{"path":"research/what-the-number-on-a-claim-means.md","content":"# What the number on a claim means: the words, the four readings, and a pick\n\n*2026-10-14. The decision under closing question 1 (session49 § 7m, row 1a), written out at the\nfounder's ask: \"Explain your pick and define each word you mean, stringently, and how it relates to\nthe current code/ontology.\" The code was read for § 3 (`deliberus/graph/qbaf.py`,\n`deliberus/relevance.py`, `deliberus/support_semantics.py`, `deliberus/evidential_weight.py`).\nNothing here is ruled; § 4 is a recommendation and § 7 defines the two things he asked about from\nthe same reply, ledger Q37 and the \"inflation fear\".*\n\n## 0. The short version\n\nEvery claim page shows a number. Four things that number could mean are on the table, and the\narithmetic that combines reasons, parts and chains cannot be chosen until one is declared, since\neach meaning has its own combination rules. The pick: **the number is the confidence the examined\ncase warrants**, computed by declared rules over what has been recorded and nothing else; **with\nseveral reasons and nothing more said it reads as the best reason** (Pollock's default); and **it\ntends toward a probability only as the independence between reasons is itself written down as\nclaims** (the founder's Bayesian limit, ledger Q35). The dial between the default and the limit is\nhow much independence has been stated. Q37 is the default built; Q4 and Q22 are the dial.\n\n## 1. The words, defined\n\nEach term below is used in exactly this sense in this note. Where the code uses another name it is\ngiven in brackets.\n\n- **Claim**: a sentence somebody could assert, stored as one node. Every node in the graph is a\n  claim (one node type since Session 9); a critical question is a potential claim until answered.\n- **The number** (`strength`, the badge): a value in [0, 1] computed for a claim from the links into\n  it and the parts under it, shown with a band (unexamined · unsettled · supported · …). It is\n  computed on read, never stored as the claim's property (ledger Q31 for links; the badge likewise).\n- **Examined**: a claim or link is examined when at least one answer, vote or scored link bears on\n  it. An unexamined claim carries no number at all (`evidential_weight.py`: Keynes's *weight of an\n  argument*, the amount examined, is kept apart from its *direction*); the display says\n  *unexamined* and never *0.5*.\n- **Standing** (`acceptability`): a supporting claim's own computed number, used when that claim\n  is in turn a reason for another. Standing is examined-case confidence one level down.\n- **Relevance**: a reading in [0, 1] of how much a supporting claim, granted true, bears on the\n  claim it supports. It is presumed by provenance (0.5 for a link a source, a person or a split\n  wrote; 0 for a machine's guess until proposed or argued) and moved by arguing a relevance claim\n  (ledger Q33, ruled 2026-09-28).\n- **Reason** (an *argument link*, `SUPPORTS` or `ATTACKS`): a claim offered as grounds for or\n  against another. It passes on standing × relevance (Q33). Fourteen reasons are fourteen links.\n- **Part** (a *decomposition link*, `DECOMPOSES_INTO`): a claim that is a component of what another\n  claim says, so that if the part is false the whole is false (the false-without-it test measures\n  need, which is the cap's dial; content parthood is the rebuild check: the audit note § 6).\n  Untagged parts are governed by the weakest (ruled 2026-08-31); a part tagged `alternative`\n  contributes by the strongest, `corroborative` by the sum.\n- **Channel**: the two ways standing reaches a claim, through its reasons (the argument channel)\n  and through its parts (the parts channel). Each has its own combination rule.\n- **Default**: the number the rules give when nothing has been said beyond the links themselves,\n  no independence claim, no joint claim, no typing of the combination.\n- **Lift**: any amount by which a claim's number exceeds what its best single reason would give it\n  alone. A lift is the thing the four readings disagree about.\n- **Limit**: the number the rules tend toward as everything that could be recorded about the\n  reasons' independence and the claim's starting value has been recorded.\n- **Independence** of two reasons: that the failure of one is no evidence about the failure of the\n  other (shared origin, shared dataset, conferring witnesses are the ways it fails). Today it is\n  recorded nowhere on the argument channel (ledger Q4 proposes sources as nodes).\n- **Invariance** (the walkthrough's desideratum): writing out what a step already assumed must not\n  move a verdict; exposing a substantive assumption nobody had granted may.\n\n## 2. The four readings, stringently\n\nEach reading says what the number *is*, what it *requires* to be well defined, and what its\n*combination rules* then have to be.\n\n**R1. The probability the claim is true, given everything recorded.