguments.SolaFide.James), with the Catholic reading as two parties: James's word as the increase of justice, which cannot be defended; and what works do before God (canon 24), which can, against the Reformed harmony. What is left to decide is the second.
2. The question splits by word and by verse. What δικαιόω denotes at 2:21, 2:24 and 2:25; what πίστις denotes at 2:14, 2:17, 2:19 and 2:24; and whether each keeps its sense through the paragraph. The grammar can now state each as its own claim, and sameSense the claim that one word means the same at two verses.
3. Evidence that discriminates between the readings, each a cited premise:
   • 2:14 asks whether "the faith" can save — the faith just described, said and not shown. The article is in the Greek; that it points back is a reading, to be rated.
   • 2:21–23: Abraham is "justified by works when he offered up Isaac" (Genesis 22), and 2:23 says this fulfilled Genesis 15:6, said of him years before. That one justification follows the other is in the texts; whether "justify" then means a second verdict, a showing, or an increase is where the readings part.
   • 2:18, "show me your faith", and the uses of δικαιόω elsewhere for being shown to be in the right (to be verified against a lexicon before any is cited).
4. Ratings audited, not assumed. Each step stays disputed until the rating auditor finds no cited reader who grants its grounds and denies its conclusion. If every step on both sides stays disputed, the solver will report that James is contested — as it now does — and the page will say so. A forced reading needs one side to rest on something the other cannot match.

The textual facts in the third item can also be checked against an annotated Greek text — that the article stands in 2:14, which words recur through 2:14–26 — rather than cited alone (MACULA Greek carries the syntax and Louw–Nida sense domains).

The checks an article audit needs

Each common charge of fallacy is a question the library can make precise. Two are built; the rest reuse machinery that exists, or that the open issues propose.

Two of these are worth a word, because Howell's article already supplies them.

• An attribution has readings, as a claim does. The objector asks how the Church can teach "that we have to earn our salvation". Against the library's Trent, that is ambiguous: if "earn" means by our own efforts, Trent denies it, and the Catholic says so; if it means works done in grace meriting an increase of justification, Trent holds it (worksMeritIncreaseOfJustification). The grammar tells these apart — works and worksOfFaith are different concepts — so an attribution check can report which reading of the attribution is fair, rather than calling it a straw man or not.
• An implicature is not an assertion. The Catholic says Luther "added the word alone—but alone is not in the original Greek text". Both claims are true of the texts, and the move is modelled as asserting exactly them. What it may be taken to imply — that the reading was new with Luther — is a different act, and a check must not charge an article with what it only implies.

Rules for checking someone else's argument

The library's own rules carry over, and four more follow from them.

• Quote, do not paraphrase. A move records the article's words exactly. A model of what an article "basically says" is a straw man in waiting.
• Every voice gets the same check. Howell's objector is checked as his Catholic is. An audit that only finds faults on one side proves nothing about the side it spared.
• Report the verdict the solver computes. An article's claim is indefensible only when the dispute says so. Howell's move is not, and the page says that.
• Apply the article's principles to the article. When an article states a principle — that the Bible cannot contradict itself, so two authors must mean different things by one word — the same principle applies to every word it uses that way.

What comes next

1. Meanings for every argument. Every argument is now analysed where a join turns on it; the rest of each argument's claims are registered and unanalysed.
2. A James dispute, with the Catholic reading as a party, so that the question the Howell hearing leaves contested is asked directly.
3. The remaining checks, in the order of the table, each as a checked certificate that reuses Because, Dilemma and the solver.
4. Articles as pages. An audit, or an ontology article, is published prose like an argument page, generated from its docstrings. Today an ontology article's prose is its module's docstrings, and the generators render arguments only.
5. The next ontology articles, one for each finding above: textual words for textual claims; baptism kept apart from the baptisms; kinds and properties told apart; faith alone stated once; and voices taken from the traditions the library already cites.

Computed ratings (design)

Status: phase one is built. Testimony.Logic.Credibility implements the checks, the ratings and the hearings below. TestimonyArguments.SolaFide.Ratings applies them to two steps of the Reformed reading of James, and TestimonyArguments.Articles.Howell2003 to Howell's move. The remaining steps are tracked in #135.

The question

Every inference step in the library carries a Confidence. The rule for disputed is that a cited source grants the step's grounds and denies its conclusion. That rule records a fact about the literature: someone dissents. It does not record the next thing a reader needs to know: is the dissent an argument, or only a disagreement?

"You are wrong because I say so" is a dissent. So is "you are wrong because the council says so". So is "you are wrong, because these texts say what your reading cannot hold". Only the last is a critique that anyone can weigh without first sharing the dissenter's allegiances.

A rating that cannot tell these apart goes wrong in two directions:

• a bare denial lowers a well-argued step as far as a strong argument would;
• an author can raise a step's rating by never looking for the strongest dissent.

So a rating should be computed. It is disputed when some dissent is credible, and otherwise the rating the step's support earns.

What makes a dissent credible

A dissent is a position, stated as an ArgumentPackage, set against a claim. The claim is either a premise, or the conclusion of a step whose grounds the dissent is given. The engine decides five checks:

1. Consistent. Its premises have a model. A self-contradictory position denies everything, so it says nothing about this claim in particular.
2. Denies the claim. Its premises entail the claim's negation.
3. Grants the grounds. It can be held together with the step's grounds. A dissent that denies a ground is a dissent from that ground, and belongs to that ground's rating.
4. Argued, not asserted. What it asserts outright (its atoms and denied atoms) does not already contradict the claim. The denial must need one of its own steps. A position that holds the claim's negation as a premise is reporting its disagreement, not arguing it.
5. Its grounds meet the standard. Every claim it asserts rests on a warrant the standard admits (Testimony.Logic.Warrant). It also asserts no bare denial, because a denial is cited nowhere and so rests on the position's own say-so.

An Assessment runs the checks once and records what they find under every standard, with the kernel's check that the engine finds it. One declaration answers the reader's question for every standard at once. Assessment.credible_iff says the answer is exact: credible as assessed if and only if Credible.

Three standards, all reported

Check 5 needs a standard. Choosing one would decide a dispute that the library exists to show, not to settle: whether a council's or a confession's word can ground a critique is the sola scriptura question, and whether Scripture is its own interpreter is the question behind it. So the standard is named, and every result is computed under each:

• Neither admits the library's own bare assertion.
• The standards check a dissent's grounds, never its inference. Every step on every side is someone's reading, cited to a commentator, a council or a confession. A rule that discounted those readings would discount all of them alike.
• A rating that differs between the first two turns on the authority question. The page says so in those words. That is a finding, not a failure.
• The third is "Scripture interprets Scripture", made a rule a dissent must meet. Westminster states it: "The infallible rule of interpretation of Scripture is the Scripture itself" (I.ix). It binds only where it applies. A dissent from a step whose grounds are all Scripture counts only if every claim it asserts is Scripture too. A scholar's argument from other evidence does not bring such a step down, however competent. Another text, read the other way, does. Elsewhere the third standard is the first. A rating that differs between them turns on whether Scripture is its own interpreter, and the page says so.
• No standard is the default. Each is reported beside the others, so a reader who does not hold Westminster's rule reads the evidence standard's verdict, and nothing is decided for that reader by fiat.

The third standard's first use is Matthew's reading of the Septuagint's παρθένος (TestimonyArguments.BornOfAVirgin.Dispute.Matthew). Matthew quotes the Greek of Isaiah 7:14 of Mary, so in the text he quotes the word means "virgin". Wegner grants Matthew's grounds and holds that the word had changed in meaning since the translator wrote it, from early Greek usage. Under the evidence and tradition standards that is a credible critique, and the step is disputed (matthew_step_ratings); in the hearing under the evidence standard nothing prevails. Under the third it is not heard, and Matthew's reading prevails (matthew_step_turns_on_the_standard). Its second is the fulfilment of Genesis 3:15 (TestimonyArguments.BornOfAVirgin.Dispute.PromiseHearing): every term of the verse met as the New Testament names it. Westermann grants the texts and denies the step from his philology of "seed"; under the evidence standard he is heard and nothing prevails, and under the third he is not, and the fulfilment prevails (promise_turns_on_the_standard). In sola fide the third standard gives what the first gives, every time.

Computing a rating

A RatedStep is a step together with its register: every dissent encoded against it, and which of them is the strongest known. Its rating under a standard is one of three:

• disputed, by every dissent credible under the standard;
• the support stands, at the confidence its citation gives, when no dissent is credible and the strongest known dissent is encoded;
• withheld, weighed as disputed, when no dissent is credible but the strongest known dissent is not encoded.

The third case is the steelman rule:

A computed rating may stand above disputed only when the strongest known dissent is encoded with its own grounds and fails a check. A dissent recorded only as a citation proves nothing either way.

The rule makes it visible when a dissent has been left out. A reader who knows a stronger dissent has a concrete thing to add: a position, with grounds, that the engine will check.

RatedStep.ratings computes the rating under every standard at once. One theorem therefore states a step's rating under each standard, and an article can argue from whichever standard it prefers. It cannot hide the preference: the other standard's rating is on the same line.

Meaning postulates

Some claims the atom type keeps apart are joined by their meanings. "In Paul, δικαιόω is forensic: a verdict, and not making righteous" denies, in so many words, "Paul's δικαιόω denotes making righteous". A propositional check cannot see that: the two are separate atoms. So each check holds the argument's meaning postulates as background. For every pair of claims whose meanings cannot both be held, the postulate is a → ¬b; where one claim's meaning asserts all another's does, it is a → b. Both are read for what the words mean: each meaning is taken apart into what it affirms and denies, and closed under the definitions the ontology articles write out, so that "faith is the only means of justification" is seen to exclude "baptism is a means of it".

Each argument lists its pairs in a HasJoins instance, beside its meanings, with proofs that the lists are exactly what the meanings contain. Its atoms take their postulates (Testimony.Logic.HasPostulates) from those lists and from nowhere else, and a check takes them from the atoms: no call site names them, so no dissent can be checked without them. Testimony.Checks.Meanings fails the build for an argument with no pinned lists, or whose postulates come from anywhere else. Testimony.Checks.Postulates fails it for any package the postulates make unsatisfiable: a package with no model entails everything.

Two claims that read one word in different senses are not held to exclude each other. Whether the senses exclude each other is itself contested: Trent holds that justification both declares and makes righteous. A postulate saying they do would hand one side's lexicon to both. A claim whose meaning says and not that sense does exclude the other, and is listed.

Sola fide has six exclusions and no entailments (TestimonyArguments.Meanings.SolaFide.joins):

• Paul's word as renewal, against the forensic sense;
• Trent's Latin of Revelation 22:11, against the Greek;
• Trent's Latin of Sirach 18:22, against the Greek;
• "James's δικαιόω is Paul's", against "James 2:24 is compatible with Paul";
• faith alone, against Trent's baptism as the instrumental cause of justification, by what "the only means" means;
• justification as forensic only, against Trent's "justification includes sanctification".

Every dissent gets the same background, whichever side it is on. Sola scriptura has one exclusion and two entailments (TestimonyArguments.Meanings.SolaScriptura.joins): Mark 7's principle against binding a commandment of men as God's word, and "Scripture is the sole infallible rule" asserting that it is infallible and that no other rule is. The virgin birth has eleven exclusions and five entailments (TestimonyArguments.Meanings.BornOfAVirgin.joins): Wegner's claim that in the Septuagint's day παρθένος meant "young woman" and did not yet mean "virgin", against Rico and Gentry's that it meant "virgin", against the laws of the Greek Pentateuch, which use it in that sense, against the status reading of Genesis 34:3, which reads it so there, and against Matthew's reading of the Greek of Isaiah 7:14; Miller's thesis that the word did not by itself connote virginity, against each of those senses, and Wegner's claim asserting it; Miller's premise that the noun of Genesis 34:3 describes Dinah as she then was, against the status reading; Brown's "Micah's silence proves nothing" against Miravalle's "it indicates a fatherless birth"; Westminster's supreme judge against "magisterial teaching settles the question"; "עַלְמָה denotes a virgin" asserting that its range admits the sense; and the laws' sense, the status reading's and Matthew's, each asserting Rico and Gentry's claim. The joins of the laws, of Genesis 34:3 and of Isaiah 7:14 are derived by what a usage is (Testimony.Ontology.Usage). The exclusions on παρθένος are the ones the Septuagint dispute turns on: Wegner's case and Miller's attack the Septuagint's witness, the laws and the status reading through them, and each attacks back. Spirit baptism has two exclusions (TestimonyArguments.Meanings.SpiritBaptism.joins): the Assemblies of God's reading of 1 Corinthians 12:13, "not Christ baptizing in the Spirit", against Dunn's and Stott's; and Luke's narratives as a pattern for believers today against Stott's "not a pattern". The second removed a horn: the Pentecostal view read with Acts as transitions has no model once the words are read, so it no longer stands as a reading to answer. The canonical witness has seven entailments (TestimonyArguments.Meanings.CanonicalWitness.joins): faith alone asserts its three parts, and Westminster's "by a faith that is never alone" asserts faith alone. Born in Bethlehem was looked at and has none: its one pair of rivals can be held together by a reader who takes the oracle as fulfilled twice. Without the postulates, Trent's reading of Paul's word would pass as granting the lexical step's forensic ground, which it denies.

Disputes hold them too: every attack is decided over what a party holds, its premises with the postulates (disputes). In the James dispute this adds one pair of defeats, both ways: the Reformed harmony and the renewal reading, whose claims about James's word exclude each other by meaning. No verdict the library states moves. establish holds premises alone; the postulates could only add entailments, and no non-entailment the library states is undone by them: Testimony.Checks.Postulates checks every ¬ Establishes, ¬ Entails and Independent result, and fails the build when a meaning would overturn one.

Stating the bridge

The standards check what a dissent asserts, not its step, because every step on every side is someone's reading. So a claim smuggled into a step escapes the check. When a dissent's own source states a claim the texts do not, in its own voice, that claim is a ground, not part of the reading, and it is encoded as one: cited to whoever states it, and checked like any other. Trent's chapter 16 is the first case: "we must believe" that the reward is rendered to merits.

The rule cuts both ways. A Reformed step that needs a claim its texts do not make must state that claim too, and it is checked the same way. Westminster's answer to chapter 16 was checked so: every claim it asserts outright is a text it gives as a proof, and only its step, a reading, is its own (westminster_answers_from_the_texts).

Hearings under a standard

Which dissents count decides two things in a dispute: who is heard, and how each step is weighed. A Register attaches assessments to a dispute's parties and rated steps to its citations. The hearing under a standard (Register.hearing) does three things:

• it hears every party that is not a dissent;
• it hears every dissent that is credible under the standard;
• it weighs each rated step at its computed rating under that standard.

So the dissents heard and the ratings weighed come from one register, under one standard, and a verdict and a rating cannot disagree about which standard they assume. Register.heard_credible proves that every dissent heard is a credible critique.

What phase one finds

Each row is rendered on the generated page with ✔ or ✘ under each standard, and with the claims a standard does not admit named. Disagreements are marked as disagreements.

James's word: how a rating moves.

• Before the steelman. Only Trent's reading of the word was encoded. It is a disagreement, so no dissent was credible. But the strongest known dissent was missing, so the computed rating was withheld under both standards (lexical_step_before_the_steelman).
• The steelman. The renewal reading argues the increase from Paul's word: Paul's δικαιόω denotes renewal, as VanLandingham argues and Augustine glossed it, and James's word is Paul's.
• After it. The step's support stands at wellSupported under the evidence standard, and it is disputed under the tradition standard (lexical_step_ratings).
• Why the standards differ. No exegete's statement that James's word is Paul's has been verified, so that ground rests on Trent's word. A verified one would make the step disputed under both standards (#139).
• The hearings agree with the rating (james_word_turns_on_the_standard). Under the evidence standard the hearing forces James's word. Under the tradition standard it weighs the step at disputed, and the question is contested.

Works as fruit, not ground: a bridge stated.

• The support. Westminster's step is wellSupported. The Lutheran World Federation and the Catholic Church confess together that good works "follow justification and are its fruits", and that what follows faith "is neither the basis of justification nor merits it" (Joint Declaration §§37, 25).
• Chapter 16's bridge. The reward texts (1 Corinthians 15:58, Hebrews 6:10, 10:35, 2 Timothy 4:8) say God rewards works. Chapter 16 adds that the reward is "rendered to their good works and merits", and that "we must believe" the justified "have truly merited eternal life". From reward to merit is the council's own step. Dulles, defending Trent, grants that "the fact that a reward is promised does not make it merited". Stated as a premise, as Trent states it, the bridge rests on the council's word (rewardRenderedToMerits).
• The rating (fruit_step_ratings). The support stands at wellSupported under the evidence standard, where neither of Trent's dissents is credible, and the step is disputed under the tradition standard, where both are.
• The hearings agree (fruit_turns_on_the_standard). Under the evidence standard the hearing forces the Reformed harmony. Under the tradition standard it is contested.
• What this does not show. It shows that Trent's denial does not stand on Scripture and evidence alone. It does not show that the reward texts teach the Reformed reading: they teach neither side's account of merit without a further claim.

The same checks, run the other way.

• Westminster's answer to chapter 16's merit premise. It argues from Hebrews 6:10 (a proof of XVI.6, and one of Trent's own four texts), Luke 17:10, Romans 4:4–5 and 1 Peter 2:5. It concludes that the reward is of grace, not rendered to merits. It is a credible critique under both standards.
• The Reformed harmony against canon 24's step and chapter 16's. It is a credible critique under both standards.
• So each of Trent's claims is disputed under both (rome_steps_ratings). Set beside fruit_step_ratings, that is the asymmetry the checks find. The Reformed dissents from Trent are critiques under either standard, while Trent's dissents from the Reformed step are critiques only where the council's word is admitted. Neither side's step is proved right by this. What differs is what each dissent rests on.
• The hearings. Under the evidence standard, the hearing forces Westminster's answer along with the harmony. Under the tradition standard, Westminster's answer and chapter 16 defeat each other, and neither is forced.

Disagreements, not critiques. Trent's reading of James's word and Howell's move each hold the denial they need as a premise (trent_on_the_word_is_asserted, howell_asserts_his_denial).

Trent's definition, and faith's sufficiency.

• The Reformed dissents. Paul's gospel and Romans 4 against the definition, Romans 4 against its reading as Paul's word, and Luke 18 against the step to "faith does not suffice" are each a credible critique under both standards. So each of those claims of Trent's is disputed under both (trent_definition_ratings).
• Trent's dissents (trent_dissents_from_the_definition_steps). Its reading of Paul's word dissents from the lexical step's ground, not the step, so that step's support stands at wellSupported under both standards. Its definition read as what God does is asserted, not argued. Its denial of sufficiency is a critique of Luke 18 under the tradition standard only.
• On the word itself, both sides hold their reading as a premise. The lexical case holds the forensic sense, cited to the lexicon; Trent holds the renewal sense, cited to itself and VanLandingham. Against each other, each is a rival reading, so the question is weighed at those premises' ratings. The argued dissent is Romans 4's, which glosses the verb by Paul's own text.

Evidence the texts refute

A dissent may rest on a claim about what a text reads, and the text may read otherwise. Such a claim is recorded as a Refutation: the claim, what the text reads, and the citation of the text. It counts only if the citation is Scripture rated consensus, so that what is struck is struck by the text and not by a reader's say-so. The refuted claim is taken out of the dissent's premises, with every step drawn from it, and every check runs on what is left. A dissent that needed the claim to deny the step no longer denies it, and is not credible under any standard; one whose denial stands on other evidence stays credible, and the page shows what was struck.

The first case is Miller's dissent from the laws of the Greek Pentateuch (TestimonyArguments.BornOfAVirgin.Dispute.Miller). He gives two uses of παρθένος of women who are not virgins. One is his "young widow" at Joel 1:8, where the Greek calls the woman νύμφην, a bride; that claim is struck. The other is Genesis 34:3, where the Greek calls Dinah a παρθένος in the verse after Shechem lies with her. That reading stands. His denial needs more than it: his premise that the noun describes Dinah as she then was, which is his reading of the verse, not the text (miller_rests_on_the_noun). Had Joel 1:8 been all his evidence, the dissent would not count (miller_on_joel_alone_does_not_count). What the rule does not do is weigh the evidence that stands: Genesis 34:3 is answered by an argument, the status reading, and an argument strikes nothing. It is weighed, in a dispute, and the next section says what follows.

Dissents overruled in a dispute

A credible dissent can still lose when it is weighed. It is overruled (Overruled) when its position, with what the texts refute struck, is a party of a dispute and belongs to no admissible set of it: however the dispute's standoffs are resolved, nothing defends it. An overruled dissent stops counting against the step, and the step's rating names it.

Phase three below explains why folding survival into ratings is circular in general: ratings decide defeats, and defeats would decide ratings. An overruling avoids the circle with one condition. The dispute must weigh the step the dissent is against at its floor, with every citation of the step's support rated disputed. The dissent is then overruled with the step at its weakest, so the overruling owes nothing to the rating it lets stand.

Miller's case from Genesis 34:3 is a party in the dispute over the Septuagint's word. The status reading of the verse defeats it, and nothing defeats the status reading, so nothing defends Miller (miller_indefensible). That dispute cites the laws' step disputed. So the laws' step stands at its cited wellSupported under every standard (laws_step_ratings). Under the evidence and tradition standards that is because Miller is overruled; under the Scripture standard, because his premise about the noun is not Scripture and he is not heard. The overruling turns on the status reading's step, rated plausible: rated disputed, it would not outrank Miller, and his dissent would count again.

Phase two: every dispute weighs computed ratings

A hearing weighs computed ratings, but a full dispute still weighs cited ones. For the James dispute these agree under the evidence standard only. The full dispute therefore forces James's word (james_words_prevail), while the hearing under the tradition standard finds it contested. Phase two (#136) declares every dispute with its register and states each verdict under both standards. Splitting Source.confidence into support and register, and enforcing the steelman rule with a linter rule, is #137.

This is not circular. A dissent's credibility depends only on entailment and warrant, never on ratings, so the computed ratings are fixed before the solver runs.

Phase three: survival, and preferences as arguments

A credible dissent can still lose the weighing. Apart from an overruling, with the step at its floor (above), survival does not feed back into the rating. Contested and DenialAnswered (Testimony.Logic.Contest) report it after the fact.

Folding survival into the rating is circular: ratings decide defeats, and defeats would decide ratings. Iterating to a fixpoint is not safe either. Lowering one step's rating can weaken a party; that can let a dissent survive that did not before; and that lowers another rating. The map is not monotone, so a fixpoint need not exist, need not be unique, and need not be reached.

The literature's answer is to make preferences themselves attackable. In Modgil's extended argumentation frameworks (Modgil 2009) an argument may attack an attack. "This step is not as strong as that one" becomes an argument with its own premises, and it can be defeated in turn.

Two kinds of preference become parties:

• A rating. For example: "this step is well supported, because its strongest dissent rests on a council's word alone".
• A standard. For example: "a council's word does not ground a critique of Scripture's sense", which is the claim the sola scriptura argument already encodes.

A reader who prefers a standard can then argue for it, and the page shows what each verdict costs if that argument falls. This is #140.

Open questions

• A dissent from a premise, not a step. The checks apply with empty grounds. The register for a textual premise (what a verse says) is mostly empty, because those premises are common ground.
• Who encodes the steelman. The rule is only as good as the search for the strongest dissent. The rating-auditor agent does that search, and a register is built from its findings (#139).
• Articles. Howell's assessment is checked but is not yet on a generated page (#141).

Performance: the engine, measured

Every argument the library adds makes every later check dearer: a dispute's defeat table is one decision per ordered pair of parties, each decided in the kernel over the parties' premises and the argument's meaning postulates. So the engine is made faster and lighter as a loop, measured at each step, until a further change makes no significant difference. How to run the loop is in the optimising-the-engine skill (.claude/skills/optimising-the-engine); this page is its ledger: what was measured, what was tried, and what came of it.

How it is measured

• Benchmarks (arguments/bench/Engine.lean, run by scripts/bench.sh): copies of real proofs and checks, each timed with the kernel's work included, with its peak memory above what its process held before. Each benchmark runs in a Lean process of its own.
• Comparison (scripts/bench-ab.sh, scripts/bench-compare.py): an ablation. The code with a change and without it are built side by side on one machine and run interleaved, and each benchmark is compared by the two-sided Mann-Whitney U test, as Google Benchmark's compare.py does it. A change counts when p < 0.05 and it is larger than the variance bound. Peak memory is compared by threshold. A calibration benchmark, which no change can move, shows whether the machine drifted during the run.
• CI runs the A/B on every pull request, against the base it merges into, and fails on a regression that the pull request does not accept, with its reason, in arguments/bench/accepted.toml.
• Build and kernel replay are measured by hand, as below, until they have a gate of their own.

Baseline

Measured on 30 October 2026, at main after #171, on a 4-core, 16 GB cloud container (the shape of CI's runner), three runs per benchmark, one run of each check.

The first run of each benchmark is 10–40% slower than the rest: warm-up, not a cache that would let later runs skip the work.

The slowest modules of the arguments' build: SolaFide.Ratings (150 s), Checks (101 s, most of it the AIF check), SolaFide.Dispute (81 s), Meanings.SolaFide (74 s) and CanonicalWitness.Results (46 s).

Rounds

Round 3, measured on one side of a scripts/bench-ab.sh run against main, five interleaved rounds: each table is benchmarked twice, searched in the kernel as before and certified, and the two are compared. A profile of one sola fide cell found that converting a party's position to clauses took 17 ms a question, and propagating to a fixed point, in the kernel, about 85 ms; atom comparisons cost nothing that mattered. So the search now runs at elaboration, and the kernel checks what it found: a model, against every clause once, or the clauses that fired, replayed once (Horn.clausesSatisfiableBy?, Testimony.Logic.Certificate). Each position is converted once per cell, and the search is not specialized at each call, which had cost 50 ms a cell in compilation. Half of sola fide's table fell from 14.2 s to 7.1 s (−50%, p = 0.008) and its peak memory from 185 to 92 MiB; the Septuagint's from 3.25 s to 1.53 s (−53%, p = 0.008), 32 to 16 MiB; one cell from 101 to 61 ms (p = 0.016). Every searched benchmark matched main (every p ≥ 0.06), and the calibration benchmark showed no drift. Measured by hand on the same machine, clean: the arguments' lake build fell from 363.5 s to 308.7 s (−15%), SolaFide.Dispute from 70 s to 48 s; the build's peak, about 13.8 GiB summed over its parallel jobs, did not move, and the kernel replay took 261 s at 8.5 GiB against main's 329 s at 8.1 GiB, one run each.

Round 2, scripts/bench-ab.sh against the commit before, five interleaved rounds. Horn.clausesSatisfiable? propagated up to five times per question, Horn.stepRebuts? and Horn.defeats? made their checks twice, and Aif.attacks re-asked, for its preferences, what the attack checks had just asked. Run by the interpreter, as the checks over every argument are, each copy was evaluated: the AIF check fell from 67.4 s to 3.75 s (−94%, p = 0.008), the postulates check by 20% (p = 0.008) and the refutations check by 24% (p = 0.016). The kernel-decided benchmarks did not move (every p ≥ 0.17): the kernel was already sharing the repeated terms. Peak memory did not move, and the calibration benchmark showed no drift. One side of a benchmark run fell from 146 s to 76 s.

Round 1 was measured by hand, before the benchmarks existed. leanchecker replays each module as a task of its own, each importing that module's whole environment, and Lean runs one task per core: four environments at once ran out of memory. Two run in 293 s; one in 500 s with about 5.2 GiB.

Fixed points

None yet. After round 3 the largest benchmarks are still the defeat tables, now about 100 ms a sola fide cell: half of it the kernel's check, of which the conversion of both positions to clauses is most, and half the search at elaboration, in the interpreter. The next hypotheses are bitmask sets for the replay as well as the model (#180), and the certified forms for the verdicts, assessments and ratings, which still search in the kernel.

Standards the library aligns to

The library's machinery was built for its own arguments, but the problems it solves are old ones, and other fields have standards for them. Where a standard fits, the library aligns to it, so that a reader who knows the standard can read the library, and so that its arguments can be read by tools built on it. This page says which standards, how far, and what is left apart.

Argument: the Argument Interchange Format

The Argument Interchange Format (AIF) is the argumentation community's common ontology of argument (Chesñevar et al. 2006; the Dundee specification, 2011). An argument is a graph of information nodes (I-nodes), which hold claims, and scheme nodes, which hold the reasoning between them: an RA-node applies an inference, a CA-node a conflict, a PA-node a preference. Claims meet only through a scheme.

Every dispute in the library is drawn as an AIF graph (Testimony.Logic.Aif):

Testimony.Checks.Aif draws every dispute under a namespace it is given and checks it against the specification's Definition 1.1, condition by condition, and its report of each graph's nodes is pinned. The arguments run it over every dispute they have (#check_aif under TestimonyArguments), and the examples over theirs.

One simplification, stated in the module: AIF wants a single conflicting element, and an attack in the library comes from everything a party holds, so the conflicting element is drawn as the attacking party's conclusion. Not yet done: exporting the graphs in AIF's JSON, for AIFdb and the tools that read it.

Attack and defeat: ASPIC+ and Dung

The library's attacks are the three of ASPIC+: a party undermines another by denying one of its premises, rebuts it by denying its conclusion, and rebuts it on a step by denying a claim it derives on the way. A defeat is an attack that survives the preference, and the preference is weakest link: a position is as strong as its least-supported premise or step, by cited rating. Which positions survive is decided by Dung's semantics — grounded, preferred, credulous and skeptical acceptance — by a solver whose every verdict carries a checked witness. See Reading the logic.

What kind of thing a word names: DOLCE and BFO

The vocabulary's terms are given categories from an upper ontology, so that a claim relates things of the kinds its relation is about. The categories are DOLCE's (ISO/IEC 21838-3; Borgo et al. 2022), built to follow the distinctions natural language draws, which is how texts and their readers speak. Each names its counterpart in Basic Formal Ontology (ISO/IEC 21838-2; Arp, Smith and Spear 2015) where BFO has one (Testimony.Semantics.Upper):

What kind of thing each of the vocabulary's concepts is, is argued in an article (Testimony.Ontology.Kinds), not assumed. For some concepts the category is the dispute: whether justification is an act or a process is what the Reformation and Trent disagree about, and an upper ontology that assigned it would have answered the question for them. Those concepts are left without a category, and the article says why.

The relations a case about time needs are aligned the same way: lasts is BFO's occupies temporal region, starts with and ends with are Allen's interval relations, and part of is the part-of relation of both. One definition follows from both ontologies and is written out, with its sources, in an article: an occurrence lasts one length of time (Testimony.Ontology.Time).

Left apart

• LKIF Core, the legal ontology. Its categories — norms, legal roles, legal actions — are for reasoning about law. The library's first case outside theology is a cross-examination, which needs testimony, time and a record, not law, so the adversarial trial is a tradition and the court's opinion a bibliography entry, and nothing of LKIF is needed. A case that turned on what a statute requires would need it.
• Inference Anchoring Theory, AIF's extension for dialogue: who asserted, questioned or conceded what, and when. The grits case is a dialogue, and its verdict turns on a withdrawal, so this is the natural next alignment. It is not done; the case states each turn as a citation instead.

Beyond theology: a case of your own

The library's arguments are about Scripture, but its machinery is not. A premise is a claim with a citation and a rating. A position is a package of premises with a conclusion. A dispute between positions is weighed by what each denies of the others, and by their cited ratings. None of that knows what a covenant is. A cross-examination, a policy debate, a review of a paper or a quarrel between historians can be stated the same way, and checked the same way.

This page shows how, with the first such case: the grits cross-examination from My Cousin Vinny (1992). The case is not in the library. It lives in examples/, in a package of its own, TestimonyExamples, which uses the library as any package built on it would. Its document is generated from its own source and is not listed among the library's arguments.

Why a separate package

The library is the machinery for stating and checking arguments, and the packages built on it are its users. Keeping them apart keeps two promises.

• A case cannot bend the library. A package that imports the library can add cases, works and checks of its own, and cannot change what a Defeats or a Verdict means. If a case needs something the library lacks — a word in the vocabulary, a kind of bibliography entry — the library gains it as a general feature, with its own documentation, and every user gets it.
• The library's documentation is about the library. The arguments it publishes are its own. A package's document is the package's: it is set the same way, by the same generator, but it is not in the library's index.

The arguments this documentation presents are such a package too: TestimonyArguments, in arguments/. Everything below is what they do, and the grits case does the same at a smaller scale.

The steps

1. A package that requires the library

# examples/lakefile.toml
name = "TestimonyExamples"
defaultTargets = ["TestimonyExamples"]
# Inside this repository: share the library's downloaded dependencies.
packagesDir = "../.lake/packages"

[[require]]
name = "testimony"
path = ".."

A package outside this repository requires the library by git instead, and fetches Mathlib's build with lake exe cache get.

2. Claims, each cited to a record

Every atom of the case is a constructor of a Claim type, and cite gives each one a label, a kind and a Source. For a trial the record is the source, and the tradition is .adversarialTrial: the parties are a witness and counsel, not schools of reading. The works the case cites go in the package's own Works.lean, tagged @[bib_entry] and verified as the library's are. The library's bibliography has entry types for films and court opinions.

The grits case cites the scene as the D.C. Circuit set it out, question by question, in Novato Healthcare Center v. NLRB (2019), with the film beside it. Each rating is argued in a comment or a docstring: the five-minute breakfast is disputed, because counsel contests it, the witness withdraws it and the court rejects it; regular grits taking twenty minutes is wellSupported, because the record holds nothing for it but counsel's word, and nothing against it.

3. Two positions at least, written before anything is proved

The library will not let a reading stand alone (linter rule L5), and a case is no different. The grits case has two: Tipton's testimony on direct examination, and counsel's case on cross-examination, which keeps Tipton's own reckoning — the time in the store is the time breakfast took — and contests only what breakfast took. Each is shown to hold (establish) and to be coherent (satisfied_by, with a named reading), and the place the testimony rests is shown by taking it away: the_five_minutes_rests_on_the_breakfast.

4. What the claims mean

The library's vocabulary reads a claim as a relation between terms. A case is about particular things and occurrences, not kinds, so a term can be a particular, named and given its upper category: the time in the store is a process, the making of breakfast an event. "Five minutes passed" says the time in the store lasts five minutes. "Breakfast took twenty" says its making lasts twenty.

