{"path":"research/what-relevance-is.md","content":"# What relevance is: separate from the argument, or read from it?\n\n**Date**: 2026-10-21 · **Type**: research and first-principles reading · **State**: nothing ruled; the\nreading in § 3 is Claude's, offered to be argued from examples (§ 4)\n\n**His question, verbatim** (2026-10-21, after asking that the map's relevance bands be drawn from the\nmachine relevance judge, and then pausing on it):\n\n> *\"Let's argue from first principles about this before we rule anything. … Ideally relate this to\n> embedding similarity but equally deeply to evidence-as-subgraph and relevance as depending on evidence,\n> as some have argued. Is relevance really a separate thing from the argumentation/subgraph or is it\n> wholly dependent on how that ends up looking, such that any estimation of it would be a premature\n> guess as to how the argumentation will evolve over time? Then it would risk being out of step with the\n> \"actual\" relevance. What IS the actual relevance? I feel like it's a separate thing but it's really\n> hard to pin down mentally.\"*\n\nAnd earlier the same day: *\"I'm not sure the machine relevance judge is what I want it to be yet, but I\nthink that's one of our best bets, so we don't get human-bottlenecked.\"*\n\nWhat the corpus already held, and which this note does not repeat: relevance as the difference a reason\nmakes, P(claim | reason) − P(claim | not reason), and the ruled two-factor rule as Jeffrey's update\n([strength-calculus-literature/bayesian-and-informal-logic.md](strength-calculus-literature/bayesian-and-informal-logic.md)\n§ 0, § 2.1); informal logic's acceptability, relevance and sufficiency (same note § 3.1); the six senses\nof the word in the corpus ([relevance-in-the-corpus-sweep.md](relevance-in-the-corpus-sweep.md) § 0b);\nthe three things under a step, facts, rule and application\n([retrofitting-the-reasons-channel.md](retrofitting-the-reasons-channel.md) § 9f); why the judge's\ndegree is unsteady ([the-chain-inside-a-link.md](the-chain-inside-a-link.md) § 10.2). New here: whether\nrelevance depends on the rest of the evidence, and what that makes of an estimate.\n\n---\n\n## 1. What the outside literature says, on the one question\n\nRead depth: the rule text and the advisory note of FRE 104 were read on the Cornell page; everything\nelse is from abstracts, secondary summaries and search results, marked where it matters. None of the\nbooks was read.\n\n**Every formal definition makes relevance relative to a body of evidence.**\n\n- **Keynes (1921).** Probability is a relation between evidence and a hypothesis, and irrelevance is\n  defined relative to the evidence one already has: new evidence is irrelevant when adding it leaves the\n  probability on the old evidence unchanged. (The exact formula was not found online; the relational\n  framing is confirmed by secondary sources. O'Donnell's paper on Keynes's weight works from his\n  definitions of irrelevance.)\n- **Carnap (1950).** Confirmation as positive relevance: e is relevant to h when the probability of h on\n  e differs from its prior, and relevance is stated *on* a body of evidence, three places, not two\n  (Gemes's reading, via secondary source; the corpus had Carnap from memory only).\n- **Bayesian networks (Pearl 1988; Verma & Pearl; Geiger & Pearl).** Whether one variable bears on\n  another is read from the graph *given what is observed*: conditioning on one node blocks a path\n  (screening off), and conditioning on a common effect opens one (explaining away). So the same two\n  nodes can be relevant, irrelevant, or relevant the other way, depending on the conditioning set.\n  (The d-separation papers were found; the book's chapter was not read.)\n- **Evidence law.** FRE 401: evidence is relevant if it has any tendency to make a fact of consequence\n  more or less probable. **FRE 104(b), read verbatim**: *\"When the relevance of evidence depends on\n  whether a fact exists, proof must be introduced sufficient to support a finding that the fact does\n  exist.\"* The advisory committee's example: *\"when a spoken statement is relied upon to prove notice to\n  X, it is without probative value unless X heard it.\"* Scholars have argued since Ball (1980) that\n  *all* evidence is conditionally relevant in this sense (ABA Litigation Journal, fall 2025).\n- **Schum (1994; Anderson, Schum & Twining).** Every item of evidence has two dimensions, relevance and\n  credibility (three credentials with inferential force). Relevance is established by an *argument*: a\n  chain of generalizations from the evidence to the matter to be proved. Evidence that bears on the\n  strength of one of those links, not on the conclusion, is *ancillary* evidence; in his large case\n  study 164 directly relevant items built the network and 231 more attached at its links. (Secondary\n  sources; the book was not read.)