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).