The library's shared ontology then does the work. One of its definitions, that an occurrence lasts one length of time, stated by both DOLCE and BFO, makes five minutes and twenty exclude each other. The case does not state that exclusion as a premise. It pins what the meanings yield (HasJoins), and the build fails if the pinned list and the meanings disagree. So the headline contradiction, tiptons_five_minutes_cannot_stand_with_the_grits, is in what "lasts" means. Its companion, apart_from_what_lasts_means_both_could_be_held, shows that without the meanings there is none.

5. A dispute, and its verdicts

The two positions become parties to a Dispute. Who defeats whom is computed from their premises and ratings, and checked by the kernel. The verdicts — the_cross_examination_prevails, tiptons_testimony_cannot_be_defended — are Verdicts, each a claim with the solver's witness for it.

A rating is load-bearing, and the case shows it. Rated as the record stood when Tipton answered "I'm a fast cook, I guess", the step from the grits is disputed. The dispute is then a standoff (at_the_fast_cook_nothing_was_decided), and the variant is one rating different, not a second list of premises. What decided it was the witness's withdrawal: "I may have been mistaken."

6. The library's checks, over the package

Every check the library runs over its own arguments takes a namespace:

#check_meanings under TestimonyExamples
#check_ontology under TestimonyExamples
#check_postulates under TestimonyExamples
#check_refutations_postulates under TestimonyExamples
#check_refutations under TestimonyExamples using unfoldSets
#check_aif under TestimonyExamples

Each report is pinned with #guard_msgs, so a change in any of them is a change a reviewer sees. The gates are the library's too: lake lint, lake exe axiom-audit, and scripts/kernel-replay.sh, given the package's root. The domain linter reads the package whenever it reads the library.

7. A document of its own

The library's harvest renders any namespace's docstrings, packages, lines and verdicts. A package harvests only its own, and sets it as the library sets its arguments:

derive_argument_bodies bodies under TestimonyExamples

latexDocument sets a title, a standing note and the harvested sections, and writeOrCheck writes the files or checks that they are current. In the examples, lake exe exampletex writes one document per case, and lake exe exampletex --check fails if a committed one is stale.

What the library does not give a package

• Words. The vocabulary's concepts and relations, the traditions and the kinds of premise are the library's, and a package cannot add to them. The grits case needed lengths of time, particulars, lasts, starts with, ends with and part of, the adversarial trial as a tradition, and empirical claims as a kind. Each was added to the library as a general feature, with its alignment to DOLCE and BFO stated (see Standards), so the next case has them.
• Ratings that mean something else. The four ratings are the library's, and so is the rule for them: a step is disputed when a cited source grants its grounds and denies its conclusion. In a trial the cited sources are the record, and the rule reads the same.

Born in Bethlehem — Micah 5:2

This page is generated from arguments/TestimonyArguments/BornInBethlehem. Every heading and paragraph below is a docstring in those files; every formula is rendered from the encoding they check. If the page and the source disagree, the page is the one that is wrong, and regenerating it is the fix.

Atoms are numbered propositional variables, numbered once for the whole page, so the same variable means the same claim in every position below. Reading the logic is the short version of what the notation means. A result marked ⚗ is one this library constructs rather than reports.

TestimonyArguments.BornInBethlehem — Phase 1 vertical slice

Matthew 2:5–6 quotes Micah 5:2 as grounds that the Messiah is born in Bethlehem. Both the Christian predictive reading and a critical reading are encoded, and the argument is carried through to a SatisfactionWitness — the first end-to-end connection from cited premises to a claim that a person meets a messianic criterion.

jesusBornInBethlehem is cited to scripture alone. That is visible in the generated manifest via scriptureOnlyAtoms, and it should be: the historicity of the Bethlehem birth is disputed in critical scholarship, and an argument that assumes it on the authority of the texts whose reading is in question is assuming part of what it sets out to show.

The argument is short enough to stay in one file. It runs on a single line of reason, which is exactly why it is the weakest of the fulfilment arguments and why critical_not_establishes costs the rival so little: deny the one interpretive premise and nothing is left standing. Compare BornOfAVirgin, which runs on four.

The claims, numbered

※ grounded in scripture alone: the reading is assumed, not argued for.

quotationEdge

Matthew explicitly quotes Micah — uncontroversial verbal citation, attested across traditions.

def quotationEdge : IntertextEdge :=
  { fromPassage := Scripture.matthew2_6, toPassage := Scripture.micah5_2,
    relation := RelationType.quotation,
    source := Scripture.na28Apparatus Scripture.matthew2_6 }

predictiveReading

The Christian predictive reading of Micah 5:2.

def predictiveReading : Interpretation :=
  { passage := Scripture.micah5_2,
    reading := "Micah 5:2 predicts the Messiah's birthplace as Bethlehem",
    asRelation := some RelationType.prediction,
    source :=
      {
        primary :=
          Reference.work Bib.keilDelitzschMinorProphets
            (Bib.Locus.adLoc Scripture.micah5_2),
        tradition := Tradition.christianTypological,
        confidence := Confidence.wellSupported } }

bornInBethlehem

The criterion this argument establishes a candidate must meet.

def bornInBethlehem : FulfillmentCriterion :=
  { name := "born in Bethlehem", basis := predictiveReading }

cite

Citation and classification for every atom. Total, so nothing is uncited.

def cite : Claim → AtomMeta

The line of reason

One strand, and the argument's whole weight is on it.

toCriterion

From the predictive reading and Matthew's intent, the criterion follows.

toFulfilment

From the criterion and the historical claim, the fulfilment follows.

predictiveLine — Predictive reading of Micah 5:2

The predictive line. Micah's oracle read as prophecy, Matthew's quotation read as a fulfilment claim, and the criterion that follows.

criticalLine — Critical reading of Micah 5:2 as a near-term oracle

The critical line: the quotation is granted and the prediction denied, so the same step delivers nothing.

Packages

christian — Christian predictive reading of Micah 5:2

The Christian predictive argument.

Grounded in scripture alone: Jesus of Nazareth was born in Bethlehem.

critical — Critical reading of Micah 5:2 as a near-term oracle

The critical reading: the quotation is granted, the prediction is not.

Grounded in scripture alone: Jesus of Nazareth was born in Bethlehem.

Results

christian_establishes

Given the Christian premises, the conclusion follows.

theorem christian_establishes : Establishes christian
-- axioms: propext, Quot.sound

criticalReading

The critical reading, written down: Micah's oracle concerns a contemporary Judaean ruler, so no messianic birthplace criterion arises and nothing about Jesus follows from it.

def criticalReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.micahPredictsBethlehem => False
    | Claim.messiahBornInBethlehem => False
    | Claim.jesusSatisfiesCriterion => False
    | x => True

critical_not_establishes

The critical reading does not establish the conclusion.

theorem critical_not_establishes : ¬Establishes critical
-- axioms: propext, Quot.sound

jesus_satisfies_bethlehem

End to end: under the Christian package, Jesus satisfies the Bethlehem criterion. This is the first result in the library that runs from cited premises through a machine-checked entailment to a claim about a person.

theorem jesus_satisfies_bethlehem : Satisfies jesus bornInBethlehem
-- axioms: propext, Quot.sound

Satisfiability

Entails is vacuously true over a premise set with no model, so a package built from contradictory premises would establish its conclusion with every gate passing. Only the package carrying a positive Establishes result needs checking: critical has a countermodel already, and a countermodel is a valuation satisfying every premise.

Not tagged @[headline] — a claim about the health of the encoding rather than about Micah.

everythingHoldsReading

The reading on which every claim in this argument holds at once.

def everythingHoldsReading : Valuation Claim :=
  fun x => True

christian_is_satisfiable

The Christian package has a model, so christian_establishes is not vacuous.

theorem christian_is_satisfiable : Satisfiable christian.premises
-- axioms: propext, Quot.sound

Born of a virgin — Isaiah 7:14, Genesis 3:15, Micah 5:2–3

This page is generated from arguments/TestimonyArguments/BornOfAVirgin. Every heading and paragraph below is a docstring in those files; every formula is rendered from the encoding they check. If the page and the source disagree, the page is the one that is wrong, and regenerating it is the fix.

Atoms are numbered propositional variables, numbered once for the whole page, so the same variable means the same claim in every position below. Reading the logic is the short version of what the notation means. A result marked ⚗ is one this library constructs rather than reports.

TestimonyArguments.BornOfAVirgin — Isaiah 7:14, Genesis 3:15, Micah 5:2–3

Matthew 1:22–23 quotes Isaiah 7:14 as grounds that the Messiah is born of a virgin. Unlike Micah 5:2 (see BornInBethlehem), the predictive reading here is heavily disputed, and the dispute is lexical: both sides grant that the Hebrew עַלְמָה (almah) denotes a young woman of marriageable age, and they dispute whether it denotes a virgin; the Septuagint's παρθένος is read as "virgin" — though whether it meant that in the translator's own day is disputed too (Dispute.Septuagint). Isaiah's immediate context — a sign to Ahaz, apparently fulfilled within the prophet's own generation (cf. Isa 8:3–4) — is read by most critical and much Jewish scholarship as having nothing to do with a future Messiah.

The argument now runs on four scriptural strands, and that changes its shape. Each is encoded as a Line — its own grounds, its own inference step, what it delivers — and the packages are assembled from those rather than from flat premise lists. Lines.lean is where the shape of the argument is legible in one screen.

The Isaianic strand is the one above, hinging on almah.

The protoevangelium strand reads Genesis 3:15 — enmity between the serpent's seed and "her seed", זֶרַע הָאִשָּׁה — as the first promise of a redeemer, and takes the matrilineal wording to mark a birth with no human father, since Hebrew ordinarily reckons זֶרַע through the man. That last step is genuinely contestable and is marked disputed. Some readers who grant the messianic reading deny it, the Lutheran commentators Leupold and Keil among them. Leupold allows that the wording refers to the virgin birth "Not primarily, but at least incidentally", and holds that "the expression used does not specifically prophesy the virgin birth, but it coincides and agrees with it under divine providence". Others affirm it: Luther and Henry. And Genesis itself speaks of a woman's seed in ordinary births, of Hagar's (16:10) and of Rebekah's (24:60). Results.Genesis and Dispute.Genesis weigh it (below).

The Michean strand reads Micah 5:2–3 — "until the time when she who is in labour has given birth" — as naming a mother and no father for the coming ruler. The objection is immediate and is encoded as the rival: this is an argument from silence, and an oracle about a woman in labour has no occasion to mention a father.

The referential strand answers the lexical dispute without entering it. almah need not mean "virgin" for Mary to be an almah. Genesis settles the compatibility outright: Rebekah is an עַלְמָה at 24:43 and a בְּתוּלָה "whom no man had known" at 24:16, the same woman under both terms. Mary was a betrothed young woman of marriageable age and conceived as a virgin, so she answers Isaiah's description on anyone's lexicon — and semantic_establishes shows that Matthew's claim therefore never required the sense the objection demands.

That reply has a price, and compatibility_does_not_establish_criterion names it: the argument is purely defensive. It defeats the objection without delivering the criterion, which still has to come from one of the four scriptural strands. What it buys is that losing the lexical dispute no longer costs the fulfilment claim.

The versional evidence is encoded in full, including the half that tells against the reading. Targum Jonathan renders עוּלֵימְתָא, "young woman", and does not read 7:14 messianically though it reads 9:5–6 and 11:1 so; Aquila, Symmachus and Theodotion render νεᾶνις. Against them, the pre-Christian Septuagint renders παρθένος — "virgin", on Rico and Gentry's reading of its Greek, though not on Wegner's (below) — and the Syriac Peshitta ܒܬܘܠܬܐ, "virgin", its only ܒܬܘܠܬܐ for עַלְמָה. So the Aramaic evidence is itself split: the Targum against the Peshitta, whose translator may have been a Jewish Christian who knew the Greek (van der Kooij), and whose 7:14 may follow the Septuagint (Chen). 1QIsaᵃ, copied before Christ, reads עַלְמָה as the Masoretic Text does. The verse has other variants, but none at the word, so no textual variant rescues either side: the dispute is about the word's sense, not its text. The usual Christian reply, that the Three revised against Christian use, is now one party's ground: Rico and Gentry's case from usage leans on it, and Davidson and Meade read the revision the other way (Dispute.Septuagint). Whether Theodotion's version is itself pre-Christian, which would give the revision a reason with no polemic in it, the library has not yet found a source to cite, and it is left out of the reckoning.

compatibility_defeats_lexical_objection is where the tension pays off. Granting every versional datum and adding the referential premises, the objection no longer reaches its conclusion — because once virginity is compatible with the word, four translators making four different choices about how much of the referent to make explicit is not evidence about the sense.

The Septuagint's own witness is weighed in full, and it does less than it is usually asked to. The argument is Irenaeus's: Jews translated Isaiah into Greek "much before the period of our Lord's advent", so their παρθένος cannot be a Christian reading put on the text (Against Heresies III.21.1). septuagintWitness_establishes grants it everything it needs and checks that it goes through. Three results then say what it rests on and what it reaches.

• It rests on one word (parthenos_is_load_bearing). Without the claim that παρθένος, in the translator's Greek, means a virgin, the Septuagint shows nothing about the woman. Rico and Gentry hold that it does, "whenever it appears in Semitic Koine Greek", and Bratcher agrees. Wegner, Rhodea and Meade deny it, and point to Genesis 34:3, where the Greek calls Dinah a παρθένος after Shechem has lain with her; Walton doubts it, from classical usage. The Greek Pentateuch, the corpus that verse comes from, uses the word in its laws where virginity is the point (Leviticus 21:13–14, Deuteronomy 22:13–21), and its law of the seduced παρθένος reads Wegner's verse otherwise: the woman a man has lain with is still the law's παρθένος, owed "the bride-price of virgins" (Exodus 22:15–16), and Genesis 34 tells Shechem's act in that law's words. Dispute.Septuagint weighs the five, and the Septuagint's side prevails (septuagint_prevails_over_wegner): the status reading of Genesis 34:3 defeats Wegner, and he, resting on a step rated disputed, is too weak to answer it. The claims about the word exclude each other by what they mean — Wegner's says the word meant a young woman and not yet a virgin — and the dispute is computed with that. The verdict turns on one rating, the status reading's step, plausible because no reader found grants its grounds and denies it, and no higher because no reader found makes it. Were it disputed, nothing would prevail; Dispute.Septuagint says so, with where the evidence on each side lies.
• A dissent counts only on evidence the texts leave standing (Dispute.Miller). The laws' step is disputed on Robert J. Miller, who gives two uses of παρθένος of women who are not virgins. His "young widow" at Joel 1:8 is a bride, νύμφην, in the Greek, so that claim is struck; his Genesis 34:3 stands as the Greek reads it, and carries his dissent (miller_survives_on_genesis). Resting on Joel 1:8 alone, the dissent would not count under any standard (miller_on_joel_alone_does_not_count).
• Scripture's own reading of the word turns on the standard (matthew_step_turns_on_the_standard). Matthew quotes the Septuagint's ἡ παρθένος of Mary, who conceived before she and Joseph came together, so in the text he quotes the word means "virgin". Wegner grants what Matthew says and holds that the word had changed in meaning since the translator wrote it. Under the evidence standard that is a credible critique, and Matthew and Wegner stand off. Under the Scripture standard — Scripture interprets Scripture, so a dissent from a step grounded in Scripture alone must rest on Scripture too — Wegner's argument from early Greek usage is not heard, and Matthew's reading prevails. Dispute.Matthew reports both.
• It shows how one early reader read Isaiah, not what Isaiah's word means (septuagint_word_rests_on_its_inference). Granted its sense, the Septuagint shows that a Jewish translator before Christ read the woman of 7:14 as a virgin — so that reading is no Christian invention. The step from his Greek to Isaiah's Hebrew is a further one, and rated disputed: Irenaeus takes it, holding the Greek inspired; Bratcher, Brown and Walton deny it. On Bratcher's and Brown's reading a rendering can follow the woman described rather than the word: the translator of Genesis wrote παρθένος for the עַלְמָה Rebekah (24:43), whom the story has already called a virgin, and elsewhere the Septuagint's translators render עַלְמָה with νεᾶνις four times. That is also the referential strand's reading of the versions.
• It leaves the conception open (septuagint_leaves_the_conception_open). The Greek says the virgin shall be with child. A woman who is a virgin when the sign is given and later conceives in the ordinary way fits it; so does a virgin who conceives as a virgin, as Justin reads it. The first is not only a rival's reading: Bratcher, who holds that παρθένος "definitely means 'virgin' in the LXX", calls it "the most reasonable explanation" of the Greek of 7:14. So even granted the word, the Septuagint does not decide, and the virginal conception comes, if it comes, from the promise of a sign (signLine) or from Matthew and Luke.

"Her seed" is weighed as the Septuagint's word is, and it too does less than it is often asked to. Genesis 3:15 names the seed as the woman's, and the strand's hinge reads that as marking a birth with no human father. Results.Genesis reads "marks" both ways (whatHerSeedMarks).

• As what the wording itself signifies, it is Luther's argument: the seed of other women "might rather be said to have been the seed of the man", but Mary's was "the true Seed of Mary". He finds the sense in the words of Genesis, and holds that Isaiah later "threw some additional light" on it. It rests on his step (her_seed_rests_on_its_inference). The Lutheran commentators Leupold and Keil, who hold the virgin birth, grant every ground and deny it; so does Jack P. Lewis (Journal of the Evangelical Theological Society, 1991), who doubts the promise reading itself but argues without needing that doubt. Weighed against Leupold and Lewis, nothing prevails (nothing_prevails_over_her_seed): Luther's reading can be defended, and so can theirs. But the tie is nearer to breaking against Luther than for him. One rating would break it against him: Lewis's step, disputed only on the Catholic apologist Jimmy Akin, who grants Lewis's point about the idiom and still calls the wording "odd", agreeing with the "many" who have "rightly seen" it as "a hint of the Virgin Birth". Two would be needed to break it for him: his own step, and the claim that Genesis 3:15 is the protoevangelium at all, which critical readers deny.
• As what the wording fits, once fulfilled, it is granted by Leupold and Keil. Leupold: "it coincides and agrees with it under divine providence". But they reach the fit from the conception, so read this way the verse confirms the virgin birth to one who already believes it, and gives no reason to believe it to one who does not.
• The promise is fulfilled in Jesus, and the fulfilment confirms it (Dispute.Protoevangelium). Every term of the verse is met as the New Testament names it: the woman's seed in the Son "made of a woman" (Galatians 4:4); the serpent in "that old serpent, called the Devil" (Revelation 12:9); its head crushed when the Son destroys the devil "through death" (Hebrews 2:14; 1 John 3:8); his heel struck in his death, and the wound not the end of him (1 Corinthians 15:3–4). Irenaeus, Calvin, Keil, Leupold and Hamilton read it so. The fulfilment confirms that the verse was a promise, by a rated step and not by deduction, and it does so without the virgin birth (the_confirmation_does_not_need_the_virgin_birth). With the virginal conception it says one thing more: the seed in whom the promise is fulfilled was of the woman alone (seed_of_the_woman_alone). That does not show the wording foretold it (the_fulfilment_does_not_reach_the_wording). Weighed against Westermann, who denies that the verse is any promise, from the collective "seed" and the form of a punishment oracle, nothing prevails (nothing_prevails_over_the_promise): the fulfilment's step is disputed on him, and his on Calvin and Keil. His "a line of descendants and not an individual" is answered from the Hebrew itself: elsewhere זֶרַע with singular forms names one descendant, at 3:15b it is "he" who strikes the serpent's own head, and the Greek translator read one person (Collins, Alexander, Leupold). That answer is disputed too, on Keil, and Collins claims for it only that the syntax is "quite consistent with" one person. The scene read whole answers him too: the serpent speaks and twists God's command, as no animal does of itself; the blow falls on the serpent itself; and God sets the enmity; so the sentence is a promise of victory over the power behind the serpent (Collins, Woudstra, Keil). Its step is plausible, and the ground it turns on, that an evil power stands behind the serpent, is disputed on Westermann. The readers before Christ do not read the verse so: Jubilees, Philo and Josephus read the serpent as an animal or an emblem. The fulfilment, with the syntax and the scene, can be defended, and so can Westermann. Under the Scripture standard the fulfilment prevails (promise_turns_on_the_standard): its grounds are all Scripture, and Westermann's dissent rests on his philology of "seed", so it is not heard. Under the evidence standard it is, and nothing prevails. Dispute.PromiseHearing reports both.
• The Septuagint's "he", αὐτός for the neuter σπέρμα, may show that a Jewish translator before Christ read the promise of one person (greekHeCase_establishes), so that reading would be no Christian invention. Collins holds it; Philo, the earliest known reader of the Greek, took the masculine as a "barbarism" meaning the mind, and Lewis leaves it open, so it is disputed. It leaves the father open (the_greek_he_leaves_the_father_open): the same Greek calls the seed Hannah asks for "him", and that son has a father.

Wegner's objection is encoded in its sharpest form, and the module shows the circle in it rather than alleging one. Wegner does not merely say that עַלְמָה means "young woman". He says that הָרָה at Isaiah 7:14 is a predicate adjective, so the clause reads "the עַלְמָה is pregnant" — already, when the sign is given — and a pregnant woman is not a virgin; the one clear Isaianic case then settles the word. wegner_establishes grants him every premise and checks that the argument goes through, because a rival worth answering has to be stated at full strength first.

The parse is not the weak point, and the encoding says so by granting it throughout: Rydelnik — cited here through Postell, who reports him at 474 — reads the same predicate adjective and draws the opposite conclusion, that the virgin is pregnant and the sign is therefore as deep as Sheol. What the grammar does not supply is that the pregnancy is an ordinary one, and that is the premise that excludes virginity. wegner_needs_ordinary_pregnancy removes it and the objection stops. readingSuppliesOrdinaryPregnancy then supplies it the way Wegner's own case does — from the near-term reading of the sign — and with the lexical conclusion turned back against that reading, the two legs close. circle_leaves_the_lexical_conclusion_open and circle_leaves_the_denial_open are the result: keep every uncontested datum, and neither end is settled — not established, and not refuted either. A cycle of implications is satisfied outright by a valuation on which all of its nodes are false, and equally by one granting Wegner's own conclusion. Nothing enters the loop, so nothing comes out of it, in either direction. That is a demonstration rather than a complaint, and it is conditional in the usual way: a defender of Wegner should deny readingSuppliesOrdinaryPregnancy and argue that the near-term reading stands on the historical evidence alone.

Postell's second reply is independent of the first and survives that defence. The other clear עַלְמָה passages Wegner himself lists are cases of virgins, so a single referent cannot be what settles the denotation — the same principle would settle it the other way. usage_parity_blocks_wegner checks it, and the atom is marked plausible rather than wellSupported because Postell's "in fact virgins" is stronger than Wegner's own discussion of Song 6:8.

The oldest reply goes to the ordinary pregnancy itself. Justin, Irenaeus and Origen answer the near-term reading with one argument. The oracle promised a sign, offered "in the depth or in the height" (7:11), and an ordinary conception happens to every woman who is not barren, so it would be no sign. Rydelnik makes the same move today. signLine encodes it, and it denies the one ground of Wegner's objection that the grammar does not supply. sign_leaves_the_lexical_conclusion_open measures what that buys: with the fathers' grounds in place of the ordinary pregnancy, Wegner's lexical conclusion is independent of what remains. The objection is blocked, and nothing is shown about the word.

The rival is written first, and Wegner holds it himself: a sign need not be a miracle. Isaiah's own children are "signs and portents" (8:18), and this sign is dated by a child's infancy (7:16), so its point may be its timing. Rhodea argues the same. reply_leaves_the_pregnancy_open shows that the reply blocks the fathers in turn, without supplying Wegner's ordinary pregnancy.

Dispute.Wegner puts the three positions together. Every one of them has a disputed weakest link, so the dispute ties (nothing_prevails_over_wegner). Both the fathers alone and Wegner with the reply are defensible resolutions of it. What would decide it is one of two ratings: whether the sign of 7:14 must be the kind offered at 7:11, and whether the reply's inference survives Rydelnik, who grants its grounds and denies its conclusion.

The critical case against the Isaianic strand is now derived rather than assumed. critical used to carry ¬isaiahPredictsVirginBirth as a bare premise; it now carries the step that produces it — that a sign given for Ahaz's generation is not also a prediction of a virgin conception — and criticalDenial_establishes checks that the step works. Berry supplies the objection: how Isaiah 7:14 was fulfilled in Ahaz's own day is itself an open question, and berry_blocks_critical_denial shows that granting him that much takes the exclusion out. It does no more than that. It does not establish the predictive reading and it does not touch the lexical dispute.

Berry also supplies a defensive lexical premise — that the semantic range of עַלְמָה does not exclude "virgin" — and admissibility_is_not_enough measures what it is worth: nothing, on its own. May mean is not does mean, and the whole Isaianic strand lives in that gap.

The compositional strand (Postell) declines the lexical fight altogether. Isaiah 7 sits inside Isaiah 2–12, a unit framed by eschatological vision at 2:1–4 and 11:1–12:6; on the principle that an oracle's meaning in a finished book is set by its literary placement rather than by the events it describes — argued from the making of canonical Jeremiah — 7:14 anticipates a future, miraculous birth. The hinge is compositionGovernsMeaning, and a reader who holds that an oracle's historical setting fixes its sense rejects it outright.

Postell also supplies the module's sharpest rival-defeater. parityDefeats NearTermExclusion observes that Isaiah 9:5–6 and 11:1–10 are read as messianic without reservation and stand on the same near-term Assyrian timeline as 7:14 — the invasion of 8:7–8, the oppressor's rod of 10:5. So a near-term setting cannot be what rules out messianic reference, or it would rule out 9 and 11 too. parity_blocks_critical_denial checks it. Notably the Targum is cited for this premise: it reads 9:5–6 and 11:1 messianically while declining to read 7:14 so, which makes it a hostile witness and therefore a strong one.

That gives the critical exclusion step two independent defeaters. Berry's is evidential — we do not know how the sign was fulfilled in Ahaz's day. Postell's is structural — the near-term setting was never the right kind of reason.

Taken together, the positions make a dispute, and the dispute has an outcome the entailment results cannot state. Dispute.lean treats the scriptural reading, the critical denial, Berry, Postell's two counterexamples and Motyer as the nodes of an argumentation framework and proves who defeats whom — a defeat being an attack derived from entailment that the cited confidences do not block. Against the scriptural reading alone, nothing_prevails_unanswered: the critical denial and the scriptural reading defeat each other, because the weakest premise on each side is disputed (christian_defeats_critical). Hear Berry and Postell, and scriptural_reading_prevails_once_replies_are_heard: nothing defeats Postell's counterexamples, they defeat the critic, and so they defend the scriptural reading — and Berry, and Motyer with Compton — against the only party that defeats them. The critic is left with no defence at all (critical_denial_indefensible). Inference steps are rated like premises, and Berry's and Motyer's are disputed, so alone they tie with the critic: nothing_prevails_on_motyer_alone, and motyer_rests_on_his_inference shows the weight of his reply is on that step. The outcome turns on Postell's inference being plausible — no cited source grants his grounds and keeps the exclusion. He gives two counterexamples, from Isaiah 9 and 11 and from Micah 5; either suffices (scriptural_reading_prevails_without_postell), and without both nothing prevails (nothing_prevails_without_the_counterexamples). It turns too on the critic's premises being disputed, as the replies, Motyer and Compton contest them.

Luke is a second witness to the conception, not to the prophecy. His account is parallel to Matthew's and independent of it, but it never quotes Isaiah 7:14. Luke 1:31 is close to the Septuagint's wording, and whether that is an allusion is disputed: lukeAllusionEdge records it as one, attributed, and annunciationFormEdge records the rival reading, on which the wording is the stock birth-announcement form that Isaiah 7:14 itself uses. Luke adds to independentAttestation; he adds nothing to the rating of the predictive reading.

hinges_jointly_load_bearing is the result worth having. No single interpretive hinge carries the argument any more — strip almah and the other three strands still deliver the criterion, which almah_not_load_bearing records. Strip all four and the argument collapses. Genesis's strand delivers it only on Luther's reading of its hinge, which nothing here forces (nothing_prevails_over_her_seed). almah_is_load_bearing_alone keeps the pre-Miravalle finding on the books: within the Isaianic strand taken by itself, the lexical premise still carries everything.

The magisterial strand is encoded separately and is not part of christian. Papal teaching on Mary's virginity in conceiving, as collated by Miravalle, is a Roman Catholic premise; this library's author does not grant that magisterial teaching settles doctrinal questions, and the encoding says so rather than quietly folding it in. catholic is the package for a reader who does grant it. magisterial_authority_is_load_bearing shows what follows for a reader who does not: that route yields nothing on its own, and the four scriptural strands have to carry the argument by themselves. The rival is cited to Westminster I.x.

Matthew's and Luke's birth narratives agree on the virgin conception while differing in nearly every other detail, and that convergence is encoded as a multiple-attestation premise — though the independence of the two traditions is itself debated, and is marked plausible rather than wellSupported.

Where things are

This argument is a directory, because at fourteen hundred lines it was one file that no one could hold in view. The dependencies run one way. Where a file outgrew three hundred lines of code, the material for the disputes over Wegner's objection, over the Septuagint's word and over the woman's seed, and the citations for the dispute over the critical denial, went into modules of their own beside it.

Shared material lives further out: passages and citation bundles in Testimony.Scripture, the Line and caseOf vocabulary in Testimony.Logic.Line, and the establish and refute_with tactics in Testimony.Logic.Tactic.

TestimonyArguments.BornOfAVirgin.Atoms — the atomic claims, and what cites them

The atoms this argument is built from, the Source shapes that recur across them, the typed intertextual edges between the passages, and the criterion the argument is about. Everything here is what the argument is about; nothing here asserts anything.

See TestimonyArguments.BornOfAVirgin for the dispute this encodes.

Recurring sources

Five works carry this argument, and each carries several atoms at the same pinpoint with the same confidence. Written out at every atom, the citation was repeated rather than the claim — and a Source differing from its neighbour by one field is hard to read as deliberate.

These are values, so an atom that cites one of them with something further says so with { ... with supporting := ... }, and the difference is the part a reader sees.

The claims, numbered

※ grounded in scripture alone: the reading is assumed, not argued for.

motyerOnIsaiah

Motyer on Isaiah 7:14: the predictive reading and the lexical premise it needs, disputed and marked so.

def motyerOnIsaiah : Source :=
  {
    primary :=
      Reference.work Bib.motyerIsaiah (Bib.Locus.adLoc Scripture.isaiah7_14),
    tradition := Tradition.christianTypological,
    confidence := Confidence.disputed }

miravalleOnGenesis

Miravalle on Genesis 3:15, in Meet Your Mother: the verse is the "Protoevangelium", "the first reference to Jesus as the future Redeemer of the world", and to speak of "the 'seed' of a woman rather than the seed of a man" is "already a hint of Mary's virginal conception of Jesus". His word is "hint": a remark in passing, not an argument from the Hebrew.

The protoevangelium strand rests on him and on Luther, the reader who argues from the wording (herSeedLine); the Michean strand rests on Miravalle alone (miravalleOnMicah). Every atom citing this is disputed.

def miravalleOnGenesis : Source :=
  { primary := Reference.work miravalleMeetYourMother,
    tradition := Tradition.romanCatholic, confidence := Confidence.disputed }

miravalleOnMicah

Miravalle on Micah 5:2–3, in Introduction to Mary: the mother "so specifically designated without a husband" conveys "the same virginal sense as we see in Isaiah 7:14". The passage is on page 18 of the 1993 printing; the library's entry is the 2020 printing, whose page could not be checked, so the book is cited whole.

def miravalleOnMicah : Source :=
  { primary := Reference.work miravalleIntroductionToMary,
    tradition := Tradition.romanCatholic, confidence := Confidence.disputed }

brownOnBirth

Brown's Birth of the Messiah, taken whole: the critical case.

confidence defaults to wellSupported, which is what the critical readings are. It is passed explicitly where a critical premise is contested: the one Brown's case presupposes rather than argues, and both premises of the critical denial, each denied by scholars this argument cites.

def brownOnBirth : optParam Confidence Confidence.wellSupported → Source :=
  fun confidence =>
    { primary := Reference.work brownBirthMessiah,
      tradition := Tradition.criticalScholarship, confidence := confidence }

postellOnIsaiah

Postell on the compositional reading, at a given pinpoint. The pinpoint matters here in a way it does not for the others: the textual observations and the interpretive principle come from different pages and carry different confidence.

def postellOnIsaiah : Bib.Locus → Confidence → Source :=
  fun l confidence =>
    { primary := Reference.work postellIsaiahMessianic l,
      tradition := Tradition.christianHistoricalGrammatical,
      confidence := confidence }

wegnerOnAlmah

Wegner on the sense of עַלְמָה, at a given pinpoint.