\n- **Pollock.** An undercutting defeater attacks the connection between a reason and its conclusion\n  without saying the conclusion is false: an object looks red, but it is lit by red light. A\n  probabilistic statement: a new fact changes the probability of the conclusion given the reason.\n- **Dancy (holism of reasons).** A feature that is a reason in one case can count against in another,\n  or count for nothing. He separates *favourers* (the reason) from *enablers* and *disablers* (facts\n  that make it a reason or stop it being one) and *intensifiers* and *attenuators*. Tsu argues the\n  enabler is not part of the reason, since it can be absent while the reason-feature stays. Vorobej\n  reduces the four to two relations, favouring and supplementation. (Abstracts and course notes.)\n- **Walton and Macagno.** Dialectical relevance: whether a move is relevant depends on the type and\n  goal of the dialogue it is made in, and a graph model can help a third party judge it (\"Profiles of\n  Dialogue for Relevance\", *Informal Logic* 36(4), 2016; abstracts only).\n- **Blair (1992), already in the corpus.** Relevance lives in the warrant: premises are relevant when\n  they belong to a set that warrants the inference, through a conditional that can be justified.\n- **Sperber & Wilson.** Relevance in cognition: an input is relevant when, processed *in a context of\n  available assumptions*, it yields a positive cognitive effect, chiefly a contextual implication (a\n  conclusion that follows from input and context together but from neither alone), less the effort.\n- **Information retrieval (Saracevic).** Relevance is stratified: system, topical, cognitive,\n  situational, motivational. Topicality, being about the same subject, is one stratum among five.\n\n**On embeddings specifically.** A 2023 study of argumentative relevance (ICWSM 2023) defines it as one\nsentence having a reasoning connection to another and addressing a point it raises, and reports that\ngeneral sentence embeddings cannot tell purely topical relevance from topical-and-logical relevance.\nWachsmuth, Syed and Stein (ACL 2018) found the best counterargument is topically *similar* and of\n*opposite* stance, so similarity finds the right neighbourhood and says nothing about bearing or\ndirection. The corpus had the two cases already: *smoke, so fire* shares no word and bears strongly;\nthe two senses of *bank* share the word and bear on nothing (`retrofitting-the-reasons-channel.md` § 9f).\n\n## 2. The answer the literature converges on\n\n**Relevance is relational and relative to background, as every formal account has it.** No account\ngives a reason a relevance on its own; each gives it a relevance *on a body of evidence*. So \"the\"\nrelevance of a link, without saying relative to what, is not yet a number.\n\n**But the dependence has structure, and the structure is what makes it workable.** What fixes a link's\nrelevance divides three ways, and the three line up with the corpus's facts, rule and application:\n\n| What fixes it | Example | Where it lives | Whose |\n|---|---|---|---|\n| a general connection between kinds of thing | *rain wets the ground* | the rule | the world, not the debate |\n| facts of the case that switch the rule on or off | *the sprinklers ran at five* (a disabler, an undercutter); *the roof is wet too* (an enabler) | the case facts | the world, found by the debate |\n| the question the dialogue is about | whether it rained, as against whether the lawn needs watering | the dialogue | the debate |\n\nSchum's ancillary evidence, Pollock's undercutter, Dancy's enablers and disablers and the law's\nconditional relevance are four names for the second row: evidence that bears on the *link*.\n\n## 3. A reading, Claude's, unruled: what *actual* relevance is\n\n**Actual relevance is the difference the reason makes given everything that is true about the case and\nthe world.** It is a fact about the world, not about the debate, and the debate does not create it: the\ndebate *finds* the facts that fix it. In that sense his feeling is right, and it is a separate thing.\n\n**Every reading of it is relative to what is known so far, the same way a claim's strength is.** The\ncurrent graph holds some of the rule's backing and some of the case facts; a reading made now is the\nrelevance *given the record*, and it moves when an enabler or a disabler is added. That is not a\npremature guess at how the argument will go. It is the best reading of the present record, and its\nhonesty depends on two things the project already does for horizon kinds: it is computed, dated and\nre-read when the record changes (*read, never set*), and it never claims to be the final value.