Like postellOnIsaiah, the pinpoint carries weight: the grammatical claim is at 471 and the near-term reconstruction that makes its conclusion bite is at 476–478, and they are not equally secure. Wegner is an evangelical arguing against a virgin-birth prediction here, which is what makes him the module's strongest lexical rival rather than one more critical voice.

def wegnerOnAlmah : Bib.Locus → Confidence → Source :=
  fun l confidence =>
    { primary := Reference.work wegnerVirginBirths l,
      tradition := Tradition.christianHistoricalGrammatical,
      confidence := confidence }

franceOnMatthew

France on Matthew 1:23, for what Matthew's quotation intends and what follows from it.

def franceOnMatthew : optParam Confidence Confidence.wellSupported → Source :=
  fun confidence =>
    {
      primary :=
        Reference.work Bib.franceMatthew
          (Bib.Locus.adLoc Scripture.matthew1_23),
      tradition := Tradition.christianHistoricalGrammatical,
      confidence := confidence }

Intertextual edges and readings

quotationEdge

Matthew explicitly quotes Isaiah, via the Septuagint's παρθένος.

def quotationEdge : IntertextEdge :=
  { fromPassage := Scripture.matthew1_23, toPassage := Scripture.isaiah7_14,
    relation := RelationType.quotation,
    source := Scripture.na28Apparatus Scripture.matthew1_23 }

protoevangeliumEdge

Genesis 3:15 read as promise rather than quotation. Typed as .promise, not .prediction: what Miravalle argues is that the protoevangelium commits to a redeemer born of a woman, and collapsing that into a prediction would beg the question the Michean and Isaianic strands are also asking.

def protoevangeliumEdge : IntertextEdge :=
  { fromPassage := Scripture.matthew1_23, toPassage := Scripture.genesis3_15,
    relation := RelationType.promise,
    source := miravalleOnGenesis }

micahMaternalEdge

Micah 5:3's maternal reference, read as a messianic theme rather than a verbal link — there is no quotation of Micah 5:3 in the birth narratives.

def micahMaternalEdge : IntertextEdge :=
  { fromPassage := Scripture.matthew1_23, toPassage := Scripture.micah5_3,
    relation := RelationType.messianicTheme,
    source := miravalleOnMicah }

lukeAllusionEdge

Luke's annunciation, read as an allusion to Isaiah 7:14. Luke never quotes the verse, but Luke 1:31 is close to its Septuagint wording, and Luke 1:27 and 1:32 bring in the house and the throne of David, as Isaiah 7:13 and 9:6–7 do. Whether that is an allusion is disputed, and both sides are recorded here: Davies and Allison find an influence from Isaiah 7:14, Fitzmyer rejects it, as Rhodea reports (71 n. 66). Typed .allusion, never .quotation: that is the difference between Luke and Matthew. See annunciationFormEdge for the rival reading of the same wording.

def lukeAllusionEdge : IntertextEdge :=
  { fromPassage := Scripture.luke1_31, toPassage := Scripture.isaiah7_14,
    relation := RelationType.allusion,
    source :=
      { primary := Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 71),
        supporting :=
          [Reference.scripture
              [Scripture.verseIn TextualTradition.nestleAland28
                  Scripture.luke1_31,
                Scripture.verseIn TextualTradition.septuagint
                  Scripture.isaiah7_14]],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.disputed } }

annunciationFormEdge

The rival reading: the wording is the birth-announcement form. Luke 1:31 is as close to the announcement to Hagar (Gen 16:11) as to Isaiah 7:14, and Isaiah 7:14 is itself an instance of the form, which Brown and others trace through Ishmael, Isaac, Samson, John and Jesus (Johnson 270 n. 6; Young 113–14). On this reading the shared wording is shared form, not dependence — typed .thematic.

def annunciationFormEdge : IntertextEdge :=
  { fromPassage := Scripture.luke1_31, toPassage := Scripture.genesis16_11,
    relation := RelationType.thematic,
    source :=
      { primary := Reference.work johnsonSamsonTypeScene (Bib.Locus.page 270),
        supporting :=
          [Reference.work youngImmanuelProphecy (Bib.Locus.pages 113 114),
            Reference.work brownProblemVirginalConception (Bib.Locus.page 31)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.wellSupported } }

predictiveReading

The Christian predictive reading of Isaiah 7:14. Far more contested than Micah 5:2 — see the module doc.

def predictiveReading : Interpretation :=
  { passage := Scripture.isaiah7_14,
    reading :=
      "Isaiah 7:14 predicts a virgin conceiving and bearing 'Immanuel', " ++
        "fulfilled in the virgin birth of the Messiah",
    asRelation := some RelationType.prediction,
    source := motyerOnIsaiah }

protoevangeliumReading

Miravalle's reading of Genesis 3:15: the seed is named as the woman's, and that is "already a hint" that no man is involved in the conception it promises.

def protoevangeliumReading : Interpretation :=
  { passage := Scripture.genesis3_15,
    reading :=
      "Genesis 3:15 promises a redeemer born of the woman's seed, the wording " ++
        "hinting at a conception with no human father",
    asRelation := some RelationType.promise,
    source := miravalleOnGenesis }

maternalReading

Miravalle's reading of Micah 5:2–3: the oracle names a mother and no father for the ruler who comes forth from Bethlehem.

def maternalReading : Interpretation :=
  { passage := Scripture.micah5_3,
    reading :=
      "Micah 5:2–3 names only the woman in labour as bearing the coming " ++
        "ruler, mentioning no father",
    asRelation := some RelationType.messianicTheme,
    source := miravalleOnMicah }

bornOfAVirgin

The criterion this argument establishes a candidate must meet.

def bornOfAVirgin : FulfillmentCriterion :=
  { name := "born of a virgin", basis := predictiveReading }

TestimonyArguments.BornOfAVirgin.Sources.Genesis — the citations of the dispute over "her seed"

The atoms of the dispute over what the wording of Genesis 3:15 says about a father: whether "her seed" signifies a birth without one, or fits such a birth once it has happened, what else might explain the wording, and what the Greek's "he" adds. Cited here and dispatched from cite by name, for the reason Sources.Wegner gives.

Luther, Leupold, Keil and Calvin are cited from their commentaries, Lewis and Collins from their articles, Henry by passage, and Akin from the publisher's site. Martin is cited whole: the library has not read his article, and quotes him only as Collins does.

wordingSignifiesAFatherlessBirthCited

wordingSignifiesAFatherlessBirth. Luther makes the argument from the wording: "Thus women continued to bring forth until the Flood; and afterwards also, until the time of Mary. But the seed of none of those women could truly be said to be the Seed of the woman, but might rather be said to have been the seed of the man. But that which was born from Mary was conceived of the Holy Ghost and was the true Seed of Mary" (Luther on the Creation 298–99). Henry: "He was likewise to be the seed of a woman only, of a virgin" (on 3:15). Akin finds in the wording "a hint of the Virgin Birth".

Luther finds the sense in the words of Genesis, and holds that Isaiah later "threw some additional light upon this glorious promise ... For it was then made certain that this Seed would not be born from the union of a man and a woman" (298). Irenaeus reads the verse of the Virgin's son, "He who should be born of a woman, [namely] from the Virgin" (Against Heresies V.21.1), though he does not argue from the wording.

disputed: Leupold and Keil, who read the verse as the promise of Christ, deny that the wording says this (posterityLine); Calvin gives both of their grounds (170) without discussing the point; and Lewis denies it from what Genesis says of Hagar and Rebekah (idiomLine).

def wordingSignifiesAFatherlessBirthCited : AtomMeta :=
  {
    label :=
      "The wording 'her seed' itself signifies a birth with no human father",
    kind := PremiseKind.interpretive,
    source :=
      { primary := Reference.work lutherOnTheCreation (Bib.Locus.pages 298 299),
        supporting :=
          [Reference.work henryCommentary
              (Bib.Locus.adLoc Scripture.genesis3_15),
            Reference.work akinWomanSeedSerpent],
        tradition := Tradition.christianTypological,
        confidence := Confidence.disputed } }

wordingFitsAFatherlessBirthCited

wordingFitsAFatherlessBirth. Leupold, asked whether the expression is "so phrased in reference to Mary and the virgin birth": "Not primarily, but at least incidentally"; "an expression is chosen that meets with literal fulfilment in Him who is virgin born and not of the seed of man. Yet we prefer to state the case thus: the expression used does not specifically prophesy the virgin birth, but it coincides and agrees with it under divine providence" (169). Keil: "in the fact that the destroyer of the serpent was born of a woman (without a human father) they were fulfilled in a way which showed that the promise must have proceeded from that Being, who secured its fulfilment not only in its essential force, but even in its apparently casual form" (102).

disputed, because it presupposes the virginal conception, which this argument rates disputed (maryConceivedAsVirgin). Among readers who grant that conception, none found denies the fit: Leupold and Keil, who deny that the wording signifies it, grant this.

def wordingFitsAFatherlessBirthCited : AtomMeta :=
  {
    label :=
      "The wording 'her seed' fits a birth with no human father, as fulfilled in Christ",
    kind := PremiseKind.interpretive,
    source :=
      { primary := Reference.work leupoldGenesis (Bib.Locus.page 169),
        supporting :=
          [Reference.work keilDelitzschPentateuch (Bib.Locus.page 102)],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.disputed } }

seedIsHerPosterityFirstCited

seedIsHerPosterityFirst. Leupold: "the expression 'her seed' in its first meaning is a collective noun and includes all who are enrolled in the struggle against Satan, without being themselves virgin born" (169) — not every descendant, for "within the circle of the broadest possible meaning of zéra' must be drawn a circle quite a bit smaller" (167). Calvin: "for who will concede that a collective noun is to be understood of one man only? ... I explain, therefore, the seed to mean the posterity of the woman generally" (170). Keil: "It does not follow from this, however, apart from other considerations, that by the seed of the woman we are to understand one solitary person, one individual only" (101).

disputed. Collins argues that the Hebrew's syntax is "quite consistent with the pattern where a single individual is in view" (145), and that on a "bottom-up" reading of the final form "it would be fair to read this as God's threat to the snake, of an individual who will engage the snake in combat and win" (146).

def seedIsHerPosterityFirstCited : AtomMeta :=
  {
    label :=
      "'Her seed' at Genesis 3:15 is first collective: her posterity, not one person",
    kind := PremiseKind.interpretive,
    source :=
      { primary := Reference.work leupoldGenesis (Bib.Locus.pages 167 169),
        supporting :=
          [Reference.work calvinGenesis (Bib.Locus.page 170),
            Reference.work keilDelitzschPentateuch (Bib.Locus.page 101),
            Reference.work collinsSyntacticalNote (Bib.Locus.pages 145 146)],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.disputed } }

womanNamedForTheDeceptionCited

womanNamedForTheDeception. Leupold: "The woman, as one factor in the enmity, is stressed to the exclusion of man because the woman was beguiled" (165); "the one tempted and brought to fall is chosen by God to produce the one that is to bring Satan to fall" (169). Calvin: "He mentions the woman on this account, because, as she had yielded to the subtlety of the devil, and being first deceived, had drawn her husband into the participation of her ruin, so she had peculiar need of consolation" (170). Henry: "God does the woman the honour to call him rather her seed, because she it was whom the devil had beguiled". Keil allows it — "even if the words had reference first of all to the fact that the woman had been led astray by the serpent" — and gives his own reason in the same key: "as it was through the woman that the craft of the devil brought sin and death into the world, so it is also through the woman that the grace of God will give to the fallen human race the conqueror" (102).

wellSupported: Lutheran, Reformed and Puritan readers give it, Henry among them, who also holds that the wording signifies a birth from a virgin. No reader found denies it.

def womanNamedForTheDeceptionCited : AtomMeta

womansSeedSaidOfOrdinaryBirthsCited

womansSeedSaidOfOrdinaryBirths. What the Hebrew reads: the angel promises Hagar that her seed, זַרְעֵךְ, will be multiplied (Genesis 16:10), and Rebekah's family blesses her seed, זַרְעֵךְ, to possess the gate of its enemies (24:60). Each seed has a father named, Abraham and Isaac. Lewis: "While it is normal in Hebrew to describe descendants by the noun zeraʿ, it is unusual (though not unique) to use the term with a feminine possessive pronoun" (299). Scripture alone, and legitimately so: the claim is about what the text reads.

def womansSeedSaidOfOrdinaryBirthsCited : AtomMeta :=
  {
    label :=
      "Genesis speaks of a woman's seed in ordinary births: Hagar's and Rebekah's",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.womensSeedInGenesis,
        supporting :=
          [Reference.work lewisWomansSeed (Bib.Locus.pages 299 300)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

lxxCallsTheSeedHeCited

lxxCallsTheSeedHe. What the Greek reads, from Rahlfs's text: καὶ ἀνὰ μέσον τοῦ σπέρματος αὐτῆς· αὐτός σου τηρήσει κεφαλήν, "and between her seed: he will watch for your head". The pronoun αὐτός is masculine, and σπέρμα is neuter. Collins: "The mismatch in gender between pronoun and antecedent is held to be evidence that the LXX translator saw this as a prophecy of a specific individual" (141). consensus: no one denies the reading.

def lxxCallsTheSeedHeCited : AtomMeta :=
  {
    label :=
      "The Greek of Genesis 3:15 calls the woman's seed 'he', though σπέρμα is neuter",
    kind := PremiseKind.textual,
    source :=
      {
        primary :=
          Reference.scripture
            [Scripture.verseIn TextualTradition.septuagint
                Scripture.genesis3_15],
        supporting :=
          [Reference.work collinsSyntacticalNote (Bib.Locus.page 141)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

lxxReadsOneDescendantCited

lxxReadsOneDescendant. Collins: "The evidence of the Greek translators makes it beyond question that the translator of Genesis 3:15 meant to convey that an individual was promised" (145). The reading "is generally acknowledged" (141), and Martin's article is its usual citation: as Collins quotes him, Martin calls the Greek "the earliest evidence of an individual messianic interpretation" (Collins 141 n. 4). Elsewhere the Greek translators use a masculine pronoun after the neuter σπέρμα when one person is meant: αὐτόν at 1 Samuel 1:11, and ὅς, αὐτός and αὐτόν at 2 Samuel 7:12–14 (Collins 144).

disputed, on Philo, the earliest known reader of this Greek. He grants that it says "he", and reads it as a "barbarism" that is correct in meaning, of the mind and not of a person: "the woman is not he, but she", and "the mind is masculine" (Allegorical Interpretation III.188). Lewis leaves the question open: "Sperma is a neuter noun in Greek and would have taken a neuter pronoun had the translators not thought of an individual", but the masculine "could be an oversight … it is possible that the translator reveals a messianic understanding—which, if true, would then be the earliest known" (300). John Day is reported to call it "simply an over-literal translation of the Hebrew"; his words could not be read, and he is not counted. The doubt Collins reports is about the Hebrew, not the Greek (141).

def lxxReadsOneDescendantCited : AtomMeta

The fulfilment, and the critical reading

What the New Testament says, cited to its text: each is a claim about what a passage reads, and none about what it means for Genesis.

serpentNamedTheDevilCited

serpentNamedTheDevil. "That old serpent, called the Devil, and Satan" (Revelation 12:9; again at 20:2): ὁ ὄφις ὁ ἀρχαῖος, the serpent of old. Collins gives these, with John 8:44, as the New Testament's identification of the serpent (147 n. 21). consensus: it is what the text reads.

def serpentNamedTheDevilCited : AtomMeta :=
  { label := "Revelation calls the devil 'that old serpent' (12:9, 20:2)",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.serpentNamedTheDevil,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

devilDestroyedThroughDeathCited

devilDestroyedThroughDeath. The Son shared flesh and blood "that through death he might destroy him that had the power of death, that is, the devil" (Hebrews 2:14), and "was manifested, that he might destroy the works of the devil" (1 John 3:8). consensus: it is what the texts read.

def devilDestroyedThroughDeathCited : AtomMeta :=
  { label := "The Son came to destroy the devil and his works, through death",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.devilDestroyedThroughDeath,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

christDiedAndRoseCited

christDiedAndRose. Christ "died for our sins", "was buried", and "rose again the third day" (1 Corinthians 15:3–4). consensus: it is what the text reads; whether it happened is not the claim.

def christDiedAndRoseCited : AtomMeta :=
  { label := "Paul says Christ died, was buried, and rose the third day",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.christDiedAndRose,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

sonMadeOfAWomanCited

sonMadeOfAWoman. God sent forth his Son, "made of a woman", γενόμενον ἐκ γυναικός (Galatians 4:4). Whether Paul alludes to Genesis 3:15 here is disputed: Hamilton reads Jesus as "born of (i.e., the seed of) the woman", after Wifall (43, 53 n. 89); Lewis holds that it says only "that the Christ became human" (303). The atom claims only what Paul says. consensus.

def sonMadeOfAWomanCited : AtomMeta :=
  { label := "Paul says God sent his Son 'made of a woman' (Galatians 4:4)",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.sonMadeOfAWoman,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

jesusFulfilsThePromiseCited

jesusFulfilsThePromise. The fulfilment, as fulfilmentLine argues it. Worded so that it says what Calvin, Keil and Leupold all hold: none of them takes "her seed" for Christ alone, and each holds that in Christ, as the head of the woman's seed, the serpent is crushed. disputed, as its step is, on Westermann.

def jesusFulfilsThePromiseCited : AtomMeta

seedWasOfTheWomanAloneCited

seedWasOfTheWomanAlone. The seed in whom the promise is fulfilled had no human father: Irenaeus reads the verse of "He who should be born of a woman, [namely] from the Virgin" (V.21.1). disputed, as the virginal conception it rests on is (maryConceivedAsVirgin).

def seedWasOfTheWomanAloneCited : AtomMeta :=
  {
    label :=
      "The seed in whom Genesis 3:15 is fulfilled was of the woman alone",
    kind := PremiseKind.interpretive,
    source :=
      {
        primary :=
          Reference.work irenaeusAgainstHeresies
            (Bib.Locus.sectionRef "V.21.1"),
        supporting :=
          [Reference.work keilDelitzschPentateuch (Bib.Locus.page 102)],
        tradition := Tradition.christianTypological,
        confidence := Confidence.disputed } }

verseIsACurseOnTheSerpentCited

verseIsACurseOnTheSerpent. "Because thou hast done this, thou art cursed" (3:14): the words of 3:15 are spoken to the serpent, as part of its sentence. Westermann classes them as a punishment oracle (260), the form-critical ground of his denial (westermannLine). wellSupported: the address and the curse are the text's; the classification is his, and is not contested by the readers cited here, who read a promise within the curse.

def verseIsACurseOnTheSerpentCited : AtomMeta :=
  {
    label :=
      "Genesis 3:14–15 is a curse on the serpent, in the form of a punishment oracle",
    kind := PremiseKind.interpretive,
    source :=
      { primary := Reference.work westermannGenesis (Bib.Locus.page 260),
        supporting :=
          [Reference.scripture
              [Scripture.verseIn TextualTradition.masoretic
                  { book := Book.genesis, chapter := 3, verse := 14 }]],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.wellSupported } }

seedIsLineNotIndividualCited

seedIsLineNotIndividual. Westermann: "The parallelism makes it clear that 'seed' refers to a line of descendants and not to an individual" (259); "it is beyond doubt that [zeraʿ] is to be understood collectively" (260). Martin holds the same of the Hebrew, as Collins quotes him: "he" is "indefensible as a translation", and the right English is "it" or "they", "the descendants of Eve" (Collins 140 n. 2). The Targums read the verse collectively, of "the sons of the woman".

Stronger than seedIsHerPosterityFirst, which Calvin, Keil and Leupold hold: they read "her seed" as her posterity first, and Keil and Leupold deny that no individual is in view. disputed: Collins answers Westermann that the woman's seed "is not unquestionably collective" (147 n. 22); Leupold, that the word "is also used in reference to an individual and not only in the collective sense" (168); Alexander, that the seed "must be understood as referring to a single individual" (363); Hamilton, that "the text switches from a collective referent to a singular one" (32). syntaxLine gives their argument.

def seedIsLineNotIndividualCited : AtomMeta

seedUsedOfOneDescendantCited

seedUsedOfOneDescendant. What the texts read, as Collins sets them out: "when zeraʿ denotes a specific descendant, it appears with singular verb inflections, adjectives, and pronouns" (144) — 2 Samuel 7:12–15, the clearest parallel (145), Genesis 21:13, 38:9 and 1 Samuel 1:11. Keil grants it: "the posterity of a man may consist of a whole tribe or of one son only" (101); so does Leupold (168). consensus: no reader found denies the readings.

def seedUsedOfOneDescendantCited : AtomMeta :=
  {
    label :=
      "Elsewhere זֶרַע with singular verbs and pronouns denotes one descendant",
    kind := PremiseKind.textual,
    source :=
      {
        primary :=
          Reference.work collinsSyntacticalNote (Bib.Locus.pages 144 145),
        supporting :=
          [Reference.work keilDelitzschPentateuch (Bib.Locus.page 101),
            Reference.work leupoldGenesis (Bib.Locus.page 168)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

strikerIsSingularCited

strikerIsSingular. What the Hebrew reads at 3:15b: הוּא, "he", masculine singular, with a singular verb, and the object is the serpent's own head, "your head", not its seed's. Collins: "it is 'he' … who will bruise 'you' (singular, i.e., the snake)" (146 n. 21). Keil grants it: "it is not over the seed of the serpent but over the serpent itself that the victory is said to be gained" (101). consensus for the form. Whether הוּא means "he" or "it" is the question the readings answer, not the form.

def strikerIsSingularCited : AtomMeta :=
  {
    label :=
      "At Genesis 3:15b the striker is singular 'he', against the serpent's own head",
    kind := PremiseKind.textual,
    source :=
      {
        primary :=
          Reference.scripture
            [Scripture.verseIn TextualTradition.masoretic
                Scripture.genesis3_15],
        supporting :=
          [Reference.work collinsSyntacticalNote (Bib.Locus.page 146),
            Reference.work keilDelitzschPentateuch (Bib.Locus.page 101)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

serpentTwistsTheCommandCited

serpentTwistsTheCommand. What the text reads: the serpent speaks, and gives back God's command of 2:17 twisted — "Yea, hath God said, Ye shall not eat of every tree of the garden?" (3:1), "Ye shall not surely die" (3:4). Collins: "the snake's wording of v. 4 reflects knowledge of 2:17", and "animals do not have faculty of speech in Bible, hence there is some intervention here (cf Nu. 22:28)" (146 n. 21). consensus: it is what the text reads.

def serpentTwistsTheCommandCited : AtomMeta :=
  {
    label :=
      "In Genesis 3 the serpent speaks, and knows and twists God's command",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.serpentTwistsTheCommand,
        supporting :=
          [Reference.work collinsSyntacticalNote (Bib.Locus.page 146)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

godSetsTheEnmityCited

godSetsTheEnmity. What the text reads: "I will put enmity" (3:15), with God as the subject. Woudstra: "The mere fact of God's 'setting' of the enmity is a tremendous initiative for good, unexpected and unmerited" (203). consensus for the wording.

def godSetsTheEnmityCited : AtomMeta :=
  { label := "God sets the enmity himself: 'I will put enmity' (3:15)",
    kind := PremiseKind.textual,
    source :=
      {
        primary :=
          Reference.scripture
            [Scripture.verseIn TextualTradition.masoretic
                Scripture.genesis3_15],
        supporting :=
          [Reference.work woudstraRecentTranslations (Bib.Locus.page 203)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

serpentIsTheInstrumentOfAPowerCited

serpentIsTheInstrumentOfAPower. Delitzsch, as Collins quotes him: "an animal is intended, but an animal not speaking of its own accord, but as made the instrument of itself by the evil principle"; and Collins: "in view of the place of the story in the structure of Genesis it is hard to believe that only a snake is intended here … the referent of the second person pronoun would actually be the dark power behind the snake" (146–47). Woudstra: "as one reads Genesis 3 one does indeed become conscious of such a force. There is a diabolical subtlety in the serpent's suggestions … Later Scripture abundantly confirms this opinion" (197). Keil: "This foe is Satan" (101–2).

disputed: Westermann sides with Holzinger, "the animal is being punished and not some demonic power behind it" (261). Of the readers before Christ, none found puts the devil behind the serpent beyond doubt: Wisdom 2:24's "envy of the devil" does not name it, and is read by some of Cain.

def serpentIsTheInstrumentOfAPowerCited : AtomMeta :=
  { label := "The serpent of Genesis 3 is the instrument of an evil power",
    kind := PremiseKind.interpretive,
    source :=
      {
        primary :=
          Reference.work collinsSyntacticalNote (Bib.Locus.pages 146 147),
        supporting :=
          [Reference.work woudstraRecentTranslations (Bib.Locus.page 197),
            Reference.work keilDelitzschPentateuch (Bib.Locus.pages 101 102),
            Reference.work westermannGenesis (Bib.Locus.page 261)],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.disputed } }

TestimonyArguments.BornOfAVirgin.Sources.NearTerm — the citations of the near-term dispute

The atoms of the dispute over the critical denial, cited here and dispatched from cite by name: the critic's two premises, that 7:14 was a near-term sign to Ahaz and that such a sign excludes a messianic sense, and the grounds of the replies to them — Berry's, Postell's Micah counterexample, and Motyer's with Compton's. (Postell's Isaiah counterexample rests on atoms the compositional strand also uses, and is cited with them in Sources.lean.)

They sit apart for the reason Sources.Wegner does: cite stays one total function, and each value below is reached from exactly one of its cases.

isaiahIsNearTermSignToAhazCited

isaiahIsNearTermSignToAhaz. The reading Justin already answers, in Trypho's form: fulfilled in Hezekiah (Dial. 67, 77). Origen's reply is a question — which child of Ahaz's day was called Immanuel? — and his conclusion that the sign was given to the house of David (Cels. I.35). Motyer denies it most directly (1970, 120, 124): the sign confirms events after the fact, and Maher-shalal-hash-baz, not Immanuel, carries the timetable. So does Compton (2007, 12): 7:14 is addressed to the house of David, in plural pronouns, and only 7:15–16, with a singular "you", to Ahaz. disputed for that reason, on the definition that re-rated the exclusion premise.

def isaiahIsNearTermSignToAhazCited : AtomMeta :=
  {
    label :=
      "Isaiah 7:14 is a near-term sign to Ahaz, fulfilled in Isaiah's generation",
    kind := PremiseKind.interpretive,
    source := brownOnBirth Confidence.disputed }

nearTermExcludesMessianicSenseCited

nearTermExcludesMessianicSense. The premise Berry and Postell deny, and Motyer with them: disputed by the library's own definition, since the contest is recorded in berryLine and postellLine. It was once cited wellSupported on Brown's authority, which let the critic outrank both replies. Compton (2007, 12–14) denies it on a third ground: the near-term part of the oracle, 7:15–16, uses the child's infancy only as a measure of time, and so does not need the child born in Ahaz's day.

def nearTermExcludesMessianicSenseCited : AtomMeta :=
  {
    label :=
      "A sign given for Ahaz's generation is not also a prediction of a virgin birth",
    kind := PremiseKind.interpretive,
    source := brownOnBirth Confidence.disputed }

nearTermFulfilmentIsUnclearCited

nearTermFulfilmentIsUnclear. Descriptively uncontroversial: the near-term referent has been taken for Isaiah's son, for Hezekiah, and for a son of Ahaz, with no settled answer. What is contestable is the use Berry puts it to. Compton surveys the candidates (5) and finds that none fits (9).

def nearTermFulfilmentIsUnclearCited : AtomMeta :=
  {
    label :=
      "How Isaiah 7:14 was fulfilled in Ahaz's own day is itself an open question",
    kind := PremiseKind.interpretive,
    source :=
      {
        primary :=
          Reference.work Bib.berryVirginBirth (Bib.Locus.pages 1653 1654),
        supporting :=
          [Reference.work comptonImmanuelProphecy (Bib.Locus.pages 5 9)],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.wellSupported } }

signGivenToHouseOfDavidCited

signGivenToHouseOfDavid. What the Hebrew says: שִׁמְעוּ־נָא בֵּית דָּוִד and לָכֶם in 7:13–14 are plural, אַתָּה in 7:16 is singular. Compton builds on it (12), Motyer notes the address to the dynasty (122). The grammar is not in dispute; what it implies is, and that is left to the step that uses it.

def signGivenToHouseOfDavidCited : AtomMeta :=
  {
    label :=
      "Isaiah 7:13–14 gives the sign to David's house, in the plural; 7:16's 'you' is Ahaz",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.immanuelAddressees,
        supporting :=
          [Reference.work comptonImmanuelProphecy (Bib.Locus.page 12),
            Reference.work youngImmanuelProphecy (Bib.Locus.page 112),
            Reference.work motyerContextContent (Bib.Locus.page 122)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

maherShalalHashBazRepeatsTheTimetableCited

maherShalalHashBazRepeatsTheTimetable. Common ground: the parallel is what leads the critics who identify the two children to identify them (Compton 5, citing Clements). Motyer (124) and Compton (13) read it the other way. The observation is shared; the reading of it is the step.

def maherShalalHashBazRepeatsTheTimetableCited : AtomMeta :=
  {
    label :=
      "Isaiah 8:4 gives Maher-shalal-hash-baz the timetable 7:16 gives the child of 7:14",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.work motyerContextContent (Bib.Locus.page 124),
        supporting :=
          [Reference.work comptonImmanuelProphecy (Bib.Locus.page 13),
            Reference.scripture Scripture.sharedTimetable],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.wellSupported } }

micahRulerFacesAssyriaCited

micahRulerFacesAssyria. What the text says. Postell cites it by the Hebrew numbering, as Micah 5:1 and 5:4–5 (481 n. 72).

def micahRulerFacesAssyriaCited : AtomMeta :=
  {
    label :=
      "Micah 5:5–6 sets the ruler from Bethlehem against the Assyrian invasion",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.micahAssyrianSetting,
        supporting :=
          [Reference.work postellIsaiahMessianic (Bib.Locus.page 481)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

micahRulerReadMessianicallyCited

micahRulerReadMessianically. Granted by the critic's own authority: "there was an expectation of the Messiah's birth at Bethlehem (Mt 2:4-6; Jn 7:42)" (Brown 1972, 26 n. 64). Postell: recognised as messianic by ancient Jewish interpreters (481 n. 72).

def micahRulerReadMessianicallyCited : AtomMeta :=
  { label := "Micah 5:2 was read messianically in first-century Judaism",
    kind := PremiseKind.historical,
    source :=
      { primary := Reference.work postellIsaiahMessianic (Bib.Locus.page 481),
        supporting :=
          [Reference.work brownProblemVirginalConception (Bib.Locus.page 26),
            Reference.scripture Scripture.bethlehemExpectation],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.wellSupported } }

TestimonyArguments.BornOfAVirgin.Sources.Septuagint — the citations of the Septuagint dispute

The atoms of the dispute over what the Septuagint's παρθένος shows, cited here and dispatched from cite by name: when and by whom the Greek Isaiah was made, what its word for the woman of 7:14 meant, the evidence each side reads, and what the translator can be taken to have meant.

They sit apart for the reason Sources.Wegner does: cite stays one total function, and each value below is reached from exactly one of its cases.

Rico and Gentry are cited from their book; Bratcher, Walton, Wegner, Rhodea and Postell from their articles; Davidson from his dictionary article; Meade from his comment on his own blog post. Three readings are known to the library only through the scholar who reports them, and each comment says so: Delling's and Tsevat's, through Rhodea, and Gray's, through Bratcher.

lxxIsPreChristianCited

lxxIsPreChristian. Irenaeus makes the argument from it: Isaiah 7:14 "was interpreted into Greek by the Jews themselves, much before the period of our Lord's advent, that there might remain no suspicion that perchance the Jews, complying with our humour, did put this interpretation upon these words" (Against Heresies III.21.1). Justin presses Trypho with the version made by "the seventy elders who were with Ptolemy" (Dialogue 71). Chrysostom makes the same point: the Seventy, "as having entered upon this work an hundred years or more before the coming of Christ, stand clear from all such suspicion" (Homilies on Matthew 5); Eusebius adds that they were "men of Hebrew race, experts in the accuracy of their knowledge of their national language" (Dem. Ev. VII.1). The rival grants the date: Wegner puts the translator "about 250–150 BC" (483). consensus.

def lxxIsPreChristianCited : AtomMeta

parthenosMeansVirginCited

parthenosMeansVirgin. Rico and Gentry: "There is no doubt that we should take the term parthenos to mean 'virgin' whenever it appears in Semitic Koine Greek: the example of Gn 34:1–3 is the exception that proves the rule" (21). Postell reports that they "insist" on it (472 n. 45). Bratcher reaches the same conclusion from the Septuagint's usage, without their argument: "parthenos definitely means 'virgin' in the LXX; only very exceptionally (and, inexplicably, in Gen. 34:3) is it used otherwise" (113).

disputed, because scholars this argument cites deny it. Wegner holds that in the translator's day the word meant "a young woman of marriageable age", and came to mean "virgin" only by the time of the New Testament (482–83). Walton: "Therefore the LXX is not necessarily betraying an interpretation as virgin by choosing this term" (293). Rhodea: "in the LXX, παρθένος need not refer to a virgo intacta" (67). Meade: "παρθενος simply means young woman in this verse and in other places in the LXX" (comment of 9 January 2013).

def parthenosMeansVirginCited : AtomMeta :=
  { label := "In the Greek of the Septuagint, παρθένος means a virgin",
    kind := PremiseKind.linguistic,
    source :=
      { primary := Reference.work ricoGentryInfantKing (Bib.Locus.page 21),
        supporting :=
          [Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 113),
            Reference.work postellIsaiahMessianic (Bib.Locus.page 472)],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.disputed } }

parthenosMeantYoungWomanCited

parthenosMeantYoungWoman. A claim about the word, not about any woman: in the translator's Greek, παρθένος meant "young woman", and did not yet mean "virgin". Wegner and Walton grant that by the New Testament it meant "virgin"; Meade and Davidson put that sense down to Christian use. The dispute is over the translator's day, two or three centuries before Matthew.

Wegner: "In early Greek literature it appears to have had the meaning of 'a young woman of marriageable age' (with or without the focus on virginity), but by NT times this word developed the more technical meaning of 'virgin'" (482). So the translator of Isaiah chose a word for a young woman, "an excellent word choice to convey what the LXX's author meant", and "in the intervening time between the LXX and the NT book of Matthew, the word παρθένος changed in meaning" (483). Rhodea follows him, with an "apparently" (67). Meade holds it too: παρθένος "simply means young woman in this verse and in other places in the LXX", and by the time of Justin it had been "hijacked or used to mean 'chaste woman' only" (comment of 9 January 2013). disputed: Rico and Gentry deny it, and so does Bratcher.

def parthenosMeantYoungWomanCited : AtomMeta :=
  {
    label :=
      "In the Septuagint's day, παρθένος meant 'young woman'; not yet 'virgin'",
    kind := PremiseKind.linguistic,
    source :=
      have __src :=
        wegnerOnAlmah (Bib.Locus.pages 482 483)
          Confidence.disputed;
      { primary := __src.primary,
        supporting :=
          [Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 67),
            Reference.work meadeAncientVersionsComment],
        tradition := __src.tradition, confidence := __src.confidence } }

earlyGreekParthenosIsYoungWomanCited

earlyGreekParthenosIsYoungWoman. Wegner (482) and Rhodea (67) both state it from BDAG 777: "a young woman of marriageable age, with or without focus on virginity". BDAG itself gives that as the word's general use "Hom.+", from Homer on, and sets against it the sense "in our lit.", the New Testament and the early Christian writings: "one who has never engaged in sexual intercourse, virgin". So the contrast in BDAG is between bodies of writing, not between periods; "early Greek" is Wegner's and Rhodea's narrowing of it, and the claim here is no more than the narrowing. BDAG gives no sense for the Septuagint. LSJ, for classical Greek: "maiden, girl", "virgin, opp. γυνή", and "of unmarried women who are not virgins" (1339). Walton: the word "does not always mean 'virgin' in classical Greek" (293). Bratcher, who holds the opposite of Wegner about the Septuagint, grants it: "at first the word was used in a general sense of 'girl', 'young woman', without any specific connotation of virginity" (112). wellSupported: Rico and Gentry grant the older usage too, and explain Genesis 34:3 by it, as an "almost anachronistic use of the word parthenos" that "corresponds to the general tendency of language in the Septuagint version of the Pentateuch", whose language is "more elevated and classical than the language of the later texts" (18). What they deny is that the older usage is the Septuagint's at large.

def earlyGreekParthenosIsYoungWomanCited : AtomMeta

greekCallsDinahParthenosCited

greekCallsDinahParthenos. What the Greek reads: Shechem "lay with her and humbled her" (34:2), and "he loved the παρθένος, and spoke to her according to the mind of the παρθένος" (34:3), where the Hebrew has נַעֲרָה, "girl", both times. Read from Rahlfs's text and the Masoretic. Wegner calls it "a good example of the meaning of παρθένος in the LXX" (483), and Rhodea draws from it that "παρθένος need not refer to a virgo intacta" (67). No one denies the reading. Rico and Gentry call it "the exception that proves the rule" (21); Bratcher, an exception made "inexplicably" (113).

The claim is what the text reads: the word, and the verse it stands in, after 34:2. Whether the noun describes Dinah as she was after 34:2 is a further claim, and a reader's (parthenosDescribesDinahAsSheThenWas).

def greekCallsDinahParthenosCited : AtomMeta

isaiahUsesParthenosForBetulahCited

isaiahUsesParthenosForBetulah. What the two texts read, and nothing more: read from Rahlfs's text of the Greek and from the Masoretic Text, the Greek Isaiah has παρθένος at 23:4, 37:22, 47:1 and 62:5 besides 7:14, and in each the Hebrew has בְּתוּלָה. The converse does not hold — at 23:12 the Greek has no παρθένος for בְּתוּלַת — and the atom does not claim it. Scripture alone, and legitimately so: the claim is about what a version reads.

def isaiahUsesParthenosForBetulahCited : AtomMeta :=
  { label := "Elsewhere in the Greek Isaiah, παρθένος renders בְּתוּלָה",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.isaianicParthenoi,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

priestMarriesAParthenosCited

priestMarriesAParthenos. What the Greek reads, from Rahlfs's text: the high priest "shall take a wife, a παρθένος, from his own kin" (γυναῖκα παρθένον ἐκ τοῦ γένους αὐτοῦ, 21:13), where the Hebrew has אִשָּׁה בִבְתוּלֶיהָ, "a woman in her virginity"; and "a widow, a woman put away, a defiled woman and a harlot, these he shall not take, but a παρθένος from his own kin" (21:14). Read from Rahlfs's text and the Masoretic. Scripture alone, and legitimately so: the claim is about what a version reads. consensus.

def priestMarriesAParthenosCited : AtomMeta :=
  {
    label :=
      "The high priest of the Greek Leviticus marries a παρθένος, not a widow or a harlot",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.priestsBride,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

partheniaProveTheBrideCited

partheniaProveTheBride. What the Greek reads, from Rahlfs's text: a husband says of his bride "I did not find τὰ παρθένια in her" (22:14), and her parents bring out "τὰ παρθένια of the girl" (22:15); if the charge is true and "παρθένια are not found for the girl", she is stoned, "for she has done folly among the sons of Israel, to play the harlot in her father's house" (22:20–21). A man who brings the charge falsely has brought "an evil name upon a παρθένος of Israel" (22:19). The Hebrew has בְּתוּלִים for the tokens.

The lexica gloss the Greek word alike: "signs of virginity, LxxDe.22.15" (LSJ 1339); "tokens of virginity" (Muraoka 535); "signs pertaining to virginity, virginity" (LEH s.v.). consensus: no reader found denies the reading.

def partheniaProveTheBrideCited : AtomMeta :=
  {
    label :=
      "In the Greek Deuteronomy, a bride without τὰ παρθένια dies for playing the harlot",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.tokensOfVirginity,
        supporting :=
          [Reference.work liddellScottJones (Bib.Locus.page 1339),
            Reference.work muraokaLexiconSeptuagint (Bib.Locus.page 535),
            Reference.work lustLexiconSeptuagint (Bib.Locus.sv "παρθένια")],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

lawsUseParthenosAsVirginCited

lawsUseParthenosAsVirgin. Bratcher makes the argument from the Greek of the laws: in Deuteronomy 22 the Hebrew's בְּתוּלִים "stands concretely for 'tokens of virginity' (LXX partheneia)", and in Leviticus 21 "the young woman so characterized is clearly a virgin (LXX parthenos)" (102, where "Lev. 21:3" is a misprint for 21:13); "The use of the cognates of parthenos in the LXX bears out the conclusion that parthenos is 'virgin'", and "All this indicates that parthenos is 'virgin' in the exact sense of the word" (113).

These are not uses of the word of a virgin, which would show nothing about its sense: Walton observes that a thousand uses of "fiancée" of virgins would not make it mean "virgin" (292). In these laws virginity is what the law turns on. The priest's παρθένος is set against the widow, the woman put away, the defiled woman and the harlot, and stands for "a woman in her virginity". The bride's τὰ παρθένια are the tokens whose absence proves her a harlot, and Walton's own test is that a word meaning "virgin" should have an abstract meaning "virginity" (292).

disputed, as its step is, on Miller (lawsLine gives his dissent, and where it breaks).

def lawsUseParthenosAsVirginCited : AtomMeta :=
  {
    label :=
      "In the Greek Pentateuch's laws, παρθένος is used in the sense 'virgin'",
    kind := PremiseKind.linguistic,
    source :=
      { primary := Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 113),
        supporting :=
          [Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 102),
            Reference.work waltonWhatsInAName (Bib.Locus.page 292),
            Reference.work millerBornDivine],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.disputed } }

seductionLawPricesAParthenosCited

seductionLawPricesAParthenos. What the Greek reads, from Rahlfs's text: "if anyone deceives a παρθένος not betrothed and lies with her, he shall endow her with a bride-price as his wife" (22:15), and if her father will not give her, "he shall pay the father silver, as much as is the bride-price of virgins", ἡ φερνὴ τῶν παρθένων (22:16), where the Hebrew has בְּתוּלָה and מֹהַר הַבְּתוּלֹת. The law calls her a παρθένος, and names what the man owes "the bride-price of virgins", after he has lain with her. What that price says of her is the step's to read (dinahLine). consensus: it is what the text reads.

def seductionLawPricesAParthenosCited : AtomMeta :=
  {
    label :=
      "In the Greek Exodus, the seduced παρθένος is owed 'the bride-price of virgins'",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.seductionLaw,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

shechemActsUnderTheLawCited

shechemActsUnderTheLaw. What the texts read, from Rahlfs's text and the Masoretic. Three words of Genesis 34 are words of the laws of the violated virgin:

• Shechem "humbled her", ἐταπείνωσεν αὐτήν, וַיְעַנֶּהָ (34:2), the verb of the man who seizes a virgin not betrothed: he shall marry her "because he humbled her" (Deuteronomy 22:29, in both texts).
• Jacob's sons say he "did folly in Israel", נְבָלָה עָשָׂה בְיִשְׂרָאֵל (34:7), the words of the bride found without the tokens of virginity, who "did folly in Israel" (Deuteronomy 22:21). The link is the Hebrew's: the Greek has ἄσχημον at 34:7 and ἀφροσύνην at Deuteronomy 22:21.
• Shechem offers the bride-price, φερνή, מֹהַר (34:12), the payment Exodus 22:15–16 requires of the man who has lain with a παρθένος.

consensus: the words are the texts', whatever is made of them.

def shechemActsUnderTheLawCited : AtomMeta :=
  {
    label :=
      "Genesis 34 tells Shechem's act in the words of the laws of the violated virgin",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.shechemUnderTheLaw,
        supporting := [Reference.scripture Scripture.seductionLaw],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

dinahIsTheLawsParthenosCited

dinahIsTheLawsParthenos. The status reading of Genesis 34:3: the Greek calls Dinah "the παρθένος" as the law of Exodus 22:15–16 calls the woman a man has lain with, naming her by the standing he took from her, and the word keeps its sense "virgin". dinahLine gives the argument and its rating. plausible, as its step is.

def dinahIsTheLawsParthenosCited : AtomMeta

matthewQuotesTheGreekVirginCited

matthewQuotesTheGreekVirgin. What Matthew reads: "ἰδοὺ ἡ παρθένος ἐν γαστρὶ ἕξει καὶ τέξεται υἱόν" (1:23), the Septuagint's words for Isaiah 7:14. Scripture alone, and legitimately so: the claim is about what the texts read. consensus.

def matthewQuotesTheGreekVirginCited : AtomMeta :=
  {
    label :=
      "Matthew 1:23 quotes Isaiah 7:14 in the Greek's own words: ἡ παρθένος",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.matthewQuotesTheSeptuagint,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

matthewSaysMaryKnewNoManCited

matthewSaysMaryKnewNoMan. What Matthew says: Mary was found with child "before they came together" (1:18), and Joseph "knew her not until she had borne a son" (1:25). This is what Matthew says, not whether it happened, which the argument rates apart (maryConceivedAsVirgin). consensus.

def matthewSaysMaryKnewNoManCited : AtomMeta :=
  { label := "Matthew says Mary conceived before she and Joseph came together",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.matthewMaryKnewNoMan,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

lxxIsaiahUsesParthenosAsVirginCited

lxxIsaiahUsesParthenosAsVirgin. Scripture's own reading of the Greek word: Matthew quotes the Septuagint's ἡ παρθένος of a woman who conceived before she and Joseph came together, so in the text he quotes, the word has the sense "virgin". The principle is Westminster's: "The infallible rule of interpretation of Scripture is the Scripture itself" (I.ix). Irenaeus: the apostles "agree with this aforesaid translation", and Matthew among them set forth the prophecies "just as the interpretation of the elders contains them" (Against Heresies III.21.3).

disputed, as its step is: Wegner grants that Matthew uses the word of Mary, a virgin, and holds that it had changed in meaning since the translator wrote it, "from 'young woman' to 'virgin,' thus also making it a suitable term to describe Mary in the first century AD" (483).

def lxxIsaiahUsesParthenosAsVirginCited : AtomMeta :=
  {
    label :=
      "In the Greek of Isaiah 7:14, which Matthew quotes, παρθένος means 'virgin'",
    kind := PremiseKind.linguistic,
    source :=
      {
        primary :=
          Reference.work westminsterConfession (Bib.Locus.sectionRef "I.ix"),
        supporting :=
          [Reference.work irenaeusAgainstHeresies
              (Bib.Locus.sectionRef "III.21.3"),
            Reference.work wegnerVirginBirths (Bib.Locus.page 483)],
        tradition := Tradition.reformedProtestant,
        confidence := Confidence.disputed } }

joelGreekCallsTheWidowParthenosCited

joelGreekCallsTheWidowParthenos. Miller's claim about the Greek: "Lament like a parthenos dressed in sackcloth for the husband of her youth (Joel 1:8)", given as a use of the word of a woman who is not a virgin (Born Divine). The Greek of Joel 1:8 does not read so: it calls the woman νύμφην, a bride, and its παρθεν- word, τὸν παρθενικόν, is of the husband (Rahlfs). Cited for what Miller holds; the text refutes it (Dispute.Miller).

def joelGreekCallsTheWidowParthenosCited : AtomMeta :=
  { label := "The Greek of Joel 1:8 calls a young widow a παρθένος (Miller)",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.work millerBornDivine,
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.disputed } }

parthenosDoesNotItselfConnoteVirginityCited

parthenosDoesNotItselfConnoteVirginity. Miller's thesis: "As in other Greek literature, parthenos in the Septuagint did not by itself connote what we mean by virginity", so that where virginity matters it "has to be inferred from the context" (Born Divine). disputed: Bratcher (113), and Rico and Gentry, hold the opposite.

def parthenosDoesNotItselfConnoteVirginityCited : AtomMeta :=
  {
    label :=
      "In the Septuagint, παρθένος did not by itself connote virginity (Miller)",
    kind := PremiseKind.linguistic,
    source :=
      { primary := Reference.work millerBornDivine,
        supporting :=
          [Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 113)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.disputed } }

parthenosDescribesDinahAsSheThenWasCited

parthenosDescribesDinahAsSheThenWas. Miller's premise: "In one passage, this term refers to a rape victim after she has been attacked (Gen 34:3)" (Born Divine). Wegner says the same, that Dinah "is called a παρθένος even after she was raped by Shechem" (483), and Muraoka's lexicon glosses the verse "so called just after having been raped" (535). It is more than the reading of the text (greekCallsDinahParthenos): that the noun says what Dinah was at the time of the verse, and so, since she was then no longer a virgin, that the word is not used there in the sense "virgin".

A noun need not say what the one it names is at the time of its verb. Enç argues that a noun phrase is read at a time of its own, which the context gives (1986); Scripture names Rahab "the harlot" long after Jericho (Hebrews 11:31, James 2:25), and Matthew "the tax collector" after his call (Matthew 10:3). So the noun at 34:3 can name Dinah by what she had been, or, as the status reading holds, by the law's name for the woman a man has lain with (dinahIsTheLawsParthenos).

wellSupported, not higher: every reader on record who takes up the verse holds it, and Rico and Gentry and Bratcher, who read the word as "virgin", grant it. The status reading and the argument from the noun contest it, but both are the library's own, and no reader has been found who makes either.

def parthenosDescribesDinahAsSheThenWasCited : AtomMeta :=
  {
    label :=
      "At 34:3 παρθένος describes Dinah as she then was, no longer a virgin (Miller)",
    kind := PremiseKind.linguistic,
    source :=
      { primary := Reference.work millerBornDivine,
        supporting :=
          [Reference.work wegnerVirginBirths (Bib.Locus.page 483),
            Reference.work muraokaLexiconSeptuagint (Bib.Locus.page 535)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.wellSupported } }

tryphoRejectsParthenosCited

tryphoRejectsParthenos. Trypho: "The Scripture has not, 'Behold, the virgin shall conceive, and bear a son,' but, 'Behold, the young woman shall conceive'" (Dialogue 67). Justin answers that Trypho's teachers "refuse to admit that the interpretation made by the seventy elders who were with Ptolemy ... is a correct one" (71). consensus: the record is Justin's, and no one doubts that the objection was made.

def tryphoRejectsParthenosCited : AtomMeta :=
  {
    label :=
      "Trypho rejects the Septuagint's 'the virgin' and reads 'the young woman'",
    kind := PremiseKind.historical,
    source :=
      { primary := Reference.work justinDialogue (Bib.Locus.sectionRef "67"),
        supporting :=
          [Reference.work justinDialogue (Bib.Locus.sectionRef "71")],
        tradition := Tradition.christianTypological,
        confidence := Confidence.consensus } }

lxxReadsAVirginCited

lxxReadsAVirgin. What Irenaeus takes the Greek to say: "the token of the Virgin" (Against Heresies III.21.1). Readers who doubt more grant this much. Bratcher: "all the LXX means by parthenos is that a young woman, at that time virgin, would in the normal way marry and bear a child" (115), which he calls "the most reasonable explanation" (116). Delling, as Rhodea quotes him: the Septuagint's usage "demands no more than the sense of a 'woman untouched by a man up to the moment of the conception (of Immanuel)'" (Rhodea 67, citing TDNT 5.833 in n. 42).

disputed, because it stands or falls with the claim about παρθένος: on Wegner's reading the translator wrote a word for a young woman, and said nothing of her virginity.

def lxxReadsAVirginCited : AtomMeta :=
  {
    label :=
      "Before Christ, a Jewish translator read the woman of Isaiah 7:14 as a virgin",
    kind := PremiseKind.interpretive,
    source :=
      {
        primary :=
          Reference.work irenaeusAgainstHeresies
            (Bib.Locus.sectionRef "III.21.1"),
        supporting :=
          [Reference.work bratcherStudyOfIsaiah (Bib.Locus.pages 115 116),
            Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 67)],
        tradition := Tradition.christianTypological,
        confidence := Confidence.disputed } }

lxxPutsTheConceptionInTheFutureCited

lxxPutsTheConceptionInTheFuture. What the Greek reads: ἰδοὺ ἡ παρθένος ἐν γαστρὶ ἕξει, "look, the virgin shall be with child", a future, where Wegner reads the Hebrew הָרָה as a present pregnancy. Rhodea notes it (67). consensus.

def lxxPutsTheConceptionInTheFutureCited : AtomMeta :=
  {
    label :=
      "The Septuagint puts the conception in the future: 'she shall be with child'",
    kind := PremiseKind.textual,
    source :=
      {
        primary :=
          Reference.scripture
            [Scripture.verseIn TextualTradition.septuagint
                Scripture.isaiah7_14],
        supporting :=
          [Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 67)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

lxxEnvisagesAVirginalConceptionCited

lxxEnvisagesAVirginalConception. Justin reads the elders' Greek so: "if He also were to be begotten of sexual intercourse, like all other first-born sons, why did God say that He would give a sign which is not common to all the first-born sons?" (Dialogue 84). Delling, as Rhodea quotes him, allows that "on the basis of LXX usage it is also possible that the translator of Is. 7:14 envisaged a non-sexual origin of the virgin's son" (67 n. 42).

disputed. Rhodea, quoting Tsevat: "The pregnancy lies in the future ...; nothing indicates that the woman is also a virgin after the conception" (67); "the evidence, then, does not demand a miraculous conception in either the Hebrew or LXX" (68). Bratcher, quoting Gray: "all, then, that the Greek translators need mean is that a woman now virgin will hereafter, in the ordinary course of nature of losing her virginity, conceive" (115–16).

def lxxEnvisagesAVirginalConceptionCited : AtomMeta :=
  {
    label :=
      "The Septuagint's translator meant that the woman conceives as a virgin",
    kind := PremiseKind.interpretive,
    source :=
      { primary := Reference.work justinDialogue (Bib.Locus.sectionRef "84"),
        supporting :=
          [Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 67)],
        tradition := Tradition.christianTypological,
        confidence := Confidence.disputed } }

TestimonyArguments.BornOfAVirgin.Sources.Versions — the Hebrew, the Syriac, and a reply

Three citations that say more than a label can: what the oldest Hebrew copy of Isaiah reads at 7:14, what the Syriac Peshitta reads and what can be said of who wrote it, and the reply to the lexical objection that leaves the word's sense aside, with the fathers who made it. Cited here and dispatched from cite by name, for the reason Sources.Wegner gives.

qumranConfirmsAlmahCited

qumranConfirmsAlmah. What the oldest Hebrew copy of Isaiah reads. 1QIsaᵃ, column VI, line 29, has הנה העלמה הרה, as the Masoretic Text has it: read in Abegg's transcription, from Ulrich and Flint's text. The verse has other variants — יהוה for אדני, and וקרא, "and one shall call", for וקראת, "and she shall call" — but none at the word. 4QIsaˡ, the one other Qumran copy of the verse, preserves too little of it to witness either way. The scroll is dated by radiocarbon to 335–122 BC at one standard deviation, and by its hand to 150–125 BC (Jull et al. 14, 19).

So the Hebrew that both sides read is the Hebrew read before Christ, and neither Christians nor their opponents changed the word. That settles the text, not the sense: the scroll has the same word, and what it means is the dispute. consensus.

def qumranConfirmsAlmahCited : AtomMeta

peshittaRendersBtultaCited

peshittaRendersBtulta. What the Syriac reads, and nothing about who wrote it or why. Van der Kooij prints the reading (271). It is the Peshitta's only ܒܬܘܠܬܐ for עַלְמָה: at Genesis 24:43, Exodus 2:8, Psalm 68:26 and Song 1:3 and 6:8 it writes the cognate ܥܠܝܡܬܐ. Who made the version is disputed: Jews, for Bloch ("a work of Jewish hands outside of Palestine", 218 n.), or a Jewish Christian who knew the Greek Isaiah, for van der Kooij (276–77, 287). Whether its 7:14 is the translator's own reading, follows the Septuagint, or was changed later, Chen finds impossible to settle: its agreement with the Greek "prevents us from drawing any certain conclusion" (104–5). So it is cited for what it reads, and not as a Jewish witness to "virgin". consensus, for the reading.

def peshittaRendersBtultaCited : AtomMeta

maryFitsIsaianicDescriptionCited

maryFitsIsaianicDescription. The referential reply: Mary was a young woman of marriageable age and a virgin, so she answers Isaiah's description whatever עַלְמָה denotes. France on Matthew 1:23, with Rico and Gentry.

The fathers gave the same answer to the Jewish "young woman", where they granted it. Cyril of Alexandria: "κἂν εἰ λέγοιτο νεᾶνις ἡ παρθένος, οὐκ ἔξω κείσεται τοῦ εἶναι παρθένος", even if the virgin were called a young woman, she will not cease to be a virgin (PG 70, 204B). Cyril of Jerusalem: "though I assent to what they say, even so I find the truth" (Catechetical Lectures 12.21). Eusebius: Christ's entry by birth "as I and the Septuagint interpret it, of a virgin, or even according to the current Jewish rendering, of a young woman" (Dem. Ev. VII.1). Each, with Chrysostom (Homilies on Matthew 5), points to Deuteronomy 22, where the betrothed νεᾶνις of 22:24–27 is the παῖς παρθένος of 22:23.

def maryFitsIsaianicDescriptionCited : AtomMeta

TestimonyArguments.BornOfAVirgin.Sources.Wegner — the citations of the sign dispute

The atoms of the dispute over Wegner's objection, cited here and dispatched from cite by name. They are the parse of הָרָה, the pregnancy it reports, what that pregnancy is taken to show, and the fathers' sign argument against it with the near-term reply to that.

They sit apart because cite is one total function over every atom. It keeps that guarantee: each value below is reached from exactly one of its cases, so an atom still cannot go uncited. What moves is only where the citation is written, which keeps Sources.lean short enough to read.

harahIsPredicateAdjectiveCited

harahIsPredicateAdjective. Deliberately not the contested step, and granted throughout. Wegner puts it at "most likely" and cites Williams' grammar §75; Rydelnik parses the clause exactly the same way and draws the opposite conclusion from it, that the virgin is pregnant and the sign is therefore as deep as Sheol (Isa 7:11).

def harahIsPredicateAdjectiveCited : AtomMeta :=
  {
    label :=
      "הָרָה at Isaiah 7:14 is a predicate adjective: the עַלְמָה is pregnant",
    kind := PremiseKind.linguistic,
    source :=
      have __src :=
        wegnerOnAlmah (Bib.Locus.page 471)
          Confidence.wellSupported;
      { primary := __src.primary,
        supporting :=
          [Reference.work postellIsaiahMessianic (Bib.Locus.page 474),
            Reference.work youngImmanuelProphecy (Bib.Locus.pages 115 116)],
        tradition := __src.tradition, confidence := __src.confidence } }

isaianicAlmahIsAlreadyPregnantCited

isaianicAlmahIsAlreadyPregnant. Granted on both sides of the dispute over this verse: Wegner reads a present pregnancy and so does Rydelnik. What they disagree about is what kind of pregnancy it is.

def isaianicAlmahIsAlreadyPregnantCited : AtomMeta :=
  {
    label :=
      "The עַלְמָה of Isaiah 7:14 is already pregnant when the sign is given",
    kind := PremiseKind.interpretive,
    source :=
      have __src :=
        wegnerOnAlmah (Bib.Locus.pages 471 472)
          Confidence.wellSupported;
      { primary := __src.primary,
        supporting :=
          [Reference.work postellIsaiahMessianic (Bib.Locus.page 468),
            Reference.work youngImmanuelProphecy (Bib.Locus.pages 116 117)],
        tradition := __src.tradition, confidence := __src.confidence } }

pregnancyAtTheSignIsOrdinaryCited

pregnancyAtTheSignIsOrdinary. The hinge of Wegner's objection, and not a lexical claim at all. He gets it from the near-term reading of the sign: the child born within nine months, everything in the oracle discharged by 701 BC. Rydelnik, parsing הָרָה as Wegner does, denies it outright. So do the fathers, on the ground that an ordinary conception would be no sign, and signLine is that argument.

def pregnancyAtTheSignIsOrdinaryCited : AtomMeta :=
  { label := "The pregnancy Isaiah 7:14 announces is an ordinary conception",
    kind := PremiseKind.interpretive,
    source :=
      have __src :=
        wegnerOnAlmah (Bib.Locus.pages 476 478)
          Confidence.disputed;
      { primary := __src.primary,
        supporting :=
          [Reference.work postellIsaiahMessianic (Bib.Locus.page 474)],
        tradition := __src.tradition, confidence := __src.confidence } }

isaianicAlmahIsNotAVirginCited

isaianicAlmahIsNotAVirgin. Wegner's conclusion about the referent. Postell states the step it rests on baldly: "since the עַלְמָה in Isaiah 7:14 is already pregnant, she obviously cannot be a virgin" (468).

def isaianicAlmahIsNotAVirginCited : AtomMeta :=
  { label := "The עַלְמָה of Isaiah 7:14 is not a virgin",
    kind := PremiseKind.interpretive,
    source :=
      have __src :=
        wegnerOnAlmah (Bib.Locus.pages 471 472)
          Confidence.disputed;
      { primary := __src.primary,
        supporting :=
          [Reference.work postellIsaiahMessianic (Bib.Locus.page 468)],
        tradition := __src.tradition, confidence := __src.confidence } }

oneReferentSettlesDenotationCited

oneReferentSettlesDenotation. Wegner's method: Isaiah 7:14 is used as proof that the word cannot mean "virgin". Rico and Gentry deny the principle — "the analysis of the Immanuel oracle does not by itself allow one to draw a conclusion concerning the meaning of the word" — and hold that the other occurrences settle it the other way (quoted at Postell 468 n. 22).

def oneReferentSettlesDenotationCited : AtomMeta :=
  {
    label :=
      "What the עַלְמָה of Isaiah 7:14 turns out to be settles what the word denotes",
    kind := PremiseKind.linguistic,
    source :=
      have __src :=
        wegnerOnAlmah (Bib.Locus.pages 471 472)
          Confidence.disputed;
      { primary := __src.primary,
        supporting :=
          [Reference.work postellIsaiahMessianic (Bib.Locus.page 468),
            Reference.work ricoGentryInfantKing (Bib.Locus.page 152)],
        tradition := __src.tradition, confidence := __src.confidence } }

otherClearAlmahCasesAreVirginsCited

otherClearAlmahCasesAreVirgins. Postell at 468 n. 22, of the three passages Wegner calls clearest. Marked plausible rather than wellSupported because it is stronger than Wegner's own text: Genesis 24:43 is uncontested, but Wegner's discussion of Song 6:8 allows that some of the עֲלָמוֹת in the harem would not be virgins.

def otherClearAlmahCasesAreVirginsCited : AtomMeta

signMustBeExtraordinaryCited

signMustBeExtraordinary. Origen's form of it: "What kind of sign, then, would that have been — a young woman who was not a virgin giving birth to a child?", tied to the sign offered "in the depth or in the height" (Cels. I.35). Justin (Dial. 84) and Irenaeus (Haer. III.21.6) argue the same, and so does every other father the library has read on the verse:

• Tertullian: a young woman's pregnancy, "a daily occurrence", "cannot possibly seem anything of a sign" (Answer to the Jews 9);
• Eusebius (Dem. Ev. VII.1);
• Cyril of Jerusalem: "the sign certainly must be something astonishing" (Cat. 12.22);
• Chrysostom: "that which is a sign must of course be beyond the course of common events" (Hom. Matt. 5);
• Jerome: the sign "novum debet esse atque mirabile", must be new and wonderful (on 7:14, PL 24, 107D);
• Cyril of Alexandria (PG 70, 204C);
• Theodoret: "Οὐδεὶς δὲ σημεῖον καλεῖ τὸ καθ' ἑκάστην γινόμενον ἡμέραν", no one calls a sign what happens every day (PG 81, 276D).

Rydelnik makes the move today, as Postell reports (474).

disputed, though the fathers are unanimous: a rating says whether competent readers contest a claim now, and two do. Wegner grants that the sign offered at 7:11 would have been miraculous, but holds that a sign may be an everyday occurrence and reads the one given at 7:14, after Ahaz refused the first, as one (469–470, 477–478); Rhodea holds that a sign does not require a miracle, and that 7:11 does not make this one (64 and n. 10).

def signMustBeExtraordinaryCited : AtomMeta

ordinaryConceptionIsNoMarvelCited

ordinaryConceptionIsNoMarvel. Irenaeus: "what great thing or what sign should have been in this, that a young woman conceiving by a man should bring forth — a thing which happens to all women that produce offspring?" Justin asks why God would give "a sign which is not common to all the first-born sons" (Dial. 84). consensus, because the rival grants it: its point is that the sign need not be a marvel, not that an ordinary conception is one (Rhodea 64).

def ordinaryConceptionIsNoMarvelCited : AtomMeta :=
  {
    label :=
      "An ordinary conception is nothing extraordinary: it happens to all women",
    kind := PremiseKind.interpretive,
    source :=
      {
        primary :=
          Reference.work irenaeusAgainstHeresies
            (Bib.Locus.sectionRef "III.21.6"),
        supporting :=
          [Reference.work justinDialogue (Bib.Locus.sectionRef "84"),
            Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 64)],
        tradition := Tradition.christianTypological,
        confidence := Confidence.consensus } }

isaianicSignsAreOrdinaryEventsCited

isaianicSignsAreOrdinaryEvents. What the text says: Rhodea lists non-supernatural signs "including elsewhere in Isaiah" (64), and Wegner a sign as "a common, everyday occurrence that has significance because of what it means, foretells, or predicts" (470). Rydelnik, as Postell reports him (474), grants the first of them: Isaiah's children are the "signs and wonders" of 8:18.

def isaianicSignsAreOrdinaryEventsCited : AtomMeta :=
  {
    label :=
      "Signs elsewhere in Isaiah are ordinary events: his children, 8:18",
    kind := PremiseKind.textual,
    source :=
      { primary := Reference.scripture Scripture.ordinaryIsaianicSigns,
        supporting :=
          [Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 64),
            Reference.work wegnerVirginBirths (Bib.Locus.page 470)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

signDatedByAChildsInfancyCited

signDatedByAChildsInfancy. What 7:16 says, and common ground about which child is left open: Wegner reads it of the child of 7:14 (477), Rydelnik of Shear-jashub (Postell 474), and Compton of a child whose infancy only measures the time (14).

def signDatedByAChildsInfancyCited : AtomMeta :=
  { label := "Isaiah 7:16 dates the deliverance by a child's infancy",
    kind := PremiseKind.textual,
    source :=
      {
        primary :=
          Reference.scripture
            [Scripture.verseIn TextualTradition.masoretic
                { book := Book.isaiah, chapter := 7, verse := 16 }],
        supporting :=
          [Reference.work wegnerVirginBirths (Bib.Locus.page 477),
            Reference.work comptonImmanuelProphecy (Bib.Locus.page 14)],
        tradition := Tradition.criticalScholarship,
        confidence := Confidence.consensus } }

TestimonyArguments.BornOfAVirgin.Sources — a citation for every atom

cite is total, so an atom without a citation does not compile. This is the file that makes that obligation concrete: every atom, each with a prose statement of what it asserts, a classification, and who says so at what pinpoint with what confidence.

It was once the largest file in the argument, and the atoms of its four disputes are now cited in modules of their own: Sources.NearTerm for the dispute over the critical denial, Sources.Wegner for the dispute over Wegner's objection, Sources.Septuagint for the dispute over the Septuagint's word, Sources.Versions for the Hebrew text, the Syriac, and the referential reply, and Sources.Genesis for the dispute over the woman's seed. cite reaches each of those citations by name from one of its cases, so it is still one total function, and a new atom still cannot be left out of it.

Several Source values recur across it and are defined in Atoms. Where an atom cites one of them with something further, it says { ... with supporting := }, so what a reader sees is the part that differs.

Inline comments carry the qualifications that do not fit a confidence field — why a premise is marked disputed when the tradition holding it is confident, which scholar is not being cited for a claim and why.

cite

Citation and classification for every atom. Total, so nothing is uncited.

def cite : Claim → AtomMeta

TestimonyArguments.BornOfAVirgin.Lines — the steps, and the lines of reason

Every inference this argument makes, and the four strands they compose into.

Inference steps carry no confidence field of their own — a step is a claim that these premises license that conclusion, which is a different kind of claim from an atom, and the library does not pretend to grade it. Where a step is contestable even though the atoms it joins are well supported, the docstring says so; berryBlocksExclusion is the clearest case.

Inference steps

One per strand, each delivering the same criterion, plus the steps that close the argument and the steps the rivals need. Keeping them separate is what makes the load-bearing results possible: a strand can be removed without touching the others.

toCriterion

Isaianic strand: from the predictive reading, the lexical premise and Matthew's intent, the criterion follows.

genesisToCriterion

Protoevangelium strand: Genesis 3:15 promises a redeemer as "her seed"; a man's line is ordinarily counted through the father; and naming the seed as the woman's marks a birth with no human father. So the Messiah must be born of a virgin.

compositionalToCriterion

Compositional strand: from Isaiah 7's placement in an eschatologically framed unit, the principle that placement governs meaning, and the future birth that follows, the criterion follows.

The weak joint is the last step. Postell's argument delivers a miraculous birth; it is matthewIntendsFulfilment that says which miracle. A reader who grants the composition and stops short of Matthew is entitled to.

parityDefeatsNearTermExclusion

Postell's parity argument. Isaiah 9:5–6 and 11:1–10 are read as messianic without reservation, and they stand on the same near-term Assyrian timeline as 7:14 — the Assyrian invasion of 8:7–8, the oppressor's rod of 10:5. So a near-term geopolitical setting cannot be what rules out messianic reference, because if it were it would rule out 9 and 11 as well.