\n\n**What a machine judge reads, then.** Asked about a bare link, a model fills in a background of its own:\nthe rule as it believes it, and default case facts. Its gate is steady across models because almost any\nbackground agrees that rain bears on wet ground. Its degree is unsteady because each model supplies a\ndifferent background, which fits the measurement (4 to 6 of 12 agreed on the step) and § 10.2 of the\nchain note, which reaches the same place from the inside: *a degree asked of an unwritten leap has no\none thing to be a reading of*.\n\n**And in the limit the separate thing dissolves into the graph.** Write the step out (the rule, its\napplication, the case facts, ledger AG14 and AL8) and the link's relevance is no longer a free number: it\nis the standing of the rule claim, reduced by any disabler that stands. The rule still carries a degree\n(*rain usually wets the ground* is reliable; *a red sky usually means rain* less so), and that degree is\nthe rule claim's own strength, argued like any claim (⚠ 22 October, raised by session b66ddc4d and\nagreed: this folds two numbers, how sure we are the rule holds and how much it confers when it does; for\n*usually* the second is not 1, and one claim carries one number, so the degree must live in the rule's\nwording or a field of its own; see `retrofitting-the-reasons-channel.md` § 9j, last note). So a relevance number on a bare link is a\n*placeholder for an unwritten claim*, and estimating it is estimating that claim's starting value, which\nis the same kind of act as presuming any claim. His two intuitions are both kept: separate as a fact\nabout the world, and read from the graph as soon as the graph says enough.\n\n**What this suggests, unruled.** (1) The judge's reading of a bare link is a starting value for the\nunwritten rule-and-application claim, to be replaced as the step is written and argued, never a final\nweight. (2) The degree is asked in a form that names one quantity (the two likelihoods, with and without\nthe reason), so that different backgrounds show as different numbers rather than as different readings\nof the question. (3) Undercutters attach to the link's relevance claim and lower the reading; ancillary\nevidence is that claim's support. (4) Embedding closeness proposes candidate pairs and never sets a\ndegree, the standing rule.\n\n## 3b. A rule's application and a link's relevance are one claim (21 October, his question, unruled)\n\n**His words, verbatim**, after the wet-lawn example and the gate example of\n`retrofitting-the-reasons-channel.md` § 9g: *\"I feel like one premise/reason that you might be aware of\nbut seems minor early on, but ends up strongly substantiated, can derail the strength of a whole claim.\nLike... maybe you are working on a new invention but don't realize until after a decade it can't work\never because of some previously unknown quirk of physics. So then it was in a way incredibly relevant but\nyou never knew the extent.\"* And: *\"Realized now when it brought up the example where an application is\nsaid to \"bear on\" the conclusion that that sounds a lot like relevance. What's the connection here?\"*\n\n**The example, whole.** Fact: *Today is Tuesday.* Rule: *This gate is open every Tuesday.* Conclusion:\n*The gate is open now.* Application: *Today being Tuesday bears on the gate being open now.* Exception:\n*Today is a public holiday* plus *The gate is closed on public holidays*, together attacking the\napplication.\n\n**The connection: the application sentence IS the link's relevance claim.** The slot has existed since\n28 September (`relevance-and-the-two-factors.md`: a link's relevance claim is the link made into a claim,\nattackable, passing no strength on), § 9g's table already labels the application so, and AD22 (unruled)\ndraws the rule as that claim's grounds. Three traditions put the exception in the same place: Pollock's\nundercutter attacks the link, not the conclusion; ASPIC+ gives every defeasible rule a name *n(r)*, a\nsentence saying the rule applies, and an undercutting attack is an argument against that name; Toulmin's\nrebuttal (*unless*) qualifies the warrant's application. So **a link's relevance is the standing of its\napplication claim: the rule's own strength, reduced by any exception that stands.** That is § 3's limit\nreached from the other side, and Hitchcock's 1992 definition of relevance as a relation among an item, a\ngoal and a situation matches § 2's three rows (rule, dialogue, case facts).\n\n**His invention case separates three things the word \"relevant\" runs together.