This is a second, independent defeater of the same critical step that Berry's objection attacks, and it is the stronger of the two: Berry says the near-term fulfilment is unclear, while parity says the near-term setting was never the right kind of reason.

micahToCriterion

Michean strand: from the maternal-only wording and the inference drawn from it, the criterion follows.

magisterialToCriterion

Magisterial strand: from papal teaching and the authority granted it, the criterion follows. Encoded, but deliberately kept out of christian.

criticalExclusion

The critical inference, made explicit: granted that Isaiah 7:14 was a sign to Ahaz, and that such a sign is not also a prediction of a virgin conception, the predictive reading is denied.

The earlier encoding of this module simply asserted the denial as a premise of critical. That was a weaker rival than the critical case actually is, and it left nothing for an objection to engage.

berryBlocksExclusion

Berry's objection: if how the sign was fulfilled in Ahaz's own day is itself unsettled, the near-term reading is not secure enough to exclude a further referent.

The step is contestable even though both atoms it joins are wellSupported — an unclear fulfilment is still a fulfilment, and Brown would answer that Isaiah 8:3–4 settles the referent well enough. The step is rated in berryLine, where it is cited disputed.

micahParityDefeatsNearTermExclusion

Postell's second counterexample: an oracle set against the Assyrian invasion, read messianically, so a near-term Assyrian setting does not exclude a messianic sense. The same inference as parityDefeatsNearTermExclusion, from a different oracle in a different book (Postell 481 n. 72).

timetablePassesToMaherShalalHashBaz

Motyer's inference: the sign of 7:14 is given to the dynasty, and the timetable that answers Ahaz's crisis passes to Maher-shalal-hash-baz, so the child of 7:14 is not a near-term sign to Ahaz. "Either we must identify Maher-shalal-hash-baz with Immanuel, or we must project Immanuel into the undated future" (Motyer 1970, 124).

This is the contested part of his reply, and it is a step rather than an atom on purpose, as Berry's and Postell's are: the two atoms it joins are what the text says, and the inference is what a reader who identifies the two children denies, and motyerLine rates it disputed for that reason.

The referential strand

Sense against reference. The steps below never claim that עַלְמָה means virgin; they claim that a virgin is an עַלְמָה, which is a different and far cheaper claim, and then ask what the lexical objection is left with.

toDescriptionFit

If virginity is compatible with the denotation of עַלְמָה, and Mary was both an עַלְמָה and a virgin, then Mary answers Isaiah's description — without the word having to carry the sense.

descriptionFitDefeatsLexicalDemand

... and if she answers it, the fulfilment claim never needed the lexical sense in the first place.

lexicalObjection

The lexical objection in full: עַלְמָה does not denote virginity, Matthew's claim requires that it does, so the fulfilment claim fails. Stated as the objector would state it, so that the reply has something real to answer.

versionalObjection

The versional route to the lexical premise: the Targum and the Three read the broad term, so the narrow sense is not the word's.

compatibilityDissolvesDivergence

The tension, dissolved. If virginity is compatible with עַלְמָה, the versions are not contradicting one another about the referent at all: the Septuagint, if its παρθένος already meant "virgin" (Dispute.Septuagint), and the Peshitta render with the narrower term, the Targum and the Three with the broader one, and both are faithful renderings of a word whose denotation admits both. The divergence stops being evidence about the sense.

Why the Peshitta has the narrower term is not settled. It is its only ܒܬܘܠܬܐ for עַלְמָה, and whether that is its translator's reading of the woman, the Septuagint's influence, or a later Christian hand, Chen finds impossible to decide (104–5). The step needs only that the rendering is a faithful one, not why it was chosen.

toFulfilment

From the criterion and the historical claim, the fulfilment follows.

Wegner's grammatical objection, and the circle Postell finds in it

The sharpest form of the lexical case. Each link is a step of its own, because the result worth having is not whether the objection is valid — it is — but which link carries its weight, and where that link comes from.

harahYieldsPresentPregnancy

Wegner's grammatical step: if הָרָה is a predicate adjective, the עַלְמָה of the sign is pregnant already, at the moment the sign is given.

ordinaryPregnancyExcludesVirginity

... and if that pregnancy is an ordinary conception, the woman it describes is not a virgin.

The second conjunct does all the work, and it is not a grammatical claim. Rydelnik parses הָרָה exactly as Wegner does and reads the same clause as the miracle itself — the virgin is pregnant — which is available to him precisely because the parse leaves this open.

referentYieldsLexicalConclusion

... and if what the one clear Isaianic referent turns out to be settles what the word denotes, the lexical conclusion follows.

readingSuppliesOrdinaryPregnancy

Where the ordinary pregnancy comes from. Not from the grammar: from the near-term reading of the sign, which has the child born within nine months and the whole oracle discharged by 701 BC.

This is Postell's charge, written as a formula rather than repeated as a complaint: "because Wegner rejects the messianic interpretation on grammatical-historical grounds, he assumes that עַלְמָה cannot mean 'virgin' in Isaiah 7:14" (468 n. 22).

lexicalConclusionTellsAgainstPrediction

The return leg. The lexical conclusion is then turned against the predictive reading, which is what the critical case does with it and what critical already assumes.

Wegner's own version of this step is weaker — Postell reports it as decreasing the likelihood of a virgin-birth prediction without ruling it out (469) — and the encoding states the strong form on purpose. The strong form is the one on which the two legs make a closed circle, and stating it is what lets circle_leaves_the_lexical_conclusion_open be checked rather than asserted. On the weaker form the loop is evidential rather than deductive, which is the difference between a vicious circle and mutual support.

usageParityBlocksReferentInference

Postell's usage parity. If a single clear referent settled the denotation, the other clear עַלְמָה passages would settle it in the opposite direction, since the women there are virgins. So that principle is not available to the objection: it proves too much, and the wrong way.

The fathers' sign argument, and the near-term reply

Wegner's objection needs the pregnancy to be an ordinary one. The oldest Christian answer to the near-term reading denies exactly that, and it does so without touching the word: the oracle promised a sign, and an ordinary conception would have been none.

extraordinarySignExcludesOrdinaryPregnancy

The sign argument. If the sign of 7:14 must be extraordinary, and an ordinary conception is nothing extraordinary, the pregnancy the sign announces is not an ordinary one.

The step assumes that the conception is the sign rather than one part of it. Wegner counts three parts in 7:14 and more in 7:15–16 (469, 477), but he does not grant the first ground and deny the conclusion: he denies the first ground.

ordinarySignsAnswerTheDemand

The near-term reply. Signs elsewhere in Isaiah are ordinary events, and this one is dated by a child's infancy, so its point is its timing and it need not be extraordinary.

The Septuagint, and what its word meant

Jews translated Isaiah into Greek before Christ and wrote παρθένος. What that shows depends on what παρθένος meant to them, and the steps below keep the two questions apart: what the translator wrote, and what the word he wrote meant.

septuagintReadsAVirgin

The Septuagint as a witness. A Jewish translator, before Christ, chose for the woman of 7:14 a word that means a virgin; so he read her as one.

dinahShowsTheOlderSense

Wegner's case that the word's sense shifted. In early Greek παρθένος meant a young woman, with or without virginity; the Septuagint calls Dinah one at 34:3, and the noun there describes her as she then was, no longer a virgin; so in the Septuagint's day the word meant "young woman", and the sense "virgin" came later.

usageShowsTheVirginSense

The case from usage. Rico and Gentry's: the Jews who rejected the Christian reading of 7:14 rejected the word itself, Trypho reading "the young woman" and the Three writing νεᾶνις. With it the library's own addition: the Greek Isaiah's παρθένος renders בְּתוּלָה wherever else it occurs. So the word meant a virgin.

translatorsReadingFixesTheWord

From the translator's reading to Isaiah's word. If the first translator read the woman of 7:14 as a virgin, the word Isaiah used of her denotes one.

The step the Septuagint is usually asked to take, and the one its grounds do not supply: it has to be granted separately, and it is rated disputed.

Irenaeus takes it because he holds the Greek inspired: the seventy elders, translating apart, agreed "in the very same words", so that "the Scriptures had been interpreted by the inspiration of God" (Against Heresies III.21.2).

Bratcher and Brown grant the ground and deny the step. Bratcher holds that the translator meant "a young woman, at that time virgin" (115), and that עַלְמָה "is neutral, so far as virginity is concerned" (105): "even if in all occurrences of the word in the Old Testament it were proven that the 'almah in each case was, in fact, a virgin, that would not prove that 'almah in Isaiah 7:14 means 'virgin'" (106). Brown holds that the translator's choice "represented a deliberate preference for understanding the young woman of Isa 7:14 as a virgin" (Birth of the Messiah 148), and that עַלְמָה puts "no stress on her virginity" (147). Walton, who doubts the ground itself, denies the step even if it is granted: "it is illegitimate to use the LXX translation to override clear lexical material in the Hebrew text", and "at best the LXX would indicate an interpretational preference rather than a linguistic necessity" (293).

Bratcher's and Brown's reason is that a rendering can follow the woman described rather than the word. The translator of Genesis wrote παρθένος for the עַלְמָה Rebekah (24:43), whom the story has already called a virgin (24:16): "historically correct — since Rebekah was a virgin", Bratcher says, but it "does not precisely translate the Hebrew" (113). Jerome reads Rebekah the other way, as showing that עַלְמָה denotes a virgin (Against Jovinianus I.32). Elsewhere the Septuagint's translators render עַלְמָה with νεᾶνις four times (Exodus 2:8; Psalm 67:26, 68:25 in English Bibles; Song 1:3; 6:8) and with νεότης, "youth", once (Proverbs 30:19), as Rahlfs's text shows; Rhodea counts the νεᾶνις cases (67 n. 34). These are other translators than Isaiah's, as the translator of Genesis 34:3 is. That is also how this argument's referential strand reads the versions (compatibilityDissolvesDivergence).

Genesis 3:15, and what "her seed" says of a father

The protoevangelium strand holds that the seed being named as the woman's marks a birth with no human father. The steps below take apart what "marks" can mean: that the wording itself signifies such a birth, which Luther argues and Leupold, Keil and Lewis deny, or that it fits one once fulfilled, which Leupold and Keil grant.

herSeedSignifiesNoFather

Luther's step. Genesis 3:15 names the seed as the woman's, it is the first promise of a redeemer, and a man's seed is ordinarily reckoned through him; so the wording itself signifies a birth with no human father.

posterityExplainsTheWording

Leupold's step. "Her seed" is first collective, the woman's posterity, and the seed is named hers because the serpent deceived her; so the wording does not itself signify a birth with no human father.

ordinaryBirthsAnswerTheWording

Lewis's step. Genesis speaks of a woman's seed in ordinary births too; so the woman's seed at 3:15 does not by itself signify a birth with no human father.

heReadsOneDescendant

The Greek's "he". The Greek refers to the neuter seed with a masculine pronoun; so its translator read the seed as one person.

The lines of reason

Four strands converge on the criterion, and each is a Line: its own grounds, its own licensing step, and what it delivers. The packages are assembled from these rather than from flat premise lists, so a variant package is a named difference — one line on different grounds — instead of twenty premises retyped with one missing.

grounds are the premises a line contributes of its own. What the strands hold in common (Mary's conception, the agreement of the two narratives) is passed to caseOf as shared, because it belongs to no single strand.

isaianicLine — Isaianic strand (Isaiah 7:14)

The Isaianic line. The predictive reading, the lexical premise, the Septuagint's rendering, and Matthew's quotation and intent. Its hinge is almahMeansVirgin, and the whole lexical dispute is about that one ground.

protoevangeliumLine — Protoevangelium strand (Genesis 3:15)

The protoevangelium line. Genesis 3:15 read as the promise of a redeemer, a man's line counted through the father, and the claim that naming the seed as the woman's marks a birth with no human father. That claim is its hinge (seedOfTheWomanImpliesNoHumanFather), and Results.Genesis says what it can bear, read either way.

micheanLine — Michean strand (Micah 5:2–3)

The Michean line. The maternal-only wording of Micah 5:3 and the inference drawn from it. Its hinge is an argument from silence, and the rival says so.

compositionalLine — Compositional strand (Isaiah 2–12)

The compositional line. Isaiah 7's placement in an eschatologically framed unit, the principle that placement governs meaning, and the future birth that follows. Its hinge is compositionGovernsMeaning.

magisterialLine — Magisterial strand (papal teaching)

The magisterial line. Papal teaching and the authority granted it.

Encoded as a line like the others and deliberately kept out of christian: its second ground is one this library's author does not grant. Keeping it a line rather than folding it into a package is what lets magisterial_authority_is_load_bearing ask what the route is worth on its own.

referentialLine — Referential reading: a virgin is an עַלְמָה

The referential line. The shared lexical ground, the Rebekah datum, and two claims about Mary — that she was a young woman of marriageable age, and that she conceived as a virgin, which is cited disputed — delivering that she answers Isaiah's description without the word having to carry the sense. The fathers answer the Jewish "young woman" the same way: Cyril of Alexandria, "even if the virgin were called a young woman, she will not cease to be a virgin".

The scroll's reading is a ground because the reply is about what the word means, not which word Isaiah wrote: 1QIsaᵃ, copied before Christ, has the Masoretic Text's עַלְמָה. If the Hebrew were in doubt the dispute would not be about the sense alone, and the reply would have more to answer.

versionalLine — Lexical objection from the ancient versions

The versional line, stated as the objector would state it: the Targum and the Three read the broad term, Qumran settles the Hebrew, and Matthew's claim is taken to need the narrow sense — so the word does not denote virginity.

wegnerLine — Wegner's grammatical objection (Isaiah 7:14)

The Wegner line. The predicate-adjective parse, the near-term setting of the sign, the ordinary pregnancy that setting supplies, and the principle that the Isaianic referent settles the word's denotation — delivering that the עַלְמָה of the sign is pregnant when it is given.

The line stops at the pregnancy and the two further moves are closing steps, because that is where the argument actually divides: the parse is common ground, and everything contestable happens after it.

lexicalSenseRequiredForFulfilment is not among its grounds and is not Wegner's view. He holds a prophetic pattern, on which Matthew's use of the verse survives the lexical finding, so the objection stops at the lexical conclusion rather than running on to the fulfilment claim.

wegnerClosingSteps

The two steps that carry Wegner's line to its lexical conclusion: the pregnancy excludes virginity, and the referent settles the word. Passed to caseOf as closing steps, so that a variant can change the grounds without retyping them.

signLine — The fathers' sign argument (Isaiah 7:11, 14)

The fathers' sign argument. Justin, Irenaeus and Origen, and every other father the library has read on the verse, and Rydelnik today: the sign of 7:14 must be extraordinary, an ordinary conception is not, so the pregnancy is no ordinary one. It denies the ground of Wegner's line that the parse does not supply, and nothing else.

Its step is rated plausible: no source cited here grants both grounds and holds the pregnancy ordinary. The rival denies the first ground instead, and the grounds are rated separately. It is not rated higher, because the step reads the conception as the whole of the sign.

ordinarySignLine — The near-term reply: a sign need not be a miracle

The near-term reply, as an argument: signs in Isaiah are ordinary events, and this one is dated by a child's infancy, so it need not be extraordinary. Wegner (469–470) and Rhodea (64–65).

septuagintLine — The Septuagint as a witness (Isaiah 7:14 in Greek)

The Septuagint as a witness. Irenaeus's argument: the Greek was made by Jews long before Christ, so its "virgin" cannot be a Christian reading put on the text. Its hinge is parthenosMeansVirgin, and the dispute over the Septuagint is about that one ground.

The step draws out its grounds: a translator who chose for the woman a word that means a virgin described her as one. It is rated plausible: no reader cited here grants that the word means a virgin and denies that the translator called her one. Bratcher and Brown, who deny the next step, grant this one: the translator meant "a young woman, at that time virgin" (Bratcher 115), "a deliberate preference for understanding the young woman of Isa 7:14 as a virgin" (Brown 148).

Walton doubts the word itself, and that dissent is counted where it belongs, in the rating of the third ground. Against the step he offers one thing more, Archer's suggestion that the translator of Isaiah "consistently showed a tendency to be imprecise in his choice of Greek terms", which "could well be the explanation of the use of parthenos here" (293). That is a guess at why the translator wrote the word, not a reading of what he wrote, and it is not counted as a dissent. The translator's own text tells against it: everywhere else in his Isaiah, παρθένος stands for בְּתוּלָה (23:4, 37:22, 47:1, 62:5; isaiahUsesParthenosForBetulah). The step is not rated higher, because none of its readers argues for it beyond the word's sense.

The main contest is over the third ground, rated disputed; the witness is no stronger than that ground, so the step's rating changes no verdict.

driftLine — Wegner on παρθένος: the word had not yet come to mean 'virgin'

Wegner on παρθένος: in the Septuagint's day the word meant "young woman", and came to mean "virgin" only by the time of the New Testament (482–83). Held by Wegner, Rhodea and Meade; disputed by Rico and Gentry, and by Bratcher. Rhodea follows Wegner, with an "apparently", and draws from Genesis 34:3 that the word "need not refer to a virgo intacta" (67). Meade holds the same, "cf. Dina in Gen 34:3", and that by Justin's day the word had been "hijacked or used to mean 'chaste woman' only" (comment of 9 January 2013).

Three grounds: the older usage; what the Greek of 34:3 reads; and that the noun there describes Dinah as she then was. The third is Wegner's own — Dinah "is called a παρθένος even after she was raped by Shechem" (483) — and Miller's, and it is not the text's: the order of the verses puts Shechem's love after his act, not the noun's description (parthenosDescribesDinahAsSheThenWas). It is written out, not left inside the step, so that a reader sees it.

The step is rated disputed, because two readers grant all its grounds and deny its conclusion. Rico and Gentry grant the older usage, that the Greek calls Dinah a παρθένος, and that she was then no longer a virgin; but Genesis 34:1–3 is "the exception that proves the rule" (21), an archaism of the Greek Pentateuch, whose language is "more elevated and classical than the language of the later texts" (18). Bratcher grants all three — "at first the word was used in a general sense of 'girl', 'young woman'" (112), and Dinah "was no longer, therefore, a 'virgin'" — and still finds that "parthenos definitely means 'virgin' in the LXX; only very exceptionally (and, inexplicably, in Gen. 34:3) is it used otherwise" (113). The Greek Isaiah, a later book by another translator, uses the word elsewhere only for בְּתוּלָה (isaiahUsesParthenosForBetulah).

Delling, in the standard theological dictionary, reads the Septuagint's usage at Isaiah 7:14 as demanding "no more than the sense of a 'woman untouched by a man up to the moment of the conception'" (TDNT 5.833, as Rhodea quotes him, 67 n. 42): a virgin until then, whatever followed. And the Greek Pentateuch, the corpus Genesis 34:3 comes from, uses the word in its laws where virginity is the point (lawsLine). One passage in the broader sense does not show that the narrower sense was missing.

usageLine — Rico and Gentry: παρθένος means 'virgin' in the Greek of the Scriptures

The case from usage. Held by Rico and Gentry; disputed by Davidson and Meade. Rico and Gentry argue from the Jewish objection itself: "Otherwise the discussion of Justin and Trypho and the change from parthenos to neanis by AQUILA, SYMMACHUS, and THEODOTION in Is 7:14 would have no raison d'être" (21).

The first ground, the Greek Isaiah's other uses of the word, is the library's own addition, read from the two texts: it is the usage of the translator whose word is in question, as Genesis 34:3 is not. What the texts read is not in dispute; what it shows can be. It shows the sense "virgin" only if בְּתוּלָה means a virgin where he renders it, and two of the four are figures for a city, the "virgin daughter" of Zion (37:22) and of Babylon (47:1). Bratcher, who argues from the same correspondence across the whole Septuagint — 45 of the 52 times בְּתוּלָה occurs — warns that where it means only a young girl, or is used figuratively, "in such cases parthenos in the LXX will have the same meaning" (113).

The step is rated disputed, on two readers who grant the Jewish objection and read it the other way: the revisers were answering a sense Christians had put on the word, not the sense its translator gave it. A. B. Davidson: the Three wrote νεᾶνις "possibly to evade the technical sense put on the word by the Christians", παρθένος having been "used generally for 'girl' or 'young woman'" (A Dictionary of the Bible II, 1899, 456). John Meade, a Septuagint scholar whose doctoral supervisor was Gentry, so that the dissent comes from within Gentry's own school, finds the revisers' change sensible "only in a context where παρθενος has been hijacked or used to mean 'chaste woman' only (which by the time of Justin Martyr, it clearly had been, since Trypho never disputes this point but only relies on his different version which had νεανις)"; for "παρθενος simply means young woman in this verse and in other places in the LXX" (comment of 9 January 2013).

The dissents on both rival steps are brief. Davidson hedges his account of the Three with a "possibly", though not his account of the word; Meade's is a blog comment, revising his own earlier view toward "young woman". Against Wegner's step, Rico and Gentry give a reason, the archaism of the Greek Pentateuch, and Bratcher calls Genesis 34:3 inexplicable without explaining it. The ratings weigh none of this: each step has a cited reader who grants its grounds and denies its conclusion, and so each is disputed. Wegner's reading can be held with all three grounds here too — it is the countermodel in usage_rests_on_its_inference — though he does not discuss the Three or Trypho. The rating matters: rated higher, this step would decide the dispute over the Septuagint in the witness's favour (Dispute.Septuagint says why).

matthewReadsTheGreek

Scripture's reading of the Greek word. Matthew quotes the Septuagint's ἡ παρθένος of a woman who conceived before she and Joseph came together; so in the text he quotes, the word has the sense "virgin".

matthewReadingSource

The citation for Scripture's reading of the Greek word, at a confidence: Westminster's rule that Scripture interprets Scripture (I.ix), Irenaeus on the apostles' agreement with the Seventy (III.21.3), and Wegner, who grants Matthew's use and denies the step (483).

def matthewReadingSource : Confidence → Source :=
  fun c =>
    {
      primary :=
        Reference.work westminsterConfession (Bib.Locus.sectionRef "I.ix"),
      supporting :=
        [Reference.work irenaeusAgainstHeresies
            (Bib.Locus.sectionRef "III.21.3"),
          Reference.work wegnerVirginBirths (Bib.Locus.page 483)],
      tradition := Tradition.reformedProtestant, confidence := c }

matthewLine — Scripture interprets Scripture: Matthew quotes ἡ παρθένος of Mary

Scripture interprets Scripture: Matthew's quotation. The Gospel quotes the Greek of Isaiah 7:14, ἡ παρθένος, of Mary, who conceived "before they came together" (1:18) and whom Joseph "knew not until she had borne a son" (1:25). If Scripture is its own interpreter — "The infallible rule of interpretation of Scripture is the Scripture itself" (Westminster I.ix) — the word in the text Matthew quotes has the sense he gives it. Its grounds are Scripture alone.

Like the case from the laws, it concludes that a passage of the Septuagint uses the word in the sense "virgin", and so, by what a usage is, that the sense was the Septuagint's, which Wegner denies. It says nothing of the Hebrew עַלְמָה.

Cited, the step is disputed. Wegner grants both grounds — the word was "a suitable term to describe Mary in the first century AD" — and denies the conclusion: it "changed in meaning from 'young woman' to 'virgin'" between the translator and Matthew (483). Whether that dissent counts is the question the standards answer differently: under the evidence and tradition standards it is a critique; under the scriptural standard, a dissent from a step whose grounds are all Scripture counts only if it rests on Scripture alone, and Wegner's rests on early Greek usage. Dispute.Matthew computes the hearing under each.

herSeedLine — Luther on 'her seed': the wording itself signifies no human father

Luther on "her seed": the wording itself signifies a birth with no human father. Held by Luther and Henry, and, as "a hint", by Akin and Miravalle; disputed by Leupold, Keil and Lewis. Irenaeus reads the verse of the Virgin's son, though he does not argue from the wording.

Luther: the seed of other women "might rather be said to have been the seed of the man. But that which was born from Mary was conceived of the Holy Ghost and was the true Seed of Mary" (Luther on the Creation 298–99). He finds the sense in the words of Genesis, and holds that Isaiah later "threw some additional light" on it: "For it was then made certain that this Seed would not be born from the union of a man and a woman" (298).

The step is rated disputed, because readers who grant all three grounds deny the conclusion. Leupold reads the verse as the promise of the victor — "Both the ultimate victory and its achievement by the seed of the woman are taught with unequivocal plainness by this word" (167). Asked whether the expression is "so phrased in reference to Mary and the virgin birth", he answers "Not primarily, but at least incidentally", and holds that "the expression used does not specifically prophesy the virgin birth" (169). Keil grants that the promise "culminates in Christ", and finds the virgin birth in its fulfilment, "even if the words had reference first of all to the fact that the woman had been led astray by the serpent", "even in its apparently casual form" (102). Lewis grants that "it is normal in Hebrew to describe descendants by the noun zeraʿ" (299); he doubts the promise reading itself, suggesting it came from "Making the woman to be the addressee", but argues on grounds that do not need that doubt: "To say that the passage is messianic does not necessarily imply that it is virgin-birth messianic" (319).

posterityLine — Leupold on 'her seed': her posterity, named for the deception

Leupold on "her seed": the wording names the woman's posterity, and names the woman because she was deceived; it does not itself signify a birth with no human father. Held by Leupold and Keil, whose two grounds Calvin gives too; disputed by Irenaeus and Henry.

Leupold: "the expression used does not specifically prophesy the virgin birth, but it coincides and agrees with it under divine providence. For it is not to be forgotten that the expression 'her seed' in its first meaning is a collective noun and includes all who are enrolled in the struggle against Satan, without being themselves virgin born" (169).

The step is rated disputed. Irenaeus grants both grounds. The enmity is kept up between the serpent and the woman's seed "until the seed did come appointed to tread down his head" (Against Heresies III.23.7), and "it was by means of a woman that he got the advantage over man at first" (V.21.1); yet he reads the verse as preaching "He who should be born of a woman, [namely] from the Virgin" (V.21.1), though without arguing from its wording. Henry gives the woman's name the same reason — "because she it was whom the devil had beguiled" — and still reads the seed as "of a woman only, of a virgin".

idiomLine — Lewis on 'her seed': Genesis says it of Hagar and Rebekah too

Lewis on "her seed": Genesis speaks of a woman's seed in ordinary births too, so the wording at 3:15 does not by itself signify a birth with no human father. Held by Lewis; disputed by Akin.

Lewis: "Had it been observed across history that Hagar's descendants whose ancestral father is Abraham are also projected with a feminine possessive suffix attached to zeraʿ (Gen 16:10), as also are Rebekah's descendants whose ancestral father is Isaac (24:60), the treatment of Gen 3:15 would likely have been different" (299–300). "A look at texts about Hagar and Rebekah in Genesis could have safeguarded interpreters from the whole misguided exegetical effort" (319).

The step is rated disputed, on one reader. Jimmy Akin, a Catholic apologist, does not discuss Hagar or Rebekah, but grants the point Lewis draws from them, that a woman's seed "is not outside the bounds of Hebrew expression", and still calls the wording "odd", and agrees with the "many" who have "rightly seen" it as "a hint of the Virgin Birth". A hint is less than a sign, and whether it denies Lewis's conclusion is arguable; it is the only dissent found.

greekHeLine — The Greek's 'he': the woman's seed read as one person

The Greek's "he": the translator of Genesis read the woman's seed as one person. Held by Collins, and by Martin as Collins quotes him; Collins calls the reading "generally acknowledged" (141). Rated disputed, on Philo, the earliest known reader of this Greek, who grants that it says "he" and reads it of the mind, a "barbarism" correct in meaning (Allegorical Interpretation III.188). Lewis leaves it open: the masculine "could be an oversight", and "it is possible that the translator reveals a messianic understanding" (300). What it does not reach in any case is whether that person has a human father (Results.Genesis).

The fulfilment of Genesis 3:15, and the critical reading

The strands above ask what the wording of Genesis 3:15 says. The reader's next question runs the other way: the Gospel tells of one who was born of a woman, was struck, and destroyed the devil. Does that fulfil the promise, and does the fulfilment confirm that it was a promise?

termsMetInJesus

The fulfilment. Each term of Genesis 3:15 met, as the New Testament names it: the woman's seed in the Son "made of a woman"; the serpent in "that old serpent, called the Devil"; its head crushed when the Son destroys the devil "through death"; his heel struck in his death, and the wound not the end of him in his rising. So in Jesus the promise is fulfilled.

fulfilmentConfirmsThePromise

The fulfilment confirms the promise. If in Jesus each term of Genesis 3:15 is met, the verse is a promise of him: the protoevangelium.

fulfilledInOneVirginBorn

Of the woman alone. If the promise is fulfilled in Jesus, and Jesus was conceived of a virgin, the seed in whom it is fulfilled had no human father.

formExcludesAPromise

Westermann's denial. "Her seed" is a line of descendants, and the verse is a punishment oracle on the serpent; such a form has no promise or prophecy, "even as its secondary meaning", so the verse is not the protoevangelium.

sceneMakesItAPromise

The scene read whole. The serpent speaks and twists God's command, as no animal does of itself; it is the instrument of an evil power; the blow falls on the serpent itself, "your head"; and God himself sets the enmity. So the sentence on the serpent is God's promise of victory over that power: the protoevangelium.

singularSyntaxNamesOne

The syntax of the striker. זֶרַע with singular verbs and pronouns denotes one descendant elsewhere; at 3:15b the striker is singular "he", against the serpent's own head; and the Greek translator read one person. So "her seed" at 3:15 is not only a line of descendants: the one who strikes is one of them.

fulfilmentSource

The citation for the fulfilment's step, at a confidence: the readers who argue it, and Westermann, who denies it.

def fulfilmentSource : Confidence → Source

fulfilmentLine — The fulfilment of Genesis 3:15: struck at the heel, he crushes the serpent's head

The fulfilment of Genesis 3:15, read from Scripture: every term of the promise is met in Jesus, as the New Testament itself names it.

• The woman's seed: God sent his Son, "made of a woman" (Galatians 4:4).
• The serpent: "that old serpent, called the Devil, and Satan" (Revelation 12:9; 20:2).
• Its head crushed: the Son shared flesh and blood "that through death he might destroy him that had the power of death, that is, the devil" (Hebrews 2:14); he "was manifested, that he might destroy the works of the devil" (1 John 3:8).
• His heel struck: he died, and rose the third day (1 Corinthians 15:3–4), a wound and not the end of him.

Irenaeus reads it so: the seed "appointed to tread down his head — which was born of Mary", against "that old serpent" (Against Heresies III.23.7), and the Lord "summed up in Himself this enmity, when He was made man from a woman, and trod upon his head" (IV.40.3). Hamilton: the one "born of woman (i.e., her seed, Gal 4:4) who 'nullified the one who has the power of death, that is, the devil' (Heb 2:14)—one might say he crushed the serpent's head" (53 n. 89). Keil: "In this sense Christ is the seed of the woman, who tramples Satan under His feet, not as an individual, but as the head" (102), with Romans 16:20 and 1 John 3:8. Leupold, of Christ's temptation and the cross: "the first crushing defeat that the seed of the woman administered … On the cross this victory was sealed" (170).

What the conclusion says, and what it does not. That in Jesus the promise is fulfilled: struck at the heel, he crushes the serpent's head. Calvin, Keil and Leupold each deny that "her seed" means Christ alone — Calvin finds the word "too violently distorted" by those who take it so, "for who will concede that a collective noun is to be understood of one man only?" — and each holds the conclusion as worded: "we must necessarily come to one head" (Calvin 170–71).

The texts it rests on, and how they are linked. Revelation's "that old serpent" names the serpent of the garden. Romans 16:20, "the God of peace shall bruise Satan under your feet shortly", is not counted: it is an allusion, and a disputed one, with Calvin (171), Keil (102) and Hamilton (42) for it, and Lewis ("one possible allusion", 303) and Collins (147 n. 24, "if Paul was alluding to this text at all") doubting it. Galatians 4:4 is cited for what it says, that the Son was made of a woman; whether Paul alludes to Genesis there is disputed too (sonMadeOfAWoman).

Its rating. disputed, on Westermann. He grants what every ground reads — none of them says the New Testament quotes Genesis 3:15 — and denies that the verse promises anyone, "even as its secondary meaning" (260), adding that "suggestions of a messianic interpretation are found in late Judaism, but not in the New Testament" (261). His reasons are the collective "seed" and the form of the verse (259–60): philology and form criticism, not a reading of Hebrews, 1 John or Revelation. Lewis, who holds that "The NT never speaks of Christ as the one who tramples the serpent" (303), denies that Scripture makes the link but not the conclusion, and is not counted.

confirmationSource

The citation for the step from the fulfilment to the promise, at a confidence: the readers who grant that Genesis 3:15 is fulfilled in Christ and call it, for that, the first promise of the gospel.

def confirmationSource : Confidence → Source :=
  fun c =>
    { primary := Reference.work leupoldGenesis (Bib.Locus.page 167),
      supporting :=
        [Reference.work keilDelitzschPentateuch (Bib.Locus.page 102),
          Reference.work calvinGenesis (Bib.Locus.pages 170 171),
          Reference.work collinsSyntacticalNote (Bib.Locus.page 146),
          Reference.work hamiltonSkullCrushingSeed (Bib.Locus.page 31),
          Reference.work irenaeusAgainstHeresies
            (Bib.Locus.sectionRef "IV.40.3")],
      tradition := Tradition.christianTypological, confidence := c }

confirmationLine — The fulfilment confirms the promise: Genesis 3:15 is the protoevangelium

The fulfilment confirms the promise. If in Jesus each term of the verse is met, the verse was a promise of him: the protoevangelium. This is not a deduction from Genesis alone. Reasoning "if the verse promised the Messiah, he would crush the serpent and be struck; Jesus did; so it promised him" would affirm the consequent. It is a step of its own: a promise whose every term is met in one person, as Scripture names them, is a promise of that person.