**\n\n| | What it measures | In the code |\n|---|---|---|\n| relevance proper | how far the conclusion moves if the reason is settled true rather than false | the hinge score (`deliberus/hinge.py` clamps a claim to 1.0 and 0.0 and records how far the root moves; it ignores the claim's present strength) |\n| doubt | how likely the reason is to be false | the reason's own strength |\n| felt importance | the two together: how much the conclusion is expected to move (decision theory's value of information) | `worth_asking` prices a question by whether an answer would cross a display band |\n\nThe premise *no law of physics forbids the mechanism* had full relevance from the first day (a required\npart: false, and the invention fails whatever else holds) and near-zero doubt, so its felt importance read\nnear zero. What the decade changed was its doubt, not its relevance; in Keynes's terms, the weight of\nevidence grew. *\"You never knew the extent\"* is exact in one way: nobody wrote the premise down, and an\nunwritten premise has no hinge score. That is coherent absence (the error class only a person outside the\nframe can catch), and § 3's *actual relevance* in its plainest form: a fact about the world, there before\nanyone read it.\n\n**Once written, the graph derails the claim the way he describes.** A required part that is refuted caps\nits whole by the weakest-part rule, as far as its requirement is argued (the requirement cap, 2026-09-17).\nThe Q34 ruling that a refuted reason adds nothing concerns reasons, not parts.\n\n**And the quirk itself can be a rule with an unwritten condition.** Abbe's limit (1873) was read for a\ncentury as forbidding optical resolution below about half a wavelength. Hell's STED microscopy (Nobel\n2014, with Betzig and Moerner) gets below it by saturating fluorescence: the resolution term depends on the\ndepletion intensity over the saturation intensity. That Abbe's derivation assumes a linear response is\nClaude's reading of that equation, not a sourced statement. Lakatos again: the counterexample exposed a\ncondition that belonged in the rule.\n\n⚠ **Withdrawn 2026-10-22**: a proposal stood here to mark load-bearing premises nobody has examined.\n§ 3c says why it fails and what replaces it.\n\n## 3c. What § 3b means for estimating relevance continually, and for the map's bands (21 October, unruled)\n\n**His words, verbatim:** *\"What are the implications for how we estimate relevance continually, so as to\nrender it wisely in the maps? This also deeply relates to the docs about what humans uniquely can\ncontribute to Deliberus, right?\"* This is a design for ledger AR4 (judging relevance at scale), proposed,\nnothing built.\n\n**Two layers, of very different cost.**\n\n1. **Writing out, once per link, by machine.** The rule and the application sentence are written under\n   the link (AG14's smallest steps), as standing work keyed on *never written* (R8), so it costs one pass\n   per link, as extraction does per source.\n2. **Reading, every time the record changes, by code.** The band's width is the application claim's\n   standing: the rule's strength, reduced by any exception that stands. No model call: it is recomputed\n   when an exception, a backing for the rule, or an argument about either is added, and dated (*read,\n   never set*).\n\n**Before a link is written out** it needs no estimate, only the fallback the code already has\n(`deliberus/relevance.py`): 0.5 when the link's writer meant it (the source asserted it, a person wrote\nit, a split cut it), 0 when a machine guessed it between other people's claims, drawn dashed until the\napplication is argued. ⚠ Corrected 2026-10-22 on his question (*\"Don't think we want/need an estimate\nfor before a link has been written out? ... it should just have a fallback value of some kind, or?\"*):\nthe first version of this section put the judge's reading there and drew its gate and degree\ndifferently; the write-out happens when the link is made, so the gap is short and the presumption covers\nit. By *link* this section means the support or attack arrow between two claims; the application\nsentence is the relevance claim attached to that arrow, and the band draws the arrow at the width its\napplication claim reads.\n\n**Exceptions narrow a band only when they stand.** A machine may propose them (the standing questions,\nand the counterexample question of `the-chain-inside-a-link.md` § 11); an unexamined claim moves nothing\nunder Q33, so a proposed exception shows as a mark on the band and narrows it once argued.\n\n**Felt importance is not drawn as a third thing.** The band shows relevance and the card's fill shows the\nsupporter's strength (his split of 20 October); the eye multiplies them.