Rated plausible. No reader found grants that Jesus fulfils the verse and denies that it is a promise: everyone found who denies the promise, Westermann among them, denies the fulfilment too, and that dissent belongs to the fulfilment's step and to the claim that the verse is the protoevangelium. Everyone who grants the fulfilment calls the verse a promise: Leupold, who finds "the ultimate victory and its achievement by the seed of the woman … taught with unequivocal plainness" (167); Keil (102); Calvin (170–71); Collins, for whom the verse, read from the end, is God's threat "of an individual who will engage the snake in combat and win" (146); Hamilton, for whom "God's first act of judgment in the Bible is accompanied by his first promise of salvation" (31). Rated no higher, because the step adds little to what its ground already says: to fulfil a promise there must have been one.

aloneLine — The seed of the woman alone: the promise fulfilled in one born of a virgin

Of the woman alone. Granted that the promise is fulfilled in Jesus, and that Mary conceived him as a virgin, the seed in whom it is fulfilled had no human father. Irenaeus joins the two: "He who should be born of a woman, [namely] from the Virgin … was preached as keeping watch for the head of the serpent" (V.21.1).

The step only joins its grounds, and anyone who grants both grants it, so it is rated consensus. What it rests on is its grounds, and both are contested: the fulfilment on Westermann, the virginal conception on the historian this argument cites. It reads the fact of the birth back into the promise; it does not find the birth in the wording, which is Luther's claim and is weighed apart (Results.Genesis).

westermannLine — Westermann: a punishment oracle on a line of descendants, and no promise

Westermann's denial: Genesis 3:15 is no promise. "The parallelism makes it clear that 'seed' refers to a line of descendants and not to an individual" (259), and the verse is a punishment oracle on the serpent: "It is not possible that such a form has either promise or prophecy as its primary or even as its secondary meaning" (260). Encoded first, as the rival to the fulfilment.

Its grounds are philology and form criticism, and so is its step: none is a reading of another text of Scripture. Its first ground is contested in its own right (seedIsLineNotIndividual, and syntaxLine against it).

Rated disputed. Calvin grants both grounds — the seed is "the posterity of the woman generally", for "who will concede that a collective noun is to be understood of one man only?" (170), and the verse is the serpent's sentence — and denies the conclusion: the promise is in the curse, and "we must necessarily come to one head" (171). Keil, who reads the seed as "the human race" and Christ "not as an individual, but as the head" (101–2), denies it too.

sceneLine — The scene read whole: God's sentence on the serpent's power

The scene read whole, from the section and not the word alone: what Genesis 3 says of the serpent, of whom the blow falls on, and of who sets the enmity.

• The serpent speaks, and knows the command. It gives back God's word of 2:17 twisted, "Ye shall not surely die" (3:4). Collins: "the snake's wording of v. 4 reflects knowledge of 2:17", and "animals do not have faculty of speech in Bible, hence there is some intervention here" (146 n. 21).
• It is the instrument of an evil power. Delitzsch, as Collins quotes him: "an animal not speaking of its own accord, but as made the instrument of itself by the evil principle". Woudstra: "There is a diabolical subtlety in the serpent's suggestions which points to a sinister background to his words" (197). This ground is disputed (serpentIsTheInstrumentOfAPower).
• The blow falls on the serpent itself: "it is the head of the serpent, not that of his zeraʿ, which is in view here" (Woudstra 199).
• God sets the enmity: "a tremendous initiative for good, unexpected and unmerited" (Woudstra 203).

So the sentence on the serpent is a promise of victory over the power behind it. Collins: "the referent of the second person pronoun would actually be the dark power behind the snake" (146–47 n. 21), and "the 'promise' for the humans is an implicature of the punishment on the snake" (147 n. 22). Keil: "This foe is Satan, who incessantly opposes the seed of the woman and bruises its heel, but is eventually to be trodden under its feet" (101–2).

Its rating. plausible. Woudstra grants every ground and does not deny the conclusion: though "this passage does not explicitly predict ultimate victory of the woman's seed", "the One who set the enmity might also be regarded as implicitly guaranteeing the ultimate success of those who are on his side", and "the term 'protevangelium' may be rightly used to describe it" (203). Westermann, who denies the conclusion, denies that the serpent is more than an animal (261), and that dissent belongs to the ground. Von Rad, as Woudstra quotes him, denies a protevangelium from "the sense of the passage" and the collective "seed" (194); he is not shown to grant the grounds. Rated no higher, because the step reads a promise out of a curse, which Collins calls "an implicature" and Woudstra "implicit".

None of this is the reading of the readers before Christ: Jubilees, Philo and Josephus read the serpent as an animal or an emblem, and none of them reads the verse as a promise. It is an exegesis of the section, from its own words.

syntaxLine — The syntax of the striker: 'he' who strikes is one descendant

The syntax of the striker, against Westermann's "a line of descendants and not an individual". Collins: when זֶרַע "denotes a specific descendant, it appears with singular verb inflections, adjectives, and pronouns" (144), and "the singular pronoun hûʾ in Genesis 3:15 is quite consistent with the pattern where a single individual is in view"; "we might wonder if the singular hûʾ in Genesis 3:15 is used precisely in order to make it plain that an individual is being promised" (145). It is "he" who strikes "you", the serpent itself, not its seed (146 n. 21). The Greek translator read one person (lxxReadsOneDescendant). Alexander: the seed "must be understood as referring to a single individual and not numerous descendants" (363); Leupold (166–68) and Hamilton (32) agree.

What it concludes is worded as they hold it: "her seed" at 3:15 is not only a line of descendants, for the one who strikes is one of them, whether or not 15a also names her posterity. Collins allows the collective too, the Messiah "as the (primary) seed, and his followers as 'seed' by virtue of their relation to him" (148 n. 24).

Paul reads the singular "seed" of the promise to Abraham as one person: "He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ" (Galatians 3:16). That is a precedent for reading the word of one, not a reading of Genesis 3:15, and no reader found takes it as one; Calvin uses it so ("So Paul, from the seed of Abraham, leads us to Christ", 171). It is not counted as a ground.

Rated disputed. Keil grants the first two grounds — "the posterity of a man may consist of a whole tribe or of one son only", and the victory is "over the serpent itself" — and denies that "by the seed of the woman we are to understand one solitary person, one individual only" (101). Collins himself claims no more than consistency, from "a fairly low level of integration" (145–46), and Alexander notes that the same singular syntax is usually read collectively at Genesis 22:17–18a and 24:60 (364).

lawsFixTheSense

The laws' sense. The high priest's παρθένος is set against the widow, the woman put away, the defiled woman and the harlot, and the bride without τὰ παρθένια dies for playing the harlot; so in these laws παρθένος is used in the sense "virgin".

lawsSource

The citation for the laws' step, at a confidence: Bratcher, the lexica on τὰ παρθένια, and Miller, who denies the step.

def lawsSource : Confidence → Source :=
  fun c =>
    { primary := Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 113),
      supporting :=
        [Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 102),
          Reference.work liddellScottJones (Bib.Locus.page 1339),
          Reference.work muraokaLexiconSeptuagint (Bib.Locus.page 535),
          Reference.work lustLexiconSeptuagint (Bib.Locus.sv "παρθένια"),
          Reference.work millerBornDivine,
          Reference.work rhodeaDidMatthewConceive (Bib.Locus.page 67)],
      tradition := Tradition.christianHistoricalGrammatical, confidence := c }

lawsLine — The laws of the Greek Pentateuch: παρθένος in the sense 'virgin'

The case from the laws. Bratcher's, from the Greek of Leviticus 21 and Deuteronomy 22 (102, 113): two laws of the Greek Pentateuch, the corpus Wegner takes Genesis 34:3 from, in which virginity is what the law turns on. The laws are in the translators' own Greek, and they are not uses of the word of a virgin, which would show nothing of its sense; the passages it rests on are where the sense is the point (lawsUseParthenosAsVirgin).

It concludes nothing about Isaiah 7:14. What it shows is that "virgin" was already a sense of παρθένος in the Septuagint's Greek, which is what Wegner denies. The step from the two passages to the Septuagint's usage is not a step of the argument: it is what a usage "as a whole" means (Testimony.Ontology.Usage), and the meanings join the laws' sense to Rico and Gentry's claim and against Wegner's (Meanings.BornOfAVirgin.joins).

The step is rated disputed, on one reader. Robert J. Miller grants what the laws require: virginity matters "in the law that priests can marry only women who are virgins (Lev 21:13-14)", and the bride of Deuteronomy 22:13–21 is charged "with not being a virgin at the time of their marriage". But "that has to be inferred from the context": "Neither word means virgin", and "As in other Greek literature, parthenos in the Septuagint did not by itself connote what we mean by virginity", for where virginity matters the Greek adds "a parthenos who has not known a man" (Genesis 24:16) (Born Divine).

Miller is kept, as every cited reader is, and the page shows where his reading breaks. He says four things of the Greek. One is answered by a reading he does not take up, one is not answered here, and two do not hold of it.

• Genesis 34:3: "this term refers to a rape victim after she has been attacked". The Greek calls Dinah a παρθένος in the verse after Shechem lies with her; that the noun describes her as she then was is Miller's premise, not the text's. Rico and Gentry explain the verse as an archaism of the Greek Pentateuch; the status reading reads it under the law of the seduced παρθένος, as the name of the standing Shechem took (dinahLine).
• Genesis 24:16: where virginity matters, the Greek adds "a parthenos who has not known a man". The clause is the Hebrew's own, וְאִישׁ לֹא יְדָעָהּ, and the Greek renders it. What it shows about either word, the page does not settle.
• A young widow: "Lament like a parthenos dressed in sackcloth for the husband of her youth (Joel 1:8)". The Greek of Joel 1:8 calls the woman νύμφην, a bride; its παρθεν- word, τὸν παρθενικόν, is of the husband (read from Rahlfs's text).
• The translators "consistently used it to translate the Hebrew almah". They used it for עַלְמָה twice, at Genesis 24:43 and Isaiah 7:14, and elsewhere wrote νεᾶνις, as Rhodea, who holds Wegner's view, notes (67 and n. 34); the word they used consistently for was בְּתוּלָה (Bratcher 112–13).

And he does not take up τὰ παρθένια, the abstract noun by which Walton's own test would fix the sense. The step is cited disputed here, on him: it is the step's floor, and the dispute over the Septuagint weighs it there. What its register computes is another matter (Dispute.Miller). Evidence a text refutes is struck before his dissent is checked, and the Greek of Joel 1:8 refutes his young widow; struck of it, his dissent still denies the step through Genesis 34:3, and is a credible critique under the evidence and tradition standards. But his case from Genesis 34:3 cannot be defended in the dispute over the Septuagint: the status reading defeats it. So his dissent is overruled, and the step stands at the wellSupported its support is cited at.

seductionLawNamesDinah

The law's name for Dinah. The law of the seduced woman calls her a παρθένος after the man has lain with her, and sets what he owes by "the bride-price of virgins"; Genesis 34 tells Shechem's act in the words of that law and its neighbours. So when the Greek calls Dinah "the παρθένος" at 34:3, it names her by the standing he took, in the sense "virgin".

dinahLine — The law's name for Dinah: Genesis 34:3 read under Exodus 22:15–16

The status reading of Genesis 34:3. Wegner's case rests on one verse: after Shechem "lay with her and humbled her" (34:2), the Greek says he "loved the παρθένος, and spoke to her according to the mind of the παρθένος" (34:3). He reads the word as said of her as she then was, a woman no longer a virgin, so that it cannot mean "virgin". This line reads it the other way: as the name of the standing Shechem took from her. A noun that names a woman says who she is in the story, not what she is at the moment of the clause: a noun phrase is read at a time of its own, which the context gives, not at its verb's (Enç 1986), as Scripture names Rahab "the harlot" long after Jericho (Hebrews 11:31, James 2:25) and Matthew "the tax collector" after his call (Matthew 10:3). The order of 34:2 and 34:3 puts Shechem's love after his act; it does not put the noun's description there.

The law does exactly this. In the Greek Exodus a man who "deceives a παρθένος not betrothed and lies with her" shall endow her as his wife, or, if her father refuses, pay "the bride-price of virgins" (22:15–16). The woman he has lain with is still the law's παρθένος, and what he owes is a virgin's price. Genesis 34 tells Shechem's act in that law's words and its neighbours': he "humbled" her (34:2), as the man who seizes a virgin has "humbled" her (Deuteronomy 22:29); his deed was "folly in Israel" (34:7, in the Hebrew), as the harlotry of a bride without the tokens of virginity is (Deuteronomy 22:21); and he offers the bride-price (34:12) that Exodus requires. So the narrative treats Dinah as the law's violated virgin. That is the use of the word the verse shows, and on that reading it is no evidence that παρθένος could mean a woman who is not a virgin.

Frymer-Kensky reads the law and the story the same way, from the Hebrew. The lover "pays the mohar habbetulot even if the father refuses to allow him to marry her", a price a seduced girl "would no longer command" (80); and she follows the Dinah story with the law of "Intercourse with an Unmarried Girl (Exodus 22.15-16 and Deuteronomy 22.28-29)", under which the father "can take the 'virgin's brideprice' from the lover" (91). She hedges the price in a note: it "might simply mean the appropriate brideprice for young girls" (80 n. 3). She does not discuss the Greek of 34:3.

What it does not settle. The Hebrew of 34:3 has נַעֲרָה, "girl", and the translator of Genesis renders that word with παρθένος elsewhere, of Rebekah (24:14, 16, 55), and with παῖς (24:28, 57). At 34:4 and 34:12, where marriage and the bride-price are in view, he writes παῖς for Dinah, not παρθένος. Rico and Gentry read 34:3 as the older, broader usage, an archaism of the Greek Pentateuch, while the Septuagint's Greek at large means "virgin" by the word (18, 21). Bratcher finds 34:3 "surprising", since Dinah "was no longer, therefore, a 'virgin' in the technical sense of the word" (113). The Greek Deuteronomy does not tell either way: its translator writes νεᾶνις for נַעֲרָה through chapter 22, of the virgin wrongly accused (22:19) as of the woman seized (22:29), so his change of word follows the Hebrew, not the woman's state.

Its rating. plausible. A step is disputed when a cited reader grants its grounds and denies its conclusion, and none has been found who does. Wegner, Rhodea, Meade, Rico and Gentry and Bratcher read 34:3 as said of a woman who is not a virgin, but none of them takes up Exodus 22:15–16 or the law's words in Genesis 34, the second ground. Frymer-Kensky grants that ground, and does not deny the conclusion; her note doubts what the first ground's law prices, and so bears on how firmly that law is read, not on this step. No reader has been found who makes the status reading of the Greek: it is built here from the texts, with Frymer-Kensky's reading of the Hebrew, and is rated no higher than plausible for that reason. The commentaries on the Greek Genesis that might settle it, Wevers's Notes and Harl's La Genèse, have not been read. A reader of them who has the law before him and still reads 34:3 of a woman no longer a virgin would make the step disputed; and the verdict of Dispute.Septuagint turns on this rating.

Miller on the laws

millerSource

The citation for Miller's steps, from a use of the word to its sense in the Septuagint's Greek. disputed: Rico and Gentry (18, 21) and Bratcher (113) grant that Genesis 34:3 calls a woman no longer a virgin a παρθένος, and still hold that the word means "virgin" in the Septuagint.

def millerSource : Source :=
  { primary := Reference.work millerBornDivine,
    supporting :=
      [Reference.work ricoGentryInfantKing (Bib.Locus.pages 18 21),
        Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 113)],
    tradition := Tradition.criticalScholarship,
    confidence := Confidence.disputed }

joelShowsNoConnotation

Joel 1:8 shows that the word does not connote virginity, Miller's way: the young widow is called a παρθένος.

dinahShowsNoConnotation

Genesis 34:3 shows the same: the Greek calls Dinah a παρθένος, and the word describes her as she then was, no longer a virgin.

contextNotWordInTheLaws

So in the laws the virginity "has to be inferred from the context", and the word is not used in the sense "virgin".

millerJoelLine — Miller: Joel 1:8 calls a young widow a παρθένος

Miller from Joel 1:8: "Lament like a parthenos dressed in sackcloth for the husband of her youth", a young widow (Born Divine). The Greek does not read so (Dispute.Miller).

millerDinahLine — Miller: Genesis 34:3 calls a woman no longer a virgin a παρθένος

Miller from Genesis 34:3: "In one passage, this term refers to a rape victim after she has been attacked (Gen 34:3)" (Born Divine). Two grounds: what the Greek reads, and Miller's premise that its noun describes Dinah as she then was. The second is his, not the text's: the order of the verses puts Shechem's love after his act, not the noun's description (dinahLine).

criticalExclusionLine — Critical denial of the predictive reading of Isaiah 7:14

The critical line: the sign was given to Ahaz, and such a sign is not also a prediction of a virgin conception, so the predictive reading is denied.

Its grounds are what the two defeaters attack. Berry replaces the second with nearTermFulfilmentIsUnclear plus berryBlocksExclusion; parity replaces it with Isaiah 9 and 11 plus parityDefeatsNearTermExclusion.

The two defeaters, as arguments in their own right

criticalDenialUnderBerry and criticalDenialUnderParity ask what the critical line is left with once a reply is in play. The lines below ask something else: what each reply concludes, taken on its own. Written this way a reply is a position with premises of its own, and so a node that can defeat, and be defeated by, the line it answers — see Dispute.lean.

berryLine — Berry's objection to the near-term exclusion

Berry's objection, as an argument: the near-term fulfilment is unclear, so the near-term reading does not exclude the messianic sense.

postellLine — Postell's parity argument against the near-term exclusion

Postell's parity argument, as an argument: Isaiah 9 and 11 are messianic on the same near-term timeline, so a near-term setting does not exclude the messianic sense.

motyerLine — Motyer's reply to the near-term reading

Motyer's reply, as an argument, with Compton: the sign is given to the house of David and the near-term timetable passes to Isaiah's son, so Isaiah 7:14 is not a near-term sign to Ahaz. The first reply to deny the critic's near-term premise rather than its exclusion premise.

micahLine — Postell's Micah counterexample to the near-term exclusion

Postell's Micah counterexample, as an argument: the ruler of Micah 5 is set against the Assyrian invasion and was read messianically, so a near-term setting does not exclude a messianic sense.

What the strands share

sharedGrounds

The premises no single strand owns: Mary's conception, and the agreement of the two birth narratives about it. Every scriptural package needs them and none of the four strands delivers them.

scripturalLines

The four scriptural strands, in the order the module doc introduces them. christian is exactly these four on shared ground.

def scripturalLines : List (Line Claim) :=
  [isaianicLine, protoevangeliumLine,
    micheanLine, compositionalLine]

TestimonyArguments.BornOfAVirgin.Packages — the positions, and the variants

A handful of these packages are positions someone holds; the rest exist to be refuted, because "this premise is load-bearing" is proved by removing it and exhibiting a countermodel, and the package with it removed has to be written down to be refuted. So the file grows with every result, and counting it here would only be one more thing to keep current.

Each variant is a named difference from christian: one line on different grounds, or one fewer line. Before Line existed each restated the whole twenty-one element premise list, where a reader could not see which premise had gone and a slip in the other twenty was invisible.

Two packages are not built from the lines, and deliberately. critical grants the texts and denies every inference drawn from them, so its premises group by kind rather than by strand. lexicalCriticalUnderCompatibility mixes the objector's grounds with the replies to them. Forcing either into caseOf would describe them as something they are not.

christian — Scriptural reading of Isaiah 7:14, Genesis 3:15 and Micah 5:2–3

The scriptural argument: four strands, no appeal to magisterial authority.

No premise here rests on scripture alone.

catholic — Roman Catholic reading (Scripture and magisterial teaching)

The Roman Catholic package: the four scriptural strands and the magisterial one. This is the position as actually held — Scripture and Tradition together — and it is kept distinct from christian because its extra premise is one this library's author does not grant.

No premise here rests on scripture alone.

magisterialOnly — Magisterial teaching alone

The magisterial route on its own, with no exegetical premise at all.

No premise here rests on scripture alone.

magisterialDenied — Magisterial teaching, with its authority denied

The magisterial route as it stands for a reader who denies that magisterial teaching settles doctrinal questions, holding with Westminster I.x that Scripture is the supreme judge.

No premise here rests on scripture alone.

isaianicWithoutAlmah — Isaianic strand (Isaiah 7:14)

The Isaianic line with the lexical premise removed, everything else it rests on retained. The one difference that most of the results below turn on.

christianWithoutAlmah — Scriptural reading, minus the lexical premise

The scriptural package with the lexical premise removed, everything else retained.

No premise here rests on scripture alone.

isaianicStrandWithoutAlmah — Isaianic strand alone, minus the lexical premise

The Isaianic strand by itself, with the lexical premise removed: the argument exactly as this module encoded it before the other three strands were added. Kept so that the earlier finding stays checkable.

No premise here rests on scripture alone.

christianWithoutAnyHinge — Scriptural reading, minus all four interpretive hinges

The scriptural package with all four interpretive hinges removed, every textual and historical premise retained.

No premise here rests on scripture alone.

isaianicStrandOnAdmissibility — Isaianic strand, with the lexical premise weakened to admissibility

The Isaianic strand with Berry's defensive lexical premise in place of the assertive one: עַלְמָה admits the sense "virgin" rather than bearing it.

No premise here rests on scripture alone.

critical — Critical reading: near-term sign, etiology, and silence

The critical reading: the quotation, the Septuagint rendering and the wording of Genesis and Micah are all granted, and every inference drawn from them is denied.

Written flat rather than from the lines above, because that is its shape: the texts first, then the critical readings of them, then the denials. It is not four strands on shared ground; it is the refusal of four strands.

No premise here rests on scripture alone.

criticalDenial — Critical denial of the predictive reading of Isaiah 7:14

The critical case for denying the predictive reading, stated as an argument in its own right rather than assumed inside critical. Its conclusion is the denial, not anything about Jesus.

No premise here rests on scripture alone.

criticalDenialUnderBerry — Critical denial, with Berry's objection in play

The same case with Berry's observation in play, and the exclusion premise no longer simply granted.

No premise here rests on scripture alone.

berryObjection — Berry's objection to the near-term exclusion

Berry's objection as a position of its own: its conclusion is that the near-term reading does not exclude the messianic sense.

No premise here rests on scripture alone.

postellParity — Postell's parity argument against the near-term exclusion

Postell's parity argument as a position of its own, with the same conclusion as Berry's reached from different grounds.

No premise here rests on scripture alone.

micahParity — Postell's Micah counterexample to the near-term exclusion

Postell's Micah counterexample as a position of its own, with the same conclusion as Berry's and Postell's Isaiah argument.

No premise here rests on scripture alone.

motyerReply — Motyer's reply to the near-term reading

Motyer's reply as a position of its own: Isaiah 7:14 is not a near-term sign to Ahaz.

No premise here rests on scripture alone.

criticalDenialUnderParity — Critical denial, with the parity argument in play

The critical denial with Postell's parity argument in play, and the exclusion premise no longer simply granted.

No premise here rests on scripture alone.

semantic — Referential reading: a virgin is an עַלְמָה

The referential argument: Mary answers Isaiah's description, so Matthew's claim never required עַלְמָה to denote virginity. Its conclusion is the denial of the objection's premise, not the criterion — see compatibility_does_not_establish_criterion.

No premise here rests on scripture alone.

semanticReachingForCriterion — Referential reading, asked for the criterion

The same premises, asked to deliver the criterion instead. They do not.

No premise here rests on scripture alone.

Wegner's objection, and the circle in it

Four variants of one line, each a named difference. wegnerLine grants everything Wegner needs; the rest take one ground away and put in its place the step that is supposed to supply it.

wegnerLexical — Wegner's grammatical objection: the עַלְמָה is already pregnant

Wegner's objection at full strength, granted every premise it needs: the predicate-adjective parse, the near-term setting of the sign, the ordinary pregnancy that setting supplies, and the principle that the Isaianic referent settles the word's denotation.

Stated first and in full, because the results that follow are about where its weight rests and are worth nothing against a weakened rival.

No premise here rests on scripture alone.

wegnerWithoutTheOrdinaryPregnancy — Wegner's grammatical objection (Isaiah 7:14)

Wegner's line with the ordinary pregnancy no longer granted. It is the one ground that goes; the parse, the near-term setting and the referent principle all stay.

wegnerWithoutOrdinaryPregnancy — Wegner's objection, with the ordinary pregnancy no longer assumed

The same objection with the ordinary pregnancy derived instead of assumed — derived as Wegner derives it, from the reading of the sign, which is not granted either.

No premise here rests on scripture alone.

wegnerInTheCircle — Wegner's grammatical objection (Isaiah 7:14)

Wegner's line as it stands inside the circle: the ordinary pregnancy gone from its grounds, and the demand that עַלְמָה carry the sense — which is what the return leg needs — put in.

wegnerCircle — Wegner's objection with both legs of the circle in place

Both legs of the circle at once, with every uncontested datum retained: the parse, the near-term setting, the referent principle, and the demand that עַלְמָה carry the sense. Asked for the lexical conclusion.

No premise here rests on scripture alone.

wegnerUnderParity — Wegner's grammatical objection (Isaiah 7:14)

Wegner's line with Postell's usage datum in place of the referent principle. The parse and the ordinary pregnancy both stay: this reply concedes the referent and contests only what may be inferred from it.

wegnerUnderUsageParity — Wegner's objection, with the usage parity reply in play

Wegner's objection with Postell's usage parity in play.

No premise here rests on scripture alone.

The fathers' sign argument, and the reply to it

signArgument — The fathers' sign argument (Isaiah 7:11, 14)

The fathers' sign argument as a position of its own: its conclusion is that the pregnancy of Isaiah 7:14 is not an ordinary one, and nothing about the word.

No premise here rests on scripture alone.

ordinarySignReply — The near-term reply: a sign need not be a miracle

The near-term reply as a position of its own: the sign of Isaiah 7:14 need not be extraordinary.

No premise here rests on scripture alone.

wegnerUnderSign — Wegner's grammatical objection (Isaiah 7:14)

Wegner's line with the sign argument in play: the ordinary pregnancy no longer granted, and the fathers' two grounds in its place. The parse, the near-term setting and the referent principle all stay.

wegnerUnderTheSign — Wegner's objection, with the fathers' sign argument in play

Wegner's objection with the fathers' sign argument in play.

No premise here rests on scripture alone.

signUnderReply — The fathers' sign argument (Isaiah 7:11, 14)

The sign argument with the near-term reply in play: its first ground no longer granted, and the reply's grounds in its place.

signArgumentUnderReply — The fathers' sign argument, with the near-term reply in play

The fathers' sign argument with the near-term reply in play.

No premise here rests on scripture alone.

The Septuagint, and what its word meant

septuagintWitness — The Septuagint as a witness (Isaiah 7:14 in Greek)

The Septuagint as a witness, as a position of its own: its conclusion is what its translator read, and nothing yet about Isaiah's word.

No premise here rests on scripture alone.

driftObjection — Wegner on παρθένος: the word had not yet come to mean 'virgin'

Wegner on παρθένος, as a position of its own: in the Septuagint's day the word meant "young woman", and not yet "virgin".

No premise here rests on scripture alone.

usageCase — Rico and Gentry: παρθένος means 'virgin' in the Greek of the Scriptures

Rico and Gentry's case from usage as a position of its own: "virgin" is a sense of παρθένος in the Septuagint's Greek.

Grounded in scripture alone: Elsewhere in the Greek Isaiah, παρθένος renders בְּתוּלָה.

lawsCase — The laws of the Greek Pentateuch: παρθένος in the sense 'virgin'

The case from the laws as a position of its own: in the Greek Pentateuch's laws, παρθένος is used in the sense "virgin".

Grounded in scripture alone: The high priest of the Greek Leviticus marries a παρθένος, not a widow or a harlot.

dinahCase — The law's name for Dinah: Genesis 34:3 read under Exodus 22:15–16

The status reading of Genesis 34:3 as a position of its own: the Greek names Dinah a παρθένος as the law names the seduced virgin, in the sense "virgin".

Grounded in scripture alone: In the Greek Exodus, the seduced παρθένος is owed 'the bride-price of virgins', Genesis 34 tells Shechem's act in the words of the laws of the violated virgin.

millerOnTheLaws — Miller: in the laws, the virginity is the context's, not the word's

Miller on the laws, as he argues it: two uses of the word of women who are not virgins, so the word does not by itself connote virginity, so the laws' virginity is the context's.

No premise here rests on scripture alone.

millerCase — Miller, from Genesis 34:3

Miller from Genesis 34:3, his case on the evidence the texts leave standing: Joel 1:8, which the Greek refutes, taken out (Dispute.Miller). The position he holds in the dispute over the Septuagint's word.

No premise here rests on scripture alone.

millerOnJoelAlone — Miller, from Joel 1:8 alone

Miller's dissent, had Joel 1:8 been all his evidence. Not his argument as he makes it, written down to show what striking a refuted claim does.

No premise here rests on scripture alone.

matthewCase — Scripture interprets Scripture: Matthew quotes ἡ παρθένος of Mary

Matthew's quotation as a position of its own: in the Greek of Isaiah 7:14, which Matthew quotes, παρθένος has the sense "virgin".

Grounded in scripture alone: Matthew 1:23 quotes Isaiah 7:14 in the Greek's own words: ἡ παρθένος, Matthew says Mary conceived before she and Joseph came together.

fulfilmentCase — The fulfilment of Genesis 3:15 confirms the promise

The fulfilment, confirming the promise, as a position: every term of Genesis 3:15 met in Jesus as the New Testament names it, and so the verse a promise of him. Two steps, each rated: the fulfilment (fulfilmentLine) and the confirmation (confirmationLine). The confirmation's ground is the fulfilment's conclusion, so it enters as a step, not as a premise.

Grounded in scripture alone: Paul says God sent his Son 'made of a woman' (Galatians 4:4), Revelation calls the devil 'that old serpent' (12:9, 20:2), The Son came to destroy the devil and his works, through death, Paul says Christ died, was buried, and rose the third day.

westermannCase — Westermann: a punishment oracle on a line of descendants, and no promise

Westermann's denial, as a position: the verse is no promise, and so no one fulfils it. He holds the confirmation's step with the fulfilment's side — what is fulfilled was promised — and runs it the other way: suggestions of a messianic reading "are found in late Judaism, but not in the New Testament" (261). So his denial that the verse is a promise is a denial that it is fulfilled in Jesus, and the package says so.

No premise here rests on scripture alone.

syntaxCase — The syntax of the striker: 'he' who strikes is one descendant

The syntax of the striker, as a position: "her seed" at 3:15 is not only a line of descendants.

No premise here rests on scripture alone.

sceneCase — The scene read whole: God's sentence on the serpent's power

The scene read whole, as a position: the verse is the protoevangelium, from the section's own words.

No premise here rests on scripture alone.

aloneCase — The seed of the woman alone

The seed of the woman alone, as a position: the fulfilment, with the virginal conception.

Grounded in scripture alone: Paul says God sent his Son 'made of a woman' (Galatians 4:4), Revelation calls the devil 'that old serpent' (12:9, 20:2), The Son came to destroy the devil and his works, through death, Paul says Christ died, was buried, and rose the third day.

septuagintWithoutTheSense — The Septuagint as a witness, with nothing granted about παρθένος

The Septuagint as a witness, with the claim about its word taken away: the rendering and its date stay, and nothing is granted about what παρθένος meant. Its conclusion no longer follows (parthenos_is_load_bearing).

No premise here rests on scripture alone.

septuagintToTheWordSource

How the step from the translator's reading to Isaiah's word is rated: Irenaeus takes it, against Theodotion and Aquila (Against Heresies III.21.1), because he holds the Greek "interpreted by the inspiration of God" (III.21.2). disputed: Bratcher grants that the translator read a virgin (115) and denies that עַלְמָה says so (105–106); Brown grants the translator's "deliberate preference" (Birth of the Messiah 148) and denies that the Hebrew stresses virginity (147); and Walton holds that the Greek shows at best "an interpretational preference rather than a linguistic necessity" (293). See translatorsReadingFixesTheWord.

def septuagintToTheWordSource : Source :=
  {
    primary :=
      Reference.work irenaeusAgainstHeresies (Bib.Locus.sectionRef "III.21.1"),
    supporting :=
      [Reference.work irenaeusAgainstHeresies (Bib.Locus.sectionRef "III.21.2"),
        Reference.work bratcherStudyOfIsaiah (Bib.Locus.pages 105 106),
        Reference.work bratcherStudyOfIsaiah (Bib.Locus.page 115),
        Reference.work brownBirthMessiah (Bib.Locus.pages 147 148),
        Reference.work waltonWhatsInAName (Bib.Locus.page 293)],
    tradition := Tradition.christianTypological,
    confidence := Confidence.disputed }

septuagintOnTheWord — The Septuagint as a witness to what עַלְמָה means

The Septuagint asked for Isaiah's word: its witness, with the step from the translator's reading to what עַלְמָה denotes added. That step is rated disputed, and the case is only as good as it is.

No premise here rests on scripture alone.

septuagintWithTheFuture — The Septuagint as a witness (Isaiah 7:14 in Greek)

The Septuagint's line with the tense of its verb among the grounds: the virgin shall be with child.

Genesis 3:15, and what "her seed" says of a father

protoevangeliumCase — Protoevangelium strand (Genesis 3:15)

The protoevangelium strand as a position of its own: Genesis 3:15 read as promise, the seed named as the woman's, and the hinge that this marks a birth with no human father, delivering the criterion. The rival whose hinge Results.Genesis reads two ways.

No premise here rests on scripture alone.

herSeedCase — Luther on 'her seed': the wording itself signifies no human father

Luther's case from the wording, as a position of its own.

No premise here rests on scripture alone.

posterityCase — Leupold on 'her seed': her posterity, named for the deception

Leupold's case from the woman's posterity, as a position of its own.

No premise here rests on scripture alone.

idiomCase — Lewis on 'her seed': Genesis says it of Hagar and Rebekah too

Lewis's case from the idiom, as a position of its own.

No premise here rests on scripture alone.

greekHeCase — The Greek's 'he': the woman's seed read as one person

The Greek's "he", as a position of its own.

No premise here rests on scripture alone.

greekHeWithThePromise — The Greek's 'he': the woman's seed read as one person

The Greek's line with the promise's grounds beside it: the seed named as the woman's, Genesis 3:15 as the first promise of a redeemer, and a man's seed reckoned through him. Luther's step is not among them.

lexicalCritical — Lexical objection from the ancient versions

The lexical objection with its versional support, stated as its holder would state it.

No premise here rests on scripture alone.

lexicalCriticalUnderCompatibility — Lexical objection, with the referential reply in play

The same objection, with the referential premises in play and its own key premise no longer simply granted.

Written flat: it is the objector's grounds and the replies to them side by side, which is neither one line nor several converging ones.

No premise here rests on scripture alone.

TestimonyArguments.BornOfAVirgin.Results — what does and does not follow

Every result about the strands, each tagged @[headline] and each followed by #print axioms so its trust base is visible in the source. The results about Wegner's objection — its validity, its circle, and the replies to it, the fathers' sign argument among them — are in Results.Wegner.

Entailments are established with establish; refutations name a countermodel and use refute_with. A countermodel here is the rival's reading written down as a valuation, which is why each one is a named definition with a docstring saying what position it encodes rather than an anonymous function.

Read hinges_jointly_load_bearing first. It is the result the four-strand encoding exists to make possible.

Results

christian_establishes

Given the scriptural premises, the conclusion follows.

theorem christian_establishes : Establishes christian
-- axioms: propext, Quot.sound

catholic_establishes

The Roman Catholic package establishes it too, unsurprisingly: it is the scriptural package with a further strand bolted on.

theorem catholic_establishes : Establishes catholic
-- axioms: propext, Quot.sound

magisterialOnly_establishes

The magisterial route carries the conclusion on its own, for a reader who grants the authority it claims.

theorem magisterialOnly_establishes : Establishes magisterialOnly
-- axioms: propext, Quot.sound

criticalReading

The critical reading, written down: עַלְמָה means "young woman", Isaiah's sign was given to Ahaz, Genesis 3:15 is an etiology, and Micah's silence about a father is only silence. No virgin-birth criterion arises.

def criticalReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.almahMeansVirgin => False
    | Claim.isaiahPredictsVirginBirth => False
    | Claim.genesis3_15IsProtoevangelium => False
    | Claim.seedOfTheWomanImpliesNoHumanFather => False
    | Claim.maternalSilenceImpliesNoHumanFather => False
    | Claim.messiahBornOfVirgin => False
    | Claim.jesusSatisfiesCriterion => False
    | x => True

critical_not_establishes

The critical reading does not establish the conclusion.

theorem critical_not_establishes : ¬Establishes critical
-- axioms: propext, Quot.sound

criticalDenial_establishes

The critical case for the denial does go through on its own terms. Stating it as an argument rather than a bare assumption is what makes the next result possible.

theorem criticalDenial_establishes : Establishes criticalDenial
-- axioms: propext, Quot.sound

berryReading

Berry's reading, written down: the sign was given to Ahaz, how it was fulfilled in his day is unclear, and so the near-term reading does not exclude a further referent — leaving the predictive reading standing.

def berryReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.nearTermExcludesMessianicSense => False
    | x => True

berry_blocks_critical_denial

Berry's objection blocks the critical denial. Grant that Isaiah 7:14 was a sign to Ahaz, and grant with Berry that how it was fulfilled in Ahaz's own day is an open question, and the denial no longer follows.

This is the narrow thing the objection does, and it is worth being clear about what it does not do. It does not establish the predictive reading, and it does not touch the lexical dispute. It removes one route to the denial — the route that runs through the near-term fulfilment — and leaves the argument where hinges_jointly_load_bearing puts it.

theorem berry_blocks_critical_denial : ¬Establishes criticalDenialUnderBerry
-- axioms: propext, Quot.sound

parityReading

The parity reading, written down: a near-term Assyrian setting is simply not the kind of reason that rules out messianic reference, since Isaiah 9 and 11 sit on that same timeline and are read messianically anyway.

def parityReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.nearTermExcludesMessianicSense => False
    | x => True

parity_blocks_critical_denial

Postell's parity argument blocks the critical denial too, and by a different route from Berry's.

Berry's objection is evidential — we do not know how the sign was fulfilled in Ahaz's day. Parity is structural — the near-term setting was never the right kind of reason, because Isaiah 9:5–6 and 11:1–10 stand on the same Assyrian timeline and are read messianically without embarrassment. An opponent who answers Berry by settling the near-term referent has not touched this.

theorem parity_blocks_critical_denial : ¬Establishes criticalDenialUnderParity
-- axioms: propext, Quot.sound

reformedReading

The Reformed objection, written down: papal teaching says what it says, and saying it settles nothing, because Scripture is the supreme judge.

def reformedReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | Claim.messiahBornOfVirgin => False
    | Claim.jesusSatisfiesCriterion => False
    | x => True

magisterial_authority_is_load_bearing

What the magisterial strand is worth to a reader who does not grant the magisterium's authority: nothing. Deny that premise and the route collapses outright, however firmly the teaching itself is attested.

This is why christian excludes it. A reader who holds with Westminster I.x that Scripture is the supreme judge of controversies loses the whole of magisterialOnly and must get the criterion from the four scriptural strands or not at all.

theorem magisterial_authority_is_load_bearing : ¬Establishes magisterialDenied
-- axioms: propext, Quot.sound

almah_not_load_bearing

The lexical premise no longer carries the argument. Strip almah and the protoevangelium and Michean strands still deliver the criterion.

Before Genesis 3:15 and Micah 5:2–3 were encoded, this module proved the opposite — and almah_is_load_bearing_alone below shows that the earlier finding was right about the Isaianic strand taken by itself. What changed is not the Isaianic evidence but the number of strands.

theorem almah_not_load_bearing : Establishes christianWithoutAlmah
-- axioms: propext, Quot.sound

withoutAlmahReading

A reading that grants everything in the Isaianic strand except the lexical premise.

def withoutAlmahReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.almahMeansVirgin => False
    | Claim.messiahBornOfVirgin => False
    | Claim.jesusSatisfiesCriterion => False
    | x => True

almah_is_load_bearing_alone

Within the Isaianic strand taken alone, the lexical premise is still load-bearing: remove it and that strand yields nothing. The earlier single-stranded encoding of this module is preserved here rather than deleted, because it is what makes almah_not_load_bearing informative — the Isaianic evidence did not get stronger, it got company.

theorem almah_is_load_bearing_alone : ¬Establishes isaianicStrandWithoutAlmah
-- axioms: propext, Quot.sound

admissibility_is_not_enough

Admissibility is not enough. Berry's lexical point is defensive — the semantic range of עַלְמָה does not exclude the sense "virgin" — and defensive is all it is. Substitute it for almahMeansVirgin and the Isaianic strand yields nothing, on the same reading that refutes the strand without any lexical premise at all.

The gap between may mean and does mean is where this argument lives, and Berry is useful against the critical denial without narrowing it.

theorem admissibility_is_not_enough : ¬Establishes
    isaianicStrandOnAdmissibility
-- axioms: propext, Quot.sound

The referential strand

semantic_establishes

The referential argument goes through. Granted only what both sides grant about the word — that עַלְמָה denotes a young woman of marriageable age, and that being a virgin does not exclude a woman from that denotation — and granted that Mary was such a woman and conceived as a virgin, Matthew's claim turns out not to have required the lexical sense at all.

Nothing here asserts that עַלְמָה means virgin. The argument is about reference, not sense, and it is cheaper for exactly that reason.

theorem semantic_establishes : Establishes semantic
-- axioms: propext, Quot.sound

lexicalCritical_establishes

The lexical objection, written down and granted its own premises.

theorem lexicalCritical_establishes : Establishes lexicalCritical
-- axioms: propext, Quot.sound

compatibilityReading

The referential reading, written down: the versions differ about which term to use and not about who is described, so the divergence settles nothing about the sense, and Matthew's claim never needed the sense.

def compatibilityReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.versionalDivergenceRefutesVirginSense => False
    | Claim.lexicalSenseRequiredForFulfilment => False
    | x => True

compatibility_defeats_lexical_objection

The referential reply defeats the lexical objection. Keep every versional datum — the Targum's עוּלֵימְתָא, the Three's νεᾶνις, the Septuagint's παρθένος, the Peshitta's ܒܬܘܠܬܐ, Qumran's confirmation of the Hebrew — add the referential premises, and the objection no longer reaches its conclusion.

The tension in the versions is not evidence against the reading once virginity is compatible with the word. It is evidence that four translators made four defensible choices about how much of the referent's description to make explicit.

theorem compatibility_defeats_lexical_objection : ¬Establishes
    lexicalCriticalUnderCompatibility
-- axioms: propext, Quot.sound

compatibilityOnlyReading

A reading on which Mary fits Isaiah's description and no criterion arises from it.

def compatibilityOnlyReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.lexicalSenseRequiredForFulfilment => False
    | Claim.messiahBornOfVirgin => False
    | Claim.jesusSatisfiesCriterion => False
    | x => True

compatibility_does_not_establish_criterion

What the referential argument costs. It is purely defensive. It defeats the objection without establishing the criterion: ask the same premises for jesusSatisfiesCriterion and they do not deliver it, because nothing in them says the Messiah must be born of a virgin — only that Mary may be described as Isaiah describes.

This is the honest price of the move, and it is worth paying. The criterion has to come from the Isaianic, protoevangelium or Michean strands; what the referential argument buys is that losing the lexical dispute no longer costs the fulfilment claim. Winning almahMeansVirgin outright was never necessary, and this says so in a form either side can check.

theorem compatibility_does_not_establish_criterion : ¬Establishes
    semanticReachingForCriterion
-- axioms: propext, Quot.sound

noHingeReading

A reading on which none of the four interpretive hinges holds: almah means "young woman", the matrilineal wording of Genesis 3:15 implies nothing about a father, Micah's silence is only silence, and Isaiah's composition does not govern the sense of 7:14. Every textual observation is granted.

def noHingeReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.almahMeansVirgin => False
    | Claim.seedOfTheWomanImpliesNoHumanFather => False
    | Claim.maternalSilenceImpliesNoHumanFather => False
    | Claim.compositionGovernsMeaning => False
    | Claim.messiahBornOfVirgin => False
    | Claim.jesusSatisfiesCriterion => False
    | x => True

hinges_jointly_load_bearing

The result worth having. No single hinge carries the argument, but the four of them jointly do: remove all four and the criterion no longer follows, with every textual and historical premise retained.

So the argument no longer hangs on the sense of עַלְמָה alone. It hangs on that or on the matrilineal wording of Genesis 3:15 or on Micah's maternal silence or on Postell's compositional reading — and an opponent must defeat all four. That is a materially stronger position than the single-stranded version, and a materially weaker one than four independent arguments would be: three of the four hinges are disputed for good reason, and the module doc says why.

theorem hinges_jointly_load_bearing : ¬Establishes christianWithoutAnyHinge
-- axioms: propext, Quot.sound

jesus_satisfies_virgin_birth

End to end: under the scriptural package, Jesus satisfies the virgin-birth criterion.

theorem jesus_satisfies_virgin_birth : Satisfies jesus bornOfAVirgin
-- axioms: propext, Quot.sound

Satisfiability

Entails is vacuously true over a premise set with no model, so a package built from contradictory premises would establish its conclusion with every gate passing. Only packages carrying a positive Establishes result need checking: one with a ¬ Establishes result is satisfiable already, its countermodel being a valuation on which every premise holds.

Several packages here deny a premise, so the all-holds reading will not serve them — a model has to be the position's own world, which is the same discipline the countermodels follow.

Not tagged @[headline]: these are claims about the health of the encoding.

everythingHoldsReading

The reading on which every claim holds at once.

def everythingHoldsReading : Valuation Claim :=
  fun x => True

christian_is_satisfiable

The scriptural package has a model.

theorem christian_is_satisfiable : Satisfiable christian.premises
-- axioms: propext, Quot.sound

catholic_is_satisfiable

The Roman Catholic package has a model.

theorem catholic_is_satisfiable : Satisfiable catholic.premises
-- axioms: propext, Quot.sound

magisterialOnly_is_satisfiable

The magisterial route has a model.

theorem magisterialOnly_is_satisfiable : Satisfiable magisterialOnly.premises
-- axioms: propext, Quot.sound

christianWithoutAlmah_is_satisfiable

The scriptural package minus the lexical premise has a model, so almah_not_load_bearing is not vacuous.

theorem christianWithoutAlmah_is_satisfiable : Satisfiable
    christianWithoutAlmah.premises
-- axioms: propext, Quot.sound

criticalDenialOwnReading

The critical denial's own world: the sign was Ahaz's, so Isaiah 7:14 is not a prediction of a virgin birth.

def criticalDenialOwnReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.isaiahPredictsVirginBirth => False
    | x => True

criticalDenial_is_satisfiable

The critical denial has a model.

theorem criticalDenial_is_satisfiable : Satisfiable criticalDenial.premises
-- axioms: propext, Quot.sound

referentialOwnReading

The referential argument's own world: Mary answers Isaiah's description, so the fulfilment claim never required the lexical sense.

def referentialOwnReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.lexicalSenseRequiredForFulfilment => False
    | x => True

semantic_is_satisfiable

The referential argument has a model.

theorem semantic_is_satisfiable : Satisfiable semantic.premises
-- axioms: propext, Quot.sound

lexicalObjectionOwnReading

The lexical objection's own world: the versions read the broad term, so עַלְמָה does not denote virginity and the criterion is not met.

def lexicalObjectionOwnReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.almahMeansVirgin => False
    | Claim.jesusSatisfiesCriterion => False
    | x => True

lexicalCritical_is_satisfiable

The lexical objection has a model.

theorem lexicalCritical_is_satisfiable : Satisfiable lexicalCritical.premises
-- axioms: propext, Quot.sound

TestimonyArguments.BornOfAVirgin.Results.Wegner — Wegner's objection, and the sign

What follows from Wegner's grammatical objection and from the replies to it: that it is valid, where its weight rests, the circle in it, Postell's usage parity, and the fathers' sign argument together with the near-term reply to that. Dispute.Wegner then asks who prevails when these meet.

Every result is tagged @[headline] and followed by #print axioms, as in Results.lean, and every countermodel is a named reading.

Wegner's objection, and the circle in it

wegner_establishes

Wegner's objection is valid on its own terms. Grant the predicate-adjective parse, grant that the pregnancy it reports is an ordinary one, and grant that the one clear Isaianic referent settles what the word denotes, and the lexical conclusion follows.

Stated first, and at full strength, because the results below are about where its weight rests and are worth nothing if the argument was weak to begin with.

theorem wegner_establishes : Establishes wegnerLexical
-- axioms: propext, Quot.sound

rydelnikReading

Rydelnik's reading, written down: הָרָה is the predicate adjective Wegner says it is, and what it announces is the miracle rather than an ordinary conception — the virgin is pregnant, a sign as deep as Sheol.

def rydelnikReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.pregnancyAtTheSignIsOrdinary => False
    | Claim.isaianicAlmahIsNotAVirgin => False
    | x => True

wegner_needs_ordinary_pregnancy

The grammar is not what carries the objection. Derive the ordinary pregnancy the way Wegner derives it — from the near-term reading of the sign — rather than granting it, and the argument no longer reaches its conclusion, with the parse itself untouched.

So the load-bearing premise is not harahIsPredicateAdjective, which both sides grant, but the reading of the sign that makes the pregnancy an ordinary one. The next result follows that premise back to where it comes from.

theorem wegner_needs_ordinary_pregnancy : ¬Establishes
    wegnerWithoutOrdinaryPregnancy
-- axioms: propext, Quot.sound

wegnerConclusionGrantedReading

Wegner's own conclusion granted: עַלְמָה does not denote a virgin, and Isaiah 7:14 is not a prediction of a virgin birth. The same two legs of the circle are satisfied on this reading as on the one below — the first because its antecedent fails, the second because its consequent holds — which is what makes the circle silent in both directions rather than merely unhelpful in one.

Not a convenience: it is the position Wegner argues for, and the reading had to be found rather than assumed. The all-true valuation that serves the same purpose in SolaScriptura does not work here, because wegnerCircle carries negated grounds.

def wegnerConclusionGrantedReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.almahMeansVirgin => False
    | Claim.isaiahPredictsVirginBirth => False
    | x => True

circleUngroundedReading

The reading that exhibits the circle: the predictive reading of Isaiah 7:14 stands, עַלְמָה may denote a virgin, and the pregnancy the sign announces is not an ordinary one. Every uncontested datum in Wegner's case is granted — the parse, the near-term setting, the referent principle — and the two legs of the circle are satisfied because each is an implication whose antecedent fails.

def circleUngroundedReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.pregnancyAtTheSignIsOrdinary => False
    | Claim.isaianicAlmahIsNotAVirgin => False
    | x => True

circle_leaves_the_lexical_conclusion_open

The circle, shown rather than alleged. Put both legs in place — the reading supplying the ordinary pregnancy, and the lexical conclusion turned back against the reading — keep every uncontested datum, and the lexical conclusion does not follow.

circleUngroundedReading is why: a cycle of implications is satisfied outright by a valuation on which every node in it is false, because each leg then has a false antecedent. Nothing enters such a loop from outside, so nothing comes out of it. That is what it means for an argument to be circular rather than sound, and it is checkable rather than merely assertable.

What this does not show is that Wegner is wrong. wegner_establishes records that his argument is valid; what the circle costs is the claim that it is an independent route to the lexical conclusion. And the result is conditional on readingSuppliesOrdinaryPregnancy, which is Postell's reading of Wegner's procedure, not Wegner's own account of it. He would say the near-term reading rests on the historical setting and stands without the lexical finding — in which case the premise is false and the circle is not there. That premise is where a defender of Wegner should press.

theorem circle_leaves_the_lexical_conclusion_open : Independent
    wegnerCircle.premises (notP Claim.almahMeansVirgin)
-- axioms: propext, Quot.sound

circle_leaves_the_denial_open

And the other end of it is no better off. The same premises, asked for the denial of the predictive reading instead of the lexical conclusion, fail in the same way and on the same reading.

Both results are needed to make the point. A circle is not an argument that fails to establish one of its nodes; it is one that establishes neither, having no premise outside itself.

theorem circle_leaves_the_denial_open : Independent wegnerCircle.premises
    (notP Claim.isaiahPredictsVirginBirth)
-- axioms: propext, Quot.sound

usageParityReading

Postell's usage reading, written down: the עַלְמָה of Isaiah 7:14 is granted to be no virgin, and a single referent still does not settle what the word denotes — because the other clear cases would settle it the other way.

def usageParityReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.oneReferentSettlesDenotation => False
    | x => True

usage_parity_blocks_wegner

Postell's second reply, and it is independent of the first. Concede the parse, concede the ordinary pregnancy, concede that the woman of Isaiah 7:14 is no virgin — and the lexical conclusion still does not follow, because the principle that carries it there would carry the other clear cases the opposite way.

This one survives the defence suggested above. An opponent who shows that the near-term reading stands on its own, and so that there is no circle, has not touched the usage parity: the method is still selective. Between them the two replies leave the objection needing both a non-circular route to the ordinary pregnancy and a reason to privilege this occurrence over Genesis 24:43.

theorem usage_parity_blocks_wegner : ¬Establishes wegnerUnderUsageParity
-- axioms: propext, Quot.sound

The fathers' sign argument

Justin, Irenaeus and Origen answer the near-term reading with one argument. The oracle promised a sign, one offered "in the depth or in the height" (7:11), and an ordinary conception happens to every woman who is not barren. So the pregnancy of 7:14 is not an ordinary one, and that is the ground of Wegner's objection that the grammar does not supply.

The near-term reply is that a sign need not be a miracle. Isaiah's own children are "signs and portents" (8:18), and this sign is dated by a child's infancy (7:16), so its point may be its timing.

referentialSignReading

The fathers' sign, with the word left to the lexicon: the pregnancy of 7:14 is no ordinary one, and עַלְמָה still does not denote a virgin. It is the referential reading's world, in which Mary is an עַלְמָה without the word carrying the sense. Every premise of Wegner's objection under the sign argument holds in it, and so does his lexical conclusion.

def referentialSignReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.almahMeansVirgin => False
    | Claim.pregnancyAtTheSignIsOrdinary => False
    | Claim.isaianicAlmahIsNotAVirgin => False
    | x => True

sign_leaves_the_lexical_conclusion_open

The sign argument blocks Wegner's objection, and settles nothing about the word. Keep the parse, the near-term setting and the referent principle, put the fathers' two grounds where the ordinary pregnancy was, and the lexical conclusion is independent of what is left. On Rydelnik's reading it fails: the virgin is pregnant, a sign as deep as Sheol. On referentialSignReading it holds.

So the argument answers the objection where wegner_needs_ordinary_pregnancy says its weight rests, and does no more. It does not show that עַלְמָה denotes a virgin, because it is not about the word at all.

theorem sign_leaves_the_lexical_conclusion_open : Independent
    wegnerUnderTheSign.premises (notP Claim.almahMeansVirgin)
-- axioms: propext, Quot.sound

nearTermSignReading

The near-term reading of the sign, in Wegner's world: a sign need not be a miracle, the pregnancy is an ordinary one, עַלְמָה does not denote a virgin, and nor, in the Septuagint's day, did παρθένος.

def nearTermSignReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.maternalSilenceImpliesNoHumanFather => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | Claim.signMustBeExtraordinary => False
    | Claim.almahMeansVirgin => False
    | Claim.parthenosMeansVirgin => False
    | Claim.lawsUseParthenosAsVirgin => False
    | Claim.dinahIsTheLawsParthenos => False
    | Claim.lxxIsaiahUsesParthenosAsVirgin => False
    | x => True

marvelAnywayReading

A sign that need not be a marvel, and is one all the same: the reader who grants the near-term reply and still holds that the pregnancy of 7:14 is no ordinary one, on other grounds than the sign.

def marvelAnywayReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.signMustBeExtraordinary => False
    | Claim.pregnancyAtTheSignIsOrdinary => False
    | x => True

reply_leaves_the_pregnancy_open

The near-term reply blocks the sign argument back, and settles nothing about the pregnancy. Put the reply's grounds and step where the fathers' first ground was, keep the second, and whether the pregnancy is an ordinary one is independent of what is left: it is on nearTermSignReading and it is not on marvelAnywayReading.

This is the reply's whole reach. It takes away the fathers' reason for denying the ordinary pregnancy; it does not supply Wegner's reason for asserting it, which still comes from the near-term reading of the sign.

theorem reply_leaves_the_pregnancy_open : Independent
    signArgumentUnderReply.premises (notP Claim.pregnancyAtTheSignIsOrdinary)
-- axioms: propext, Quot.sound

Satisfiability

As in Results.lean: only a package with a positive Establishes result needs a model named, and the sign argument and the reply are given theirs in Dispute.Wegner, where they are established.

wegnerOwnReading

Wegner's own world: the one clear Isaianic referent is not a virgin, so the word does not denote virginity.

def wegnerOwnReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.almahMeansVirgin => False
    | x => True

wegnerLexical_is_satisfiable

Wegner's objection has a model.

theorem wegnerLexical_is_satisfiable : Satisfiable wegnerLexical.premises
-- axioms: propext, Quot.sound

TestimonyArguments.BornOfAVirgin.Results.Septuagint — what the Septuagint shows

A reader's question, in a reader's words: the Jews who translated Isaiah into Greek, before Christ, wrote παρθένος — "virgin". Doesn't that settle it?

The argument is old. Irenaeus makes it against Theodotion and Aquila: the verse "was interpreted into Greek by the Jews themselves, much before the period of our Lord's advent, that there might remain no suspicion that perchance the Jews, complying with our humour, did put this interpretation upon these words" (Against Heresies III.21.1). This module encodes it at full strength and asks three things of it, one result each.

What it rests on. Take away the claim that παρθένος, in the translator's Greek, means a virgin, and the Septuagint no longer shows that its translator read the woman as one (parthenos_is_load_bearing). Everything turns on that word, and whether it means "virgin" there is exactly what the sources dispute. Rico and Gentry hold that it does "whenever it appears in Semitic Koine Greek", and Bratcher agrees. Wegner, Rhodea and Meade hold that in the translator's day it still meant a young woman, as it does of Dinah after Shechem has lain with her (Genesis 34:3), and Walton that the translator's choice of it "is not necessarily betraying an interpretation as virgin". Wegner and Walton grant that by the New Testament the word meant "virgin"; Meade and Davidson put that sense down to Christian use. The dispute is over the translator's day, two or three centuries before Matthew. The Greek Pentateuch's laws use the word where virginity is the point, and its law of the seduced παρθένος reads Genesis 34:3 itself otherwise: the woman a man has lain with is still the law's παρθένος, and owed "the bride-price of virgins" (Exodus 22:15–16). Dispute.Septuagint weighs all five, and the Septuagint's witness prevails, with Rico and Gentry, the laws and that reading of Genesis 34:3; Wegner cannot be defended (septuagint_prevails_over_wegner). The verdict turns on one rating, the status reading's step, plausible on the readers found.

What it would show, if the word means "virgin". How one early reader read Isaiah: a Jewish translator, before Christ, read the woman of 7:14 as a virgin, so reading her so is no Christian invention. It would not show what Isaiah's own word means without a further step, rated disputed (septuagint_word_rests_on_its_inference). A translator can render the woman described rather than the word. The translator of Genesis wrote παρθένος for the עַלְמָה Rebekah (24:43), whom the story has already called a virgin (24:16): a rendering "historically correct — since Rebekah was a virgin", Bratcher says, that "does not precisely translate the Hebrew" (113). Elsewhere the Septuagint's translators, of other books than Isaiah, render עַלְמָה with νεᾶνις, "young woman", four times. That is how this argument's referential strand already reads the versions.

What it leaves open, even then. The Greek says the virgin shall be with child. A woman who is a virgin when the sign is given and conceives later by a man fits those words as well as a virgin who conceives as a virgin does (septuagint_leaves_the_conception_open). That is not only a rival's reading. Bratcher, who holds that παρθένος "definitely means 'virgin' in the LXX" (113), reads the Greek of 7:14 so: "a young woman, at that time virgin, would in the normal way marry and bear a child" (115), "the most reasonable explanation" (116). So the Septuagint, granted every word, does not by itself say that the conception was without a man. Justin and Irenaeus read it so, from the promise of a sign (signLine, weighed in Dispute.Wegner); the word alone does not.

The Septuagint as a witness

Each reading below is a model: a way every claim of the argument could stand at once, named for what it says of the Septuagint and of the woman of 7:14. It settles those as its namesake does. Where the argument's joins require a side on questions this module does not touch, it takes the scriptural reading's: that Micah's mention of a mother and no father does mean something, and that Scripture, not the magisterium, is the judge. Every other claim it leaves true, and none of them bears on the results it is used for.

virginConceivesReading

Justin's reading of the elders' Greek, with Rico and Gentry's sense of the word: παρθένος means a virgin, the translator read the woman of 7:14 as one, and she conceives as one — "a sign which is not common to all the first-born sons" (Dialogue 84). So she is not already pregnant when the sign is given, and her pregnancy is no ordinary one. Wegner's claim is false in it: the word already had the sense "virgin". So are Miller's thesis and his premise that the noun of Genesis 34:3 describes Dinah as she then was: the noun names her.

def virginConceivesReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.parthenosDescribesDinahAsSheThenWas => False
    | Claim.harahIsPredicateAdjective => False
    | Claim.isaianicAlmahIsAlreadyPregnant => False
    | Claim.pregnancyAtTheSignIsOrdinary => False
    | Claim.isaianicAlmahIsNotAVirgin => False
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | x => True

archaismReading

Rico and Gentry's reading of Genesis 34:3: the word there is said of Dinah as she then was, no longer a virgin, an archaism of the Greek Pentateuch, "the exception that proves the rule" (21); and in the Septuagint at large it means a virgin. So the verse uses the word otherwise, and the status reading is false in it; Wegner's claim is false too. Otherwise as Justin reads the elders' Greek (virginConceivesReading).

def archaismReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.dinahIsTheLawsParthenos => False
    | Claim.harahIsPredicateAdjective => False
    | Claim.isaianicAlmahIsAlreadyPregnant => False
    | Claim.pregnancyAtTheSignIsOrdinary => False
    | Claim.isaianicAlmahIsNotAVirgin => False
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | x => True

septuagintWitness_establishes

The Septuagint, read with Rico and Gentry, is a witness from before Christ. Grant that the Greek Isaiah renders עַלְמָה with παρθένος, that it was made by Jews before Christ, and that παρθένος in its Greek means a virgin, and it follows that a Jewish translator, before Christ, read the woman of 7:14 as a virgin.

That is the whole of what it delivers: a claim about how the first translator read the verse. It does not show that παρθένος meant "virgin" in the translator's day: that is granted here, and rated disputed (parthenos_is_load_bearing). Nor does it show what עַלְמָה means (septuagint_word_rests_on_its_inference), or how the woman conceived (septuagint_leaves_the_conception_open).

theorem septuagintWitness_establishes : Establishes septuagintWitness
-- axioms: propext, Quot.sound

septuagintWitness_is_satisfiable

The Septuagint as a witness has a model.

theorem septuagintWitness_is_satisfiable : Satisfiable
    septuagintWitness.premises
-- axioms: propext, Quot.sound

wegnerDriftReading

Wegner's reading: in the translator's day παρθένος meant "young woman", with or without virginity, and did not yet mean "virgin"; so the Greek does not show that its translator read the woman of 7:14 as a virgin, nor anything about how she conceived, and עַלְמָה does not denote a virgin either. The woman of 7:14 is already pregnant when the sign is given, and the sign need not be a miracle. Wegner does not take up the laws of the Greek Pentateuch. This reading extends his view to them as Miller reads them: the laws say what they say, and the word in them still means "young woman". Nor does he take up Exodus 22:15–16; in this reading Genesis 34 is told in that law's words, and Dinah is still called a παρθένος in the older sense.

def wegnerDriftReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.parthenosMeansVirgin => False
    | Claim.lawsUseParthenosAsVirgin => False
    | Claim.dinahIsTheLawsParthenos => False
    | Claim.lxxIsaiahUsesParthenosAsVirgin => False
    | Claim.lxxReadsAVirgin => False
    | Claim.lxxEnvisagesAVirginalConception => False
    | Claim.almahMeansVirgin => False
    | Claim.signMustBeExtraordinary => False
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | x => True

parthenos_is_load_bearing

The word carries the whole witness. Keep the rendering and its date — the Greek has παρθένος, and Jews made it before Christ — and grant nothing about what παρθένος meant to them, and the Septuagint no longer shows that its translator read the woman as a virgin. On Wegner's reading the word was the ordinary one for a young woman of marriageable age.

So whoever argues from the Septuagint has to win the claim about the word. Its date, which the rival grants, does not help without it.

theorem parthenos_is_load_bearing : ¬Establishes septuagintWithoutTheSense
-- axioms: propext, Quot.sound

From the translator's reading to Isaiah's word

septuagintOnTheWord_establishes

Add the step from the translator's reading to Isaiah's word, rated disputed, and the case concludes that עַלְמָה denotes a virgin. It is only as good as that step.

theorem septuagintOnTheWord_establishes : Establishes septuagintOnTheWord
-- axioms: propext, Quot.sound

septuagintOnTheWord_is_satisfiable

The Septuagint asked for Isaiah's word has a model.

theorem septuagintOnTheWord_is_satisfiable : Satisfiable
    septuagintOnTheWord.premises
-- axioms: propext, Quot.sound

translatorDescribesTheWomanReading

The referential reading of the Septuagint: its translator read the woman of 7:14 as a virgin, with a word that means one, and עַלְמָה still denotes only a young woman of marriageable age. He described the woman, not the word, and the woman is a virgin.

def translatorDescribesTheWomanReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.parthenosDescribesDinahAsSheThenWas => False
    | Claim.almahMeansVirgin => False
    | Claim.harahIsPredicateAdjective => False
    | Claim.isaianicAlmahIsAlreadyPregnant => False
    | Claim.isaianicAlmahIsNotAVirgin => False
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | x => True

septuagint_word_rests_on_its_inference

The Septuagint shows how its translator read the woman, not what Isaiah's word means. Grant everything the witness rests on, παρθένος as "virgin" included, and grant that the translator read the woman of 7:14 as a virgin: עַלְמָה can still denote only a young woman, as the referential strand reads it. The step from the one to the other is the weight, and it is rated disputed: Bratcher and Brown grant that the translator read the woman as a virgin and deny that עַלְמָה says so, and Walton holds that the Greek shows "at best ... an interpretational preference rather than a linguistic necessity" (293). On Bratcher's reading (113), the Septuagint's translators render the woman, not the word: παρθένος for Rebekah, whom the story calls a virgin (Genesis 24:43), and νεᾶνις at Exodus 2:8, Psalm 67:26 (68:25 in English Bibles), Song 1:3 and 6:8. Jerome reads Rebekah the other way, as showing that עַלְמָה denotes a virgin (Against Jovinianus I.32).

So the Septuagint cannot by itself settle the claim that עַלְמָה itself denotes a virgin, however its word is read. If its word means "virgin", what it can do is what the referential strand already needs: show that a virgin answers the description.

theorem septuagint_word_rests_on_its_inference : ¬Entails
    septuagintLine.premises (p Claim.almahMeansVirgin)
-- axioms: propext, Quot.sound

What the Greek leaves open

nowAVirginReading

Bratcher's reading of the Greek, who holds that its word means a virgin: "a young woman, at that time virgin, would in the normal way marry and bear a child" (115). Rhodea gives the Greek the same reading, granting its sense for argument's sake and quoting Tsevat: "The pregnancy lies in the future ...; nothing indicates that the woman is also a virgin after the conception" (67). The word means a virgin, the translator read her as one, and she is one when the sign is given; she conceives later, by a man.

def nowAVirginReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.parthenosDescribesDinahAsSheThenWas => False
    | Claim.lxxEnvisagesAVirginalConception => False
    | Claim.harahIsPredicateAdjective => False
    | Claim.isaianicAlmahIsAlreadyPregnant => False
    | Claim.isaianicAlmahIsNotAVirgin => False
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | x => True

septuagint_leaves_the_conception_open

Granted every word, the Septuagint leaves the conception open. Keep the rendering, its date, παρθένος as "virgin", the reading it delivers, and the tense of the verb — the virgin shall be with child — and whether its translator meant a conception without a man is independent of all of it. On Bratcher's reading, who holds that the word means a virgin, she is a virgin when the sign is given and later conceives in the ordinary way; Rhodea reads it so too, granting the sense for argument's sake. On Justin's she conceives as a virgin. Both readings keep every premise.

No premise here speaks to how she conceives, so the result says only that the Greek's own words leave it open. Justin's argument that an ordinary conception would be no sign is the sign argument's, and is weighed in Dispute.Wegner.