\n\n⚠ **The mark proposed here on 21 October is withdrawn** (2026-10-22, on his challenge: *\"How do we\nidentify those claims beforehand? Most claims are initially unexamined, they don't have a subgraph in many\ncases, since extraction stops at some depth right\"*). Four holes: nearly every claim is unexamined, so\n*unexamined* sorts nothing; a hinge score needs written structure and most claims have none below them;\nevery required part of a weakest-part whole has a high hinge, so it would fire on all of them; and the\ninvention's premise was unwritten, so no mark on a written claim could ever have landed on it. What\nreaches an unwritten defeater is a question, not a mark: the counterexample question of\n`the-chain-inside-a-link.md` § 11 (*describe a situation where the rule holds and the conclusion\nfails*), asked by a machine of each application as standing work, ordered by how much rests on the\nconclusion downstream. Proposed, unruled. Same correction in § 3b.\n\n*His answer, 2026-10-22, verbatim:* *\"The everything is unexamined flaw is of course temporary and we\nshould always aim to fill up more of the graph to know the case and topic deeper\"* · *\"We are doing\nphilosophical inquiry whether we do it and write it down or keep it in our heads. (Writing it down in the\ngraph is preferable so we can evaluate whether the graph works because the idea is that the graph should\nhelp in the long run if we get the whole object model and epistemic engine of Deliberus right.) Same goes\nfor machines asking that question. But that's an excellent machine pass to run regularly and perhaps even\nas a daemon, to saturate the graph with meaningful real content\"*. So of the four holes only the last is\nlasting: *nearly every claim is unexamined* describes today's graph, which the standing passes are meant\nto fill. The counterexample question is his chosen pass for that filling, as standing work under R8.\n\n**Where the human acts land.** Each row of § 2's table has a different natural supplier, and three of the\nfour acts in `what-human-judgment-is-for.md` change a band:\n\n| What fixes relevance | Who supplies it best | The act |\n|---|---|---|\n| the rule | the machine proposes it well (rungs 0–4 of `derivability-of-missing-considerations.md`) | a person argues it |\n| case facts that switch it off (*the keeper is ill today*) | someone, or a feed such as a calendar, positioned to know | act four, evidence from where one stands |\n| the premise nobody wrote (*physics forbids the mechanism*) | someone outside the frame | act one, *\"nobody here has said X\"* |\n| the dialogue's question (whether it rained, as against whether to water the lawn) | someone who sees the question is wrong | act two, the reframe |\n\nSo the band is where a human contribution becomes visible on the map: the machine supplies the general\nrule cheaply, and the facts that switch it off are, more often than anything else in the graph, local and\npositional. Act three (refusing a rendering of one's own position) changes no band.\n\n## 3d. The gate example stress-tested against the shipped strength code (22 October)\n\n**His ask, verbatim:** *\"Would the graph computations match common sense expectations if we allow it to\nrecompute in different scenarios with different sets of premises and rules and exceptions to the rules,\nwhich are arguments in their own right deeper in the graph ofc, and so on, recursively\"*.\n\nRun: `what-relevance-is/gate_scenarios_run.py` (no model, no graph; `compute_claim_badge` fed by hand in\n§ 3b's drawing: the application is the link's relevance claim, the rule its required part, an exception\nan argument of fact plus rule attacking it). Expectations were written before the first run. *Established*\n= an examined claim at 0.9.\n\n| Case | Expected | Relevance as shipped | Conclusion as shipped | Relevance, weakest-link reading |\n|---|---|---|---|---|\n| Tuesday, rule standing | clearly open | 0.507 | 0.520 | 0.900 |\n| + holiday, closure rule standing | doubtful | 0.507 | 0.520 | 0.090 |\n| holiday claim refuted | open again | 0.507 | 0.520 | 0.720 |\n| closure rule defeated by a market-day rule | open again | 0.507 | 0.520 | 0.819 |\n| rule shaky (0.6) | leaning open, less | 0.500 | 0.519 | 0.600 |\n| nobody checked the day | no lean | 0.507 | unexamined | — |\n| a second independent sign | more open | 0.507 | 0.571 | 0.900 (lines do not add) |\n\n**Finding one: as shipped, the relevance channel cannot see an exception.** Reading relevance as the\nrelevance claim's computed strength keeps it within a hair of 0.5: a claim built from parts reads 0.507\nhowever solid the parts (the up-transmission whisper, `weakest-link-arithmetic-and-the-merge-hunch.md`),\nand an attack from an argument at 0.507 removes 0.5 × 0.007 of energy. Even the strongest single attack\nthe calculus allows moves the relevance claim only from 0.507 to 0.502. So the established holiday,\nits refutation and its defeat all leave the band where it was.