The result has two halves: the Greek does not show that the translator meant a conception without a man, and does not show that he did not. If its sense is granted, the Septuagint's word answers the objection that the virgin reading was a Christian invention; it does not supply the virginal conception. That comes, if it comes, from the promise of a sign (signLine), or from Matthew and Luke.

theorem septuagint_leaves_the_conception_open : Independent
    septuagintWithTheFuture.premises (p Claim.lxxEnvisagesAVirginalConception)
-- axioms: propext, Quot.sound

TestimonyArguments.BornOfAVirgin.Results.Genesis — what "her seed" says of a father

A reader's question, in a reader's words: Genesis 3:15 promises that "her seed" will strike the serpent's head — the woman's seed, not the man's. Doesn't that already point to a virgin conception? And doesn't the Greek, which calls the seed "he", make it plainer?

The short answer: it may, but the text does not settle it. Whether naming the seed as the woman's says there will be no human father is a live dispute among readers most of whom hold the virgin birth, and the library finds it a tie (nothing_prevails_over_her_seed, in Dispute.Genesis). That the wording fits the virgin birth, once it has happened, Luther's side and Leupold and Keil all grant. The Greek may show that its translator expected one person; it does not show how that person would be born.

The protoevangelium strand of this argument holds, as a premise, that the seed being named as the woman's marks a birth with no human father (seedOfTheWomanImpliesNoHumanFather). "Marks" is vague on purpose, as its holders leave it: Miravalle's own word is "hint". This module asks what it can mean, and what each meaning can bear.

Read as what the wording itself signifies, it is Luther's argument: the seed of other women "might rather be said to have been the seed of the man", but Mary's was "the true Seed of Mary" (Luther on the Creation 298–99). He finds the sense in the words of Genesis, and holds that Isaiah later "threw some additional light" on it, so that "it was then made certain" (298). herSeedCase_establishes grants him every ground and checks that the argument goes through. It rests on his step (her_seed_rests_on_its_inference). The Lutheran commentators Leupold and Keil, who hold the virgin birth, grant every ground and deny the step. Leupold, asked whether the expression is "so phrased in reference to Mary and the virgin birth", answers "Not primarily, but at least incidentally": it "does not specifically prophesy the virgin birth" (169). Keil finds the virgin birth in the promise's fulfilment, "even if the words had reference first of all to the fact that the woman had been led astray" (102). Jack P. Lewis denies the step too, pointing to Hagar and Rebekah, whose seed Genesis also calls theirs (299–300); he doubts the promise reading itself, but his argument does not need that doubt.

Read as what the wording fits, once fulfilled, it is granted by Leupold and Keil, who deny the first reading. Leupold: "it coincides and agrees with it under divine providence" (169). Keil: the promise was fulfilled "even in its apparently casual form" (102). But they reach the fit from the conception: the wording is seen to fit once the birth is known. Read this way, the verse confirms the virgin birth to one who already believes it, and gives no reason to believe it to one who does not. That is what the reading's own grounds say; it is not a separate theorem. whatHerSeedMarks sets out both readings and what answers each.

The promise, and its fulfilment. Whether the wording foretold a virgin birth is one question. Whether the promise is fulfilled in Jesus is another, and it does not need the first. Every term of the verse is met as the New Testament names it: the woman's seed, the Son "made of a woman" (Galatians 4:4); the serpent, "that old serpent, called the Devil" (Revelation 12:9); its head crushed, when the Son destroys the devil "through death" (Hebrews 2:14); his heel struck, in his death and rising. That fulfilment confirms that the verse was a promise, and it does so for a reader who denies the virginal conception too. With the virginal conception, it says one thing more: the seed in whom the promise is fulfilled was of the woman alone. Dispute.Protoevangelium weighs the fulfilment against Westermann's denial that the verse is a promise at all.

The Greek's "he". The Septuagint calls the woman's seed "he", αὐτός, though σπέρμα is neuter, and Collins finds it "beyond question that the translator of Genesis 3:15 meant to convey that an individual was promised" (145) (greekHeCase_establishes). If so, it shows how one Jewish translator before Christ read the promise, and reading it of one person is no Christian invention. But the earliest known reader of that Greek did not read it so: Philo calls the masculine "as to its language, a barbarism, but, as to the meaning … a correct expression", and takes "he" of the mind (Allegorical Interpretation III.188). The claim is disputed on him. No other text before Christ reads the verse of one victor; the Targums, later, read it of "the sons of the woman", with a remedy "in the days of the King Messiah" (Lewis 301). Whether the Hebrew says so is a further question: Collins argues that its syntax is "quite consistent with the pattern where a single individual is in view" (145), and reports that many think it does not (141); Lewis, who grants the Greek's reading, allows that the masculine "could be an oversight" (300). Either way, the Greek says nothing of a father (the_greek_he_leaves_the_father_open): the same Greek calls the seed Hannah asks for "him" (1 Samuel 1:11), and the seed promised to David "he" (2 Samuel 7:12–14), and each has a father. Irenaeus, quoting the verse as the Greek gives it, "He shall be on the watch for thy head", reads it of "He who should be born of a woman, [namely] from the Virgin" (Against Heresies V.21.1); but he does not argue from the pronoun to the conception, and no reader found does.

Dispute.Genesis weighs Luther's case against Leupold's and Lewis's.

Two readings of the woman's seed

Each reading below is a model: one way every claim of the argument could be true at once, named for what it says of the wording of Genesis 3:15. Some pairs of claims in this argument cannot both be true, so each model has to take a side on them; on questions this module does not touch it takes the scriptural reading's side: that the Septuagint's παρθένος means a virgin, that Micah's mention of a mother and no father does mean something, and that Scripture, not the magisterium, is the judge. Every other claim it leaves true, and none of them bears on the results it is used for.

lutherReading

Luther's reading: the seed named as the woman's, and not a man's, signifies a birth with no human father, and the promise is fulfilled in one so born.

def lutherReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.parthenosDescribesDinahAsSheThenWas => False
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | x => True

leupoldReading

Leupold's reading: the promise is of the victor, "her seed" is first collective, the woman's posterity, the woman is named because she was deceived, and the wording does not itself signify a birth without a human father — though it fits one, as fulfilled. Lewis's claims hold in it too: Genesis speaks of a woman's seed in ordinary births. And "her seed", though collective first, is not only a line of descendants: "the word is also used in reference to an individual" (168).

def leupoldReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.wordingSignifiesAFatherlessBirth => False
    | Claim.seedIsLineNotIndividual => False
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.parthenosDescribesDinahAsSheThenWas => False
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | x => True

The wording read as signifying

herSeedCase_establishes

Luther's case from the wording goes through. Grant that Genesis 3:15 names the seed as the woman's, that it is the first promise of a redeemer, that a man's seed is ordinarily reckoned through him, and Luther's step from these to the wording's sense: the wording signifies a birth with no human father.

It does not show that the step is sound — Leupold, Keil and Lewis deny it (her_seed_rests_on_its_inference) — nor that the promise was fulfilled.

theorem herSeedCase_establishes : Establishes herSeedCase
-- axioms: propext, Quot.sound

herSeedCase_is_satisfiable

Luther's case has a model: his own reading.

theorem herSeedCase_is_satisfiable : Satisfiable herSeedCase.premises
-- axioms: propext, Quot.sound

her_seed_rests_on_its_inference

The wording's sense rests on Luther's step. Grant every ground — the seed named as the woman's, Genesis 3:15 as the first promise of a redeemer, a man's seed reckoned through him — and it still does not follow that the wording signifies a birth with no human father. Leupold and Keil grant those grounds and deny it, and Lewis, granting the messianic reading for argument's sake, denies it too. On Leupold's reading the seed is named the woman's because she was deceived, and "her seed" is first collective, her posterity.

So the claim does not follow from the grounds alone: it needs Luther's step, rated disputed. That does not show the step is wrong, only that the wording, which both sides read, does not decide between them.

theorem her_seed_rests_on_its_inference : ¬Entails herSeedLine.grounds (p
    Claim.wordingSignifiesAFatherlessBirth)
-- axioms: propext, Quot.sound

posterityCase_establishes

Leupold's case goes through on its own grounds.

theorem posterityCase_establishes : Establishes posterityCase
-- axioms: propext, Quot.sound

posterityCase_is_satisfiable

Leupold's case has a model: his own reading.

theorem posterityCase_is_satisfiable : Satisfiable posterityCase.premises
-- axioms: propext, Quot.sound

idiomCase_establishes

Lewis's case goes through on its own grounds.

theorem idiomCase_establishes : Establishes idiomCase
-- axioms: propext, Quot.sound

idiomCase_is_satisfiable

Lewis's case has a model: Leupold's reading, in which Lewis's claims hold too.

theorem idiomCase_is_satisfiable : Satisfiable idiomCase.premises
-- axioms: propext, Quot.sound

The Greek's "he"

greekHeCase_establishes

The Greek reads one person. Grant that the Septuagint refers to the woman's seed with the masculine αὐτός, though σπέρμα is neuter, and the step Collins and Martin take from it, and its translator read the seed as one person.

That is all it delivers: who that person is, and how he is born, it does not say.

theorem greekHeCase_establishes : Establishes greekHeCase
-- axioms: propext, Quot.sound

greekHeCase_is_satisfiable

The Greek's line has a model.

theorem greekHeCase_is_satisfiable : Satisfiable greekHeCase.premises
-- axioms: propext, Quot.sound

the_greek_he_leaves_the_father_open

The Greek's "he" leaves the father open. Keep the Greek's masculine "he" and the reading of one person drawn from it, and every ground of Luther's case — the seed named as the woman's, the first promise of a redeemer, a man's seed reckoned through him — and whether the wording signifies a birth with no human father is independent of all of it. On Luther's reading it does; on Leupold's, granted the Greek, it does not.

The result has two halves: the Greek does not show that the one person promised has no human father, and does not show that he has one. The plain reason is in the Greek itself: it calls the seed Hannah asks for "him" (1 Samuel 1:11), and the seed promised to David "he" (2 Samuel 7:12–14), as Collins shows (144), and each has a father. One person, called "he", can have a father. What the Greek shows is how its translator read the promise: of one person. Collins argues that the Hebrew's syntax is "quite consistent with the pattern where a single individual is in view" (145); Leupold reaches one person at the promise's end, and Keil reaches Christ "not as an individual, but as the head" of the woman's posterity (102). No reader found argues that the Greek's "he" answers Lewis's point from Hagar and Rebekah.

theorem the_greek_he_leaves_the_father_open : Independent
    greekHeWithThePromise.premises (p Claim.wordingSignifiesAFatherlessBirth)
-- axioms: propext, Quot.sound

What "marks" means: the dilemma

asWhatTheWordingSignifies

The hinge read as what the wording itself signifies: Luther's reading, and the one Miravalle and Henry give.

def asWhatTheWordingSignifies : Reading Claim :=
  { name := "as what the wording itself signifies",
    commits := p Claim.wordingSignifiesAFatherlessBirth,
    source :=
      { primary := Reference.work lutherOnTheCreation (Bib.Locus.pages 298 299),
        supporting :=
          [Reference.work miravalleMeetYourMother,
            Reference.work henryCommentary
              (Bib.Locus.adLoc Scripture.genesis3_15)],
        tradition := Tradition.christianTypological,
        confidence := Confidence.disputed } }

asWhatTheWordingFits

The hinge read as what the wording fits, once fulfilled: Leupold's and Keil's reading, which rests the fit on the virginal conception itself.

def asWhatTheWordingFits : Reading Claim :=
  { name := "as what the wording fits, once fulfilled",
    commits := p Claim.wordingFitsAFatherlessBirth,
    grounds :=
      [p Claim.maryConceivedAsVirgin,
        p Claim.maryConceivedAsVirgin 🡒
          p Claim.wordingFitsAFatherlessBirth],
    source :=
      { primary := Reference.work leupoldGenesis (Bib.Locus.page 169),
        supporting :=
          [Reference.work keilDelitzschPentateuch (Bib.Locus.page 102)],
        tradition := Tradition.christianHistoricalGrammatical,
        confidence := Confidence.disputed } }

protoevangeliumAsSignifying — Protoevangelium strand (Genesis 3:15), read as what the wording itself signifies

The protoevangelium strand with its hinge read as Luther reads it.

No premise here rests on scripture alone.

protoevangeliumAsFitting — Protoevangelium strand (Genesis 3:15), read as what the wording fits, once fulfilled

The protoevangelium strand with its hinge read as Leupold reads it.

No premise here rests on scripture alone.

protoevangeliumAsSignifying_is_satisfiable

The strand, read as Luther reads its hinge, is consistent: its premises can all be true together, so any answer to it must come from outside it.

theorem protoevangeliumAsSignifying_is_satisfiable : Satisfiable
    protoevangeliumAsSignifying.premises
-- axioms: propext, Quot.sound

protoevangeliumAsFitting_is_satisfiable

The strand, read as Leupold reads its hinge, is consistent too.

theorem protoevangeliumAsFitting_is_satisfiable : Satisfiable
    protoevangeliumAsFitting.premises
-- axioms: propext, Quot.sound

posterity_does_not_reach_the_fit

Leupold has no quarrel with the second reading; he holds it. Read as what the wording fits once fulfilled, the strand's hinge can be held with every premise of Leupold's case.

theorem posterity_does_not_reach_the_fit : Satisfiable (posterityCase.premises
    ++ protoevangeliumAsFitting.premises)
-- axioms: propext, Quot.sound

idiom_does_not_reach_the_fit

Nor does Lewis. The idiom of Hagar and Rebekah bears on what the wording signifies, not on what it fits once fulfilled.

theorem idiom_does_not_reach_the_fit : Satisfiable (idiomCase.premises ++
    protoevangeliumAsFitting.premises)
-- axioms: propext, Quot.sound

whereTheSignifyingReadingMeetsLeupold

Why Leupold stands against the hinge, read as Luther reads it. The crux is Leupold's step: "her seed" is first collective, the woman's posterity, and the woman is named because she was deceived, so the wording does not itself signify a birth without a human father. No one can hold both Leupold's case and the hinge read Luther's way; which gives way is the dispute's question, and Dispute.Genesis finds a tie. What cannot be held with Leupold is the hinge together with the reading, nothing else in the strand, and the step is rated disputed: Irenaeus grants both its grounds, and Henry the second, and both read the verse of the Virgin's son.

Why Leupold on 'her seed': her posterity, named for the deception stands against Protoevangelium strand (Genesis 3:15), read as what the wording itself signifies.

• The crux: \((P_{50} \land P_{56} \land P_{57}) \rightarrow \lnot P_{54}\), a premise of Leupold on 'her seed': her posterity, named for the deception.
• What it does: its conclusion does not follow without it.
• Granted: \(P_{50}\), \(P_{56}\), \(P_{57}\), which the break also needs.
• Where the rival breaks: \(P_{53}\), \(P_{53} \rightarrow P_{54}\) cannot be held together with \((P_{50} \land P_{56} \land P_{57}) \rightarrow \lnot P_{54}\) and \(P_{50}\), \(P_{56}\), \(P_{57}\); each is needed for the break, and without the crux they stand.
• What this rests on:
  • \(P_{50}\) Genesis 3:15 says that 'her seed' will strike the serpent's head — consensus: Gen 3:15; bhs-1997, app. Gen 3:15
  • \(P_{56}\) 'Her seed' at Genesis 3:15 is first collective: her posterity, not one person — disputed: leupold-exposition-genesis-1942, pp. 167–169; calvin-commentary-genesis-1847, p. 170; keil-delitzsch-pentateuch-1866, p. 101; collins-syntactical-note-1997, pp. 145–146
  • \(P_{57}\) The seed is called the woman's because the serpent deceived the woman — well supported: leupold-exposition-genesis-1942, p. 165; leupold-exposition-genesis-1942, p. 169; calvin-commentary-genesis-1847, p. 170; henry-commentary-whole-bible, ad loc. Gen 3:15; keil-delitzsch-pentateuch-1866, p. 102
  • the step itself — disputed: leupold-exposition-genesis-1942, p. 169; keil-delitzsch-pentateuch-1866, pp. 101–102; calvin-commentary-genesis-1847, p. 170; irenaeus-against-heresies-180, §III.23.7; irenaeus-against-heresies-180, §V.21.1; henry-commentary-whole-bible, ad loc. Gen 3:15

whereTheSignifyingReadingMeetsLewis

Why Lewis stands against the hinge, read as Luther reads it. The crux is Lewis's step: Genesis speaks of Hagar's and Rebekah's seed too, so the woman's seed at 3:15 does not by itself signify a birth without a human father. Rated disputed, on Jimmy Akin, who grants that a woman's seed "is not outside the bounds of Hebrew expression" and agrees with the "many" who have "rightly seen" the wording as "a hint of the Virgin Birth".

Why Lewis on 'her seed': Genesis says it of Hagar and Rebekah too stands against Protoevangelium strand (Genesis 3:15), read as what the wording itself signifies.

• The crux: \((P_{50} \land P_{58}) \rightarrow \lnot P_{54}\), a premise of Lewis on 'her seed': Genesis says it of Hagar and Rebekah too.
• What it does: its conclusion does not follow without it.
• Granted: \(P_{50}\), \(P_{58}\), which the break also needs.
• Where the rival breaks: \(P_{53}\), \(P_{53} \rightarrow P_{54}\) cannot be held together with \((P_{50} \land P_{58}) \rightarrow \lnot P_{54}\) and \(P_{50}\), \(P_{58}\); each is needed for the break, and without the crux they stand.
• What this rests on:
  • \(P_{50}\) Genesis 3:15 says that 'her seed' will strike the serpent's head — consensus: Gen 3:15; bhs-1997, app. Gen 3:15
  • \(P_{58}\) Genesis speaks of a woman's seed in ordinary births: Hagar's and Rebekah's — consensus: Gen 16:10; Gen 24:60; lewis-womans-seed-1991, pp. 299–300
  • the step itself — disputed: lewis-womans-seed-1991, pp. 299–300; lewis-womans-seed-1991, p. 319; akin-woman-seed-serpent-1999

whatHerSeedMarks

What the woman's seed marks, read both ways. The claim is the protoevangelium strand's hinge: the seed being named as the woman's marks a birth with no human father. These are the two readings found in the sources; a reader with a third would add a third horn.

Read as what the wording itself signifies (Luther's reading), it cannot be held together with Leupold's case or with Lewis's. Each breaks it at a step rated disputed, not at a ground. Leupold's grounds, that the seed is named the woman's because she was deceived and that "her seed" is first collective, her posterity, are rated wellSupported and disputed; Lewis's, that Genesis says "her seed" of Hagar and of Rebekah, each with a father, is common ground. What is contested is the step from them to "so the wording does not signify a birth without a father". A reader who takes those steps rejects Luther's reading. One who grants the grounds and refuses the steps need not, as Irenaeus does with Leupold's and Akin with Lewis's. "Cannot be held together" says that no one can hold both, not which gives way: Dispute.Genesis weighs that, and finds a tie.

Read as what the wording fits, once fulfilled (Leupold's and Keil's reading), neither case touches it: Leupold and Keil hold it. But the reading rests on the virginal conception itself (maryConceivedAsVirgin). That is rated disputed because Brown, the historian this argument cites, leaves the question unresolved; the rating records that it is contested, not that the library doubts it. On this reading the strand can show that the promise suits a birth already believed, not that the promise foretold it.

Neither reading is a straw man: read either way, the strand's premises can all be true together.

Every reading of \(P_{53}\), answered. Protoevangelium strand (Genesis 3:15) holds \(P_{53}\). It is read 2 ways here, and each reading is checked; none can be left out.

1. Read as what the wording itself signifies. The claim commits Protoevangelium strand (Genesis 3:15) to \(P_{54}\) — so read by luther-on-the-creation-1904, pp. 298–299; miravalle-meet-your-mother-2014; henry-commentary-whole-bible, ad loc. Gen 3:15 (disputed).

Against Leupold on 'her seed': her posterity, named for the deception, it cannot be held. Where it breaks:

Why Leupold on 'her seed': her posterity, named for the deception stands against Protoevangelium strand (Genesis 3:15), read as what the wording itself signifies.

• The crux: \((P_{50} \land P_{56} \land P_{57}) \rightarrow \lnot P_{54}\), a premise of Leupold on 'her seed': her posterity, named for the deception.
• What it does: its conclusion does not follow without it.
• Granted: \(P_{50}\), \(P_{56}\), \(P_{57}\), which the break also needs.
• Where the rival breaks: \(P_{53}\), \(P_{53} \rightarrow P_{54}\) cannot be held together with \((P_{50} \land P_{56} \land P_{57}) \rightarrow \lnot P_{54}\) and \(P_{50}\), \(P_{56}\), \(P_{57}\); each is needed for the break, and without the crux they stand.
• What this rests on:
  • \(P_{50}\) Genesis 3:15 says that 'her seed' will strike the serpent's head — consensus: Gen 3:15; bhs-1997, app. Gen 3:15
  • \(P_{56}\) 'Her seed' at Genesis 3:15 is first collective: her posterity, not one person — disputed: leupold-exposition-genesis-1942, pp. 167–169; calvin-commentary-genesis-1847, p. 170; keil-delitzsch-pentateuch-1866, p. 101; collins-syntactical-note-1997, pp. 145–146
  • \(P_{57}\) The seed is called the woman's because the serpent deceived the woman — well supported: leupold-exposition-genesis-1942, p. 165; leupold-exposition-genesis-1942, p. 169; calvin-commentary-genesis-1847, p. 170; henry-commentary-whole-bible, ad loc. Gen 3:15; keil-delitzsch-pentateuch-1866, p. 102
  • the step itself — disputed: leupold-exposition-genesis-1942, p. 169; keil-delitzsch-pentateuch-1866, pp. 101–102; calvin-commentary-genesis-1847, p. 170; irenaeus-against-heresies-180, §III.23.7; irenaeus-against-heresies-180, §V.21.1; henry-commentary-whole-bible, ad loc. Gen 3:15

Against Lewis on 'her seed': Genesis says it of Hagar and Rebekah too, it cannot be held. Where it breaks:

Why Lewis on 'her seed': Genesis says it of Hagar and Rebekah too stands against Protoevangelium strand (Genesis 3:15), read as what the wording itself signifies.

• The crux: \((P_{50} \land P_{58}) \rightarrow \lnot P_{54}\), a premise of Lewis on 'her seed': Genesis says it of Hagar and Rebekah too.
• What it does: its conclusion does not follow without it.
• Granted: \(P_{50}\), \(P_{58}\), which the break also needs.
• Where the rival breaks: \(P_{53}\), \(P_{53} \rightarrow P_{54}\) cannot be held together with \((P_{50} \land P_{58}) \rightarrow \lnot P_{54}\) and \(P_{50}\), \(P_{58}\); each is needed for the break, and without the crux they stand.
• What this rests on:
  • \(P_{50}\) Genesis 3:15 says that 'her seed' will strike the serpent's head — consensus: Gen 3:15; bhs-1997, app. Gen 3:15
  • \(P_{58}\) Genesis speaks of a woman's seed in ordinary births: Hagar's and Rebekah's — consensus: Gen 16:10; Gen 24:60; lewis-womans-seed-1991, pp. 299–300
  • the step itself — disputed: lewis-womans-seed-1991, pp. 299–300; lewis-womans-seed-1991, p. 319; akin-woman-seed-serpent-1999

2. Read as what the wording fits, once fulfilled. The claim commits Protoevangelium strand (Genesis 3:15) to \(P_{55}\) — so read by leupold-exposition-genesis-1942, p. 169; keil-delitzsch-pentateuch-1866, p. 102 (disputed). It rests the reading on \(P_{79}\), \(P_{79} \rightarrow P_{55}\).

Against Leupold on 'her seed': her posterity, named for the deception, it is not reached: Leupold on 'her seed': her posterity, named for the deception holds, and can be held together with it.

Against Lewis on 'her seed': Genesis says it of Hagar and Rebekah too, it is not reached: Lewis on 'her seed': Genesis says it of Hagar and Rebekah too holds, and can be held together with it.

TestimonyArguments.BornOfAVirgin.Dispute — who prevails over Isaiah 7:14

The results in Results.lean ask what each package entails. This module asks what happens when the packages meet: the scriptural reading, the critical denial of the predictive reading, and four replies to that denial — Berry's objection, Postell's two counterexamples (Isaiah 9 and 11, and Micah 5), and Motyer's reply, with Compton's — taken together as one dispute.

Who defeats whom is not stipulated. Each defeat below is a theorem about the packages' premises, and so is each absence of one (see Testimony.Logic.Dispute for how an attack is derived from entailment and filtered by cited confidence). The defeats are these:

• The critical denial defeats the scriptural reading. It entails the negation of the scriptural premise that Isaiah 7:14 predicts a virgin birth, a premise cited as disputed.
• The scriptural reading defeats the critical denial back. It undermines none of the critic's premises, but it concludes the opposite, so it rebuts; and the weakest link on each side is disputed, so neither outranks the other.
• Berry and both of Postell's counterexamples defeat the critical denial, by contradicting its premise that a near-term sign excludes a messianic sense, cited disputed.
• Motyer defeats it too, by contradicting its other premise: that 7:14 is a near-term sign to Ahaz at all, also cited disputed.
• The critical denial defeats Berry and Motyer back, but neither counterexample. It rebuts all four. Berry's and Motyer's inferences are contested — a cited source grants each one's grounds and denies its conclusion — so they are no stronger than the critic. Postell's inference is not, and both counterexamples outrank it.

What follows

Faced with the scriptural reading alone, nothing prevails: the two defeat each other, and the grounded extension is empty. Add the replies and the scriptural reading prevails. Nothing defeats Postell's counterexamples; they defeat the critic, which is the only party that defeats the scriptural reading, Berry or Motyer; and so all five stand. The critical denial belongs to no admissible set at all, because nothing answers Postell. Take away either counterexample and the scriptural reading still prevails; take away both and nothing does.

This is the result entailment could not state. Adding premises never removes a conclusion; adding arguments can change what a dispute forces, and here it turns an open question into a settled one. The replies do not show that the predictive reading is true. They show that, on these premises and these ratings, the case against it does not survive them.

What the ratings decide

These outcomes rest on the cited confidences as much as on the premises, and the inferences are rated as the premises are: disputed when a cited source grants a step's grounds and denies its conclusion. Before they were rated, a reply that put its contested move in a step was weighed by its observations alone, and every reply outranked the critic. Rated, only one does.

The critic's two premises are disputed: Berry, Postell and Motyer contest the exclusion, Motyer and Compton the near-term sign. Its inference is consensus, because it only applies the exclusion to 7:14.

Berry's inference is disputed. Watts grants that the chronology is uncertain and still reads 7:14 of Hezekiah, as Compton reports. Motyer's is disputed for the same reason: those who identify the two children grant both his observations and keep the near-term sign, and motyer_rests_on_his_inference proves that the whole weight of his reply falls on that step. So each ties with the critic, and heard alone Motyer settles nothing (nothing_prevails_on_motyer_alone).

Postell's inference is plausible. It is a counterexample to the exclusion — an oracle on the Assyrian timeline, read messianically — and he gives two: Isaiah 9 and 11, and Micah 5, whose messianic reading Brown himself grants. No source cited here grants either set of grounds and keeps the exclusion.

The verdict rests on that inference. Without Postell's Isaiah argument the scriptural reading still prevails, on the Micah counterexample (scriptural_reading_prevails_without_postell), so an attack on the grounds of either — dating Isaiah 11 later, say — leaves it standing. Without both, every party is defeated by someone and nothing prevails (nothing_prevails_without_the_counterexamples). The two share one inference, so they share one weakness: rated disputed, it would tie both with the critic as Berry's and Motyer's do. A critic who granted that such an oracle is read messianically and still held the exclusion — most likely by denying that Micah 5 or Isaiah 9 is a sign to Ahaz — would be the source to find.

What the church fathers add, and what they cannot

The predictive reading is not a modern apologetic. Justin, Irenaeus, Origen and Jerome all argue it, and Sources.lean cites them for it: for the prediction itself, and for עַלְמָה as a virgin. Every father the library has read on the verse — Tertullian, Eusebius, Cyril of Jerusalem, Chrysostom, Cyril of Alexandria and Theodoret besides — argues that an ordinary conception would have been no sign at all. Several grant the Jewish "young woman" and answer as the referential reading does: a young woman can be a virgin, as the betrothed νεᾶνις of Deuteronomy 22:23–27 is, whom 22:23 calls a παῖς παρθένος. None asks whether παρθένος could itself mean a girl who is not a virgin; the question Wegner raises was not theirs. That strengthens the attestation of the scriptural premises, and none of it changes a rating.

The fathers' witness cannot change a rating, because of what disputed means here: actively contested by competent scholars. The fathers are the earliest witnesses to the contest as well as to the reading. Justin records Trypho's answer — "young woman", and fulfilled in Hezekiah — and Irenaeus names Theodotion and Aquila. An older witness does not make a contested claim uncontested. What decides the result here is the same definition applied to the other side: both of the critic's premises are contested too, and the library records who contests them.

The sign argument is encoded as an argument in its own right, signLine. It answers Wegner's objection rather than the critical denial, so it is weighed in Dispute.Wegner, where it ties with Wegner (nothing_prevails_over_wegner).

The replies as positions

Each reply is an argument in its own right, so it must hold together and deliver its conclusion before it can take part in a dispute.

repliesStandReading

The world Berry and Postell describe: everything holds except that a near-term sign excludes a messianic sense. The scriptural reading holds in it too. A reading cannot hold both claims about the Septuagint's παρθένος, and this one takes Rico and Gentry's; the scriptural reading needs neither, and Dispute.Septuagint weighs the two.

def repliesStandReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.parthenosDescribesDinahAsSheThenWas => False
    | Claim.nearTermExcludesMessianicSense => False
    | x => True

berryObjection_establishes

Berry's objection delivers its conclusion.

theorem berryObjection_establishes : Establishes berryObjection
-- axioms: propext, Quot.sound

berryObjection_is_satisfiable

Berry's objection has a model.

theorem berryObjection_is_satisfiable : Satisfiable berryObjection.premises
-- axioms: propext, Quot.sound

postellParity_establishes

Postell's parity argument delivers its conclusion.

theorem postellParity_establishes : Establishes postellParity
-- axioms: propext, Quot.sound

postellParity_is_satisfiable

Postell's parity argument has a model.

theorem postellParity_is_satisfiable : Satisfiable postellParity.premises
-- axioms: propext, Quot.sound

Postell's Micah counterexample

Postell's second counterexample is Micah 5, the Bethlehem oracle: a ruler set against the Assyrian invasion, and read messianically in first-century Judaism — which Brown, the critic's own authority, grants. It is the same inference as the Isaiah counterexample from a different oracle, so it guards against an attack on Postell's grounds and not against one on his inference.

laterMessianicReading

The rival reading, written first: Micah's ruler is a near-term Davidic king, and the messianic reading of him came later. Both grounds hold — the Assyrian setting and the first-century expectation — and so does the exclusion.

def laterMessianicReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.isaiahPredictsVirginBirth => False
    | x => True

micah_parity_rests_on_its_inference

The Micah counterexample rests on its inference: on the later-reading account both grounds hold and the exclusion stands.

theorem micah_parity_rests_on_its_inference : ¬Entails micahLine.grounds (notP
    Claim.nearTermExcludesMessianicSense)
-- axioms: propext, Quot.sound

micahParity_establishes

The Micah counterexample delivers its conclusion.

theorem micahParity_establishes : Establishes micahParity
-- axioms: propext, Quot.sound

micahParity_is_satisfiable

The Micah counterexample has a model.

theorem micahParity_is_satisfiable : Satisfiable micahParity.premises
-- axioms: propext, Quot.sound

Motyer's reply

Motyer's reply, with Compton's, denies the critic's other premise: that 7:14 is a near-term sign to Ahaz at all. It is built as Berry's and Postell's are. Its grounds are what the text says — the sign given to the house of David in the plural, and 8:4 repeating for Maher-shalal-hash-baz the timetable 7:16 gives the child — and the contested move is the step that joins them, rated disputed because a cited reading grants the grounds and denies what the step concludes.

sameChildReading

The rival reading, written first: the one that identifies the two children. Isaiah 8:1–4 retells the sign of 7:14–16 for Isaiah's own son, so the sign was a near-term one after all. Both of Motyer's observations hold in it — it is the reading his inference has to rule out.

def sameChildReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.isaiahPredictsVirginBirth => False
    | x => True

motyer_rests_on_his_inference

Motyer's reply rests on his inference, not on his observations. On the reading that identifies the two children, the sign is given to the house of David, 8:4 repeats the timetable of 7:16, and 7:14 is still a near-term sign to Ahaz. The two grounds do not decide the question; the step does, and a reader who contests the reply contests the step.

theorem motyer_rests_on_his_inference : ¬Entails motyerLine.grounds (notP
    Claim.isaiahIsNearTermSignToAhaz)
-- axioms: propext, Quot.sound

motyerReading

The world Motyer describes, with Berry and Postell: the sign is not a near-term one, and a near-term sign would not exclude a messianic sense anyway. Everything else holds — the scriptural reading and all four replies with it — and, as in repliesStandReading, Rico and Gentry's side is taken on παρθένος.

def motyerReading : Valuation Claim :=
  fun a =>
    match a with
    | Claim.maternalSilenceProvesNothing => False
    | Claim.magisteriumIsDoctrinallyAuthoritative => False
    | Claim.parthenosMeantYoungWoman => False
    | Claim.parthenosDoesNotItselfConnoteVirginity => False
    | Claim.parthenosDescribesDinahAsSheThenWas => False
    | Claim.isaiahIsNearTermSignToAhaz => False
    | Claim.nearTermExcludesMessianicSense => False
    | x => True

motyerReply_establishes

Motyer's reply delivers its conclusion.

theorem motyerReply_establishes : Establishes motyerReply
-- axioms: propext, Quot.sound

motyerReply_is_satisfiable

Motyer's reply has a model.

theorem motyerReply_is_satisfiable : Satisfiable motyerReply.premises
-- axioms: propext, Quot.sound

Strength: the weakest link of each position

Premises and inferences alike: a position is no stronger than the least supported thing it assumes, and an inference is something it assumes.

christian_strength

The scriptural reading is no stronger than its least supported premise, which is cited disputed.