\n\n**Finding two: the weakest-link reading matches common sense on order and roughly on size.** Reading each\nline of reasoning as its weakest piece and the exception as removing the rule's use in proportion to its\nstanding (ledger Q38, Pollock's degree of justification, not shipped) gives 0.90, 0.09, back up after\nrefutation and after defeat, lower for the shaky rule. Its one miss: a *refuted* holiday (0.2) still cuts\nrelevance by a fifth, because it counts 0.2 as standing; the Q34 ruling that a refuted claim counts for\nnothing would set it to zero and restore 0.9.\n\n**Finding three: even with a sensible relevance, the conclusion barely moves.** One established fact with\nan established rule and relevance 0.9 lifts the conclusion only to 0.557 (0.600 at most for any single\nreason), the damping of ledger Q27. Common sense says *clearly open*. So the band could be made right and\nthe card's fill would still read the gate as unsettled; the two are separate decisions.\n\n**What this means for § 3c.** The model-free recompute is right in shape and inert in the shipped\narithmetic. It needs the relevance claim read as a line (weakest piece, exceptions as removal), which is\nQ38 applied to relevance, and the conclusion's damping is Q27's question. Both are strength-semantics\nrulings, his.\n\n## 3e. The fallbacks are priors, and the weakest-piece reading was proposed and never put to him (22 October)\n\n**His words, verbatim:** *\"Fallback values are made up\"* · *\"Yes, of course!!! Why was this not ruled\nalready omg. Why was this not mentioned in the retrofitting parts/reasons docs?\"* · *\"The fallback values:\nthese relate to all earlier thinking on what sensible priors are in Deliberus right?!\"*\n\n**The fallbacks are priors.** The relevance presumptions (0.5 when the writer meant the link, 0 when a\nmachine guessed it) are the link-side twin of the 0.5 every claim starts at, and\n`starting-values-and-the-problem-of-the-prior.md` § 0 names both as made-up shape: *\"links already get\npresumptions by who wrote them (relevance 0.5 or 0)\"*, and *\"every claim starts at 0.5\"* is the wrong\nconstant. Its answer (ledger Q35, unruled) carries over: a start comes from the claim's kind through a\nreference-class claim computed in Deliberus. Under § 3b a relevance claim's start is its rule's start, so\na link's fallback is the start of the kind of rule under it (*opening-hours rules usually hold*, *a sign\nof this kind is usually reliable*), and who wrote the link is its first evidence, never its start.\n\n**The weakest-piece reading was in the retrofit note, unruled.** Ledger Q38 (*the ropes*, proposed\n2026-10-15): within one argument the weakest premise governs, across arguments the best one (*line* was its old name; ruled 2026-10-22 in its widened form, `retrofitting-the-reasons-channel.md` § 9h).\n`retrofitting-the-reasons-channel.md` § 8 gives *\"the weakest governs within the inference\"* for a step\nfrom a rule and a case, with the exceptions as standing questions, and § 9b point 3 saw the conflict:\n*\"As the relevance claim, the rule's strength combines with the fact's as a product (Q33). As a premise\nbeside the fact, the weakest of the two governs\"*, left open. Two things kept it from him: Q38 sits among\nthe open rows waiting its arc, and nobody ran an exception through the code, so nobody saw that the\nshipped arithmetic reads the relevance claim at 0.507 whatever its rule, which makes the choice between\nproduct and minimum moot until the relevance claim is read as a line (§ 3d).\n\n## 3f. Is a rule's *usually* a hedge to strip? (22 October, his question, Claude's reading, unruled)\n\n**His words, verbatim:** *\"Hm is this just a case of the kind of hedge that should be stripped? And instead\nreplaced with exactly phrased and evaluated exceptions? Or am I oversimplifying?\"* And, the same message,\non method: *\"I always wanna settle the theory and whatever we can know from first principles and philosophy\nbefore we do any empirical testing or eval or spend any tokens or talk to/ask/consult random person/user or\nwhatever.\"*\n\n**Not a hedge; a scope word, which the ruled guard already keeps.** A hedge (*may*, *probably*) is the\nauthor's standing toward a claim, and stripping it leaves the claim unchanged (AM6). *Usually* says how\nmany cases the rule covers; strip it and *a red sky usually means rain* becomes *a red sky means rain*, a\ndifferent and false claim. AM6's widening keeps scope words for exactly this reason\n(`three-minds-and-the-leap.md` § 5b, guard 3: *\"Scope words are not hedges\"*), and in formal semantics\n*usually* is an adverb of quantification over cases, not an epistemic modal (Lewis 1975, from memory).\n\n**But his instinct is right for one kind of rule, and the kind can be told apart by one question:** when\nthe rule's condition holds and its outcome fails, does the failure call for an explanation?\n- **Yes: a normic rule** (Martin Smith's term, *Between Probability and Certainty*, 2016, from memory). The\n  gate shut on a Tuesday makes someone ask why: a holiday, a broken lock. Here *usually* can go, replaced as\n  he says: *the gate is open every Tuesday* plus named exceptions, each an exception claim that attacks the\n  application in a case where it holds (§ 3b). The degree conferred, when no exception stands, is 1. This is\n  Pollock's defeasible reason with its defeaters, and Reiter's default with its exceptions.\n- **No: a statistical rule.** Rain failing after a red sky needs no reason; it is how often it happens. No\n  list of exceptions exhausts it, because the failures have no kind. Here *usually* is replaced by the\n  proportion in the words (*about a third of red-sky mornings bring rain*), which is the sharpening the\n  testable-bets note asks of any scope word (`testable-bets/prediction-markets-resolution-practice.md`\n  item 3: a threshold and a population, kept beside the original wording).\n- **Mixed rules** are common: some failures have reasons, the rest are chance. The named exceptions go in as\n  claims, the unexplained remainder as a proportion.\n\n**What this does to the two-numbers point (§ 3, and retrofit § 9j's last note).** Written either way, the\ndegree a rule confers is no longer a second number: it is 1 for a normic rule unless an exception stands,\nand stated in the words for a statistical one. So one claim keeps one number, its credence that the\nrule as written holds, and the relevance of a link in a case is that credence, reduced by any exception\nthat stands. A rule left with a bare *usually* is underspecified, and that is a gap to show with a move\n(*make it exact: name the exceptions or state how often*), not a degree for a machine to guess.\n\n**The cost, owned.** An exception list is never complete (McCarthy's qualification problem, 1980, from\nmemory): unnamed exceptions can only live in the rule's credence, as the chance that the rule as written\nis false. That is the honest place for them, and naming them later moves doubt from the rule into\nexception claims that can be argued one at a time.\n\n**Ruled the next turn (ledger AT1, AT2)**, founder: *\"This is what I was after. The second number falls.\nInteresting.\"* and *\"The relevant machine pass needs to ask itself your explanation and rule type question\ncertainly.\"* What follows from it for normative reasons, for trying rule sets out over cases, and for the\nlenses: `normic-rules-normative-reasons-and-trying-rules-out.md`.\n\n**⚠ Outside read, 22 October (session b66ddc4d), filed at his word: the second number falls for a normic\nrule only.** For a statistical rule it moves into the sentence and stays a number the arithmetic needs:\n*about a third of red-sky mornings bring rain* may hold at credence 0.9, and the degree it confers on *rain\ntoday* is one third. Read literally, the clause above (*the relevance of a link in a case is that\ncredence*) would hand red sky 0.9. So the pass that writes the statistical form must also read the\nproportion out of the words (a field, or a parse), and in a case the relevance is credence × proportion,\nreduced by any exception that stands. No run has seen this: all seven cases in\n`what-relevance-is/gate_scenarios_run.py` are the Tuesday gate, and case 5 models *usually* as a weak\ncredence on the rule, which is the fold AT1 dissolves. One red-sky case in that script is the test.\n\n**This session's answer (def1f520, same night, Claude's reading, unruled): the gap is real, and it has the\nsame shape for both kinds.** AT1 stands in what it says: a rule claim keeps one *strength*, how sure we are\nthat the rule as written holds. What the outside read found is that the relevance in a case needs one more\nquantity, and that it is not a second strength but how often the outcome follows in cases like this one:\n- a statistical rule states it in its words (*a third*), so relevance = the rule's strength × the stated\n  proportion (0.9 × ⅓ = 0.3 for red sky);\n- a normic rule's outcome follows unless an exception holds, so relevance = the rule's strength × the chance\n  that no named exception holds in this case, and that chance is carried by the exception claims\n  themselves, attacking the application with their own strength (*today is a public holiday*).\n\nThe two are one formula, and the difference is where the case's particulars enter. A stated proportion is a\nfact about a population, and a case belongs to many populations (red-sky mornings, red-sky mornings in\nOctober, red-sky mornings with an east wind), so the statistical form inherits the reference-class problem\n(Reichenbach, from memory). Named exceptions let the particulars of the case in one by one. So where failures\ncan be explained, the normic form is the more exact of the two, and the pass prefers it; the statistical form\nis for failures with no kind.\n\n## 4. Examples to argue from (his ask: two or three, one at a time)\n\n1. **The wet lawn.** *The lawn was wet this morning* supports *it rained last night*. Then *the\n   sprinklers ran at five* arrives, then *the roof was wet too*. Put to him first, 2026-10-21.\n2. *(held for the next turn)* A reason whose relevance depends on the dialogue's question rather than\n   on any fact.\n3. *(held)* A reason with high embedding similarity and no bearing, and one with low similarity and\n   strong bearing.\n\n## Sources\n\n- [FRE 104, Cornell LII](https://www.law.cornell.edu/rules/fre/rule_104) (text and advisory note, read)\n- [Understanding FRE 104(b), ABA Litigation Journal, fall 2025](https://www.americanbar.org/groups/litigation/resources/litigation-journal/2025-fall/understanding-federal-rule-of-evidence-104b)\n- [Keynes, A Treatise on Probability (summary)](https://en.wikipedia.org/wiki/A_Treatise_on_Probability) · [O'Donnell, Keynes's weight of argument](https://resolve.cambridge.org/core/journals/philosophy-of-science/article/abs/keyness-weight-of-argument-and-poppers-paradox-of-ideal-evidence/73C20E0C3A3E36B492FFED7F09AA79C3)\n- [Gemes on Carnap's relevance](https://sas-space.sas.ac.uk/732/1/K_Gemes_Carnap.pdf)\n- [Verma & Pearl, Causal Networks: Semantics and Expressiveness](https://arxiv.org/pdf/1304.2379) · [Geiger & Pearl, On the Logic of Causal Models](https://arxiv.org/pdf/1304.2355)\n- [Schum, The evidential foundations of probabilistic reasoning (review)](https://pmc.ncbi.nlm.nih.gov/articles/PMC3750218) · [Inference networks and the evaluation of evidence](https://arxiv.org/pdf/1301.6737)\n- [Pollock's undercutters and rebutters (Verheij)](https://www.ai.rug.nl/~verheij/teaching/defarg/attack/tsld007.htm) · [Limitations of skeptical default reasoning](https://arxiv.org/pdf/1302.1536)\n- [Dancy, course notes (Harvard PHIL250Z)](https://scholar.harvard.edu/sites/scholar.harvard.edu/files/sberker/files/phil250z-meeting8-dancy.pdf) · [Vorobej, Informal Logic 2012](https://distantreader.org/stacks/journals/il/il-3421.pdf) · [Tsu, abstract](https://um.edu.mo/fah/conference/natural_cognition2015/rationality_and_rivals/Tsu.html)\n- Walton & Macagno, \"Profiles of Dialogue for Relevance\", *Informal Logic* 36(4), 2016 (abstract, via search; no page read)\n- [Hitchcock, \"Relevance\", *Argumentation* 6 (1992)](https://link.springer.com/article/10.1007/BF00154329) (abstract only)\n- ASPIC+ naming function and undercutting, via [Prakken, COMMA 2012](https://webspace.science.uu.nl/~prakk101/pubs/comma12reb.pdf) and [Lehtonen et al., KR 2024](https://proceedings.kr.org/2024/49/kr2024-0049-lehtonen-et-al.pdf) (search summaries; formal definition not read)\n- Toulmin's rebuttal, via [Holbrook's handout](https://people.ohio.edu/holbrook/Toulmin.pdf) (secondary)\n- [Nobel Prize in Chemistry 2014, popular information](https://nobelprize.org/prizes/chemistry/2014/popular-information) · [STED microscopy](https://en.wikipedia.org/wiki/STED_microscopy) · [Light microscopy review, arXiv:1412.3255](https://arxiv.org/pdf/1412.3255)\n- [Wilson & Sperber, Relevance Theory (2004)](https://www.dan.sperber.fr/wp-content/uploads/2004_wilson_relevance-theory.pdf)\n- [Saracevic's stratified model, as summarized](https://informationr.net/ir/12-1/paper281.html)\n- [Argumentative relevance and sentence embeddings, ICWSM 2023](https://www.csc2.ncsu.edu/faculty/mpsingh/papers/societal/ICWSM-23-argumentation.pdf) · [Wachsmuth, Syed & Stein, ACL 2018](https://papers.cool/venue/P18-1023@ACL)\n\n## Cross-references\n\n[relevance-and-the-two-factors.md](relevance-and-the-two-factors.md) (the ruled rule) ·\n[relevance-in-the-corpus-sweep.md](relevance-in-the-corpus-sweep.md) ·\n[strength-calculus-literature/bayesian-and-informal-logic.md](strength-calculus-literature/bayesian-and-informal-logic.md) ·\n[the-chain-inside-a-link.md](the-chain-inside-a-link.md) § 10 ·\n[retrofitting-the-reasons-channel.md](retrofitting-the-reasons-channel.md) § 9f ·\n[scheme-bounded-decomposition-and-evidence-as-subgraph.md](scheme-bounded-decomposition-and-evidence-as-subgraph.md)\n(his 2013 board's three axes, *truthiness, relevance, controversiality*; relevance as an inferential claim) ·\n[checks-on-machines-and-people.md](checks-on-machines-and-people.md) § 3–4\n"}