** Requires a coherent\nassignment across all claims at once (three rival explanations cannot each be 0.5), a starting\nvalue for every claim that is not an indifference prior (Q35: 0.5 for all is incoherent as a prior\nover all claims), and the independence structure between reasons (a joint probability, not two\nmarginals). Combination rules: product for conjunction given independence, noisy-OR or log-odds\nfor independent reasons, nothing computable when independence is unknown. Pollock's argument\nagainst this as the *operating* reading: a reasoner cannot compute independence from the syntax of\nits own record (logical equivalence is undecidable, truth-functional equivalence slow), so the\ndegrees a reasoner can actually hold do not obey the calculus, and the computation it does run is\nwhat makes them true (`pollock-against-accrual-and-the-overlap-check.md` § 1b). His ground is a\nreal-time agent; here the independence can be *contributed*, which is why R1 survives as the\nlimit (§ 4). ⚠ *2026-10-15, on the founder's challenge (\"we have the solution, dammit? The\nsameness detection, the keeper of the seven keys\"): \"contributed\" should have named its\ninstruments. Reformulation and dependence in content are the keeper's `same`, `contains` and\n`overlaps` (built, live in auto-connect, not yet run between the sibling reasons of one claim);\nshared origin is sources as nodes (ledger Q4, unbuilt); a person files \"these are one argument\ntwice\" as a claim. `retrofitting-the-reasons-channel.md` § 4, § 5.*\n\n**R2. The confidence the examined case warrants.** The number is a function of the recorded\narguments for and against the claim that have been examined, computed by declared rules, and of\nnothing else: not of what the world holds, not of what the corpus is a sample of. Requires: a\nrule per channel, a rule for chains, and an explicit statement of the default and of what lifts\nit. Properties: participation-dependent (a claim nobody examined has no number); non-probabilistic\n(no coherence across rivals is required, since each number is about its own record); open-world\n(absence of a record is not a record of absence). Combination rules are a free choice under this\nreading, which is exactly why they must be declared and tested against cases (§ 6).\n\n**R3. An ordinal degree under declared rules.** Only the order of claims is meaningful; 0.7 above\n0.6 says *more supported*, never *by how much*. Requires: rules that preserve order under the\noperations people perform (adding a reason, answering a question). The display bands already treat\nthe number this way. Cost: the arithmetic underneath (QEM, an energy sum then a squash) is\ncardinal, and a cardinal engine read ordinally invites the lift to mean something nobody declared.\n\n**R4. The bottleneck of one argument.** The number is the strength of the best single argument\nfor the claim, each argument as strong as its weakest step (Pollock's weakest link along a chain,\nhis maximum across arguments). Requires nothing about independence, which is its virtue. Cost:\ntwo independent reasons never justify more than one, which both Pollock's own lactose case and the\nfounder's intuition reject.\n\n## 3. As built (read 2026-10-14)\n\n`qbaf.py`: for each incoming argument link, `contribution = relevance × (standing − 0.5)`\n(Q33), signed by polarity; **the contributions are summed** across links; the parts channel adds\n`subclaim_energy` (weakest part for untagged and `necessary`, maximum for `alternative`, sum for\n`corroborative`); the total energy is squashed by QEM around a base of 0.5; a required part caps the\nwhole (`necessary_ceiling`). `evidential_weight.read_evidence` then decides whether the claim is\nexamined at all; if not, no number is shown. The chain under a link is not computed: a machine's\nstep is a claim that moves no strength (ledger AG12), and a link with its middle claim written in\nas a real chain scores lower than the bare link (0.500 against 0.519, the audit note § 13 case 6),\nsince the middle claim is unexamined and so contributes nothing.\n\nSo the built number is **R2-shaped in its scaffolding** (examined-only, participation-dependent,\nopen-world) **with R1's indifference prior as its base** (0.5) **and a combination rule on the\nargument channel that no reading chose**: the sum is the gradual-semantics tradition's house rule\n(`pollock-against-accrual-and-the-overlap-check.md` § 3), under which a claim with ten modest\nreasons reads higher than one with the best of them, whether or not the ten share an origin.\n\n## 4. The pick, and why\n\n**R2, with R4 as its default and R1 as its limit.**\n\n- *R2 and not R1*: the graph cannot supply what R1 requires (independence recorded nowhere;\n  starting values all 0.5; no coherence across rivals), and the corpus has said *standing, not\n  probability* since the weakest-link note § 1f. Pollock gives the reason it is not a temporary\n  shortfall: the operating number of any reasoner is what its own record lets it compute.\n- *R4 as the default and not the sum*: with nothing said about independence, the honest number for\n  several reasons is the best of them. Pollock's slope (reformulations of one argument are not two\n  arguments, and no detector of reformulation is complete) means a sum can only be defended by\n  detection, while the maximum removes the payoff of adding links, which is this project's own law\n  for strategy-class hazards. The parts channel already made this choice (the weakest part,\n  2026-08-31); the argument channel is the odd one out.\n- *R1 as the limit and not rejected*: the founder's intuition (Q35, verbatim: *\"every claim in\n  Deliberus will ultimately have a subgraph which is equivalent to the already-guess in the\n  probability/Bayes perspective\"*) is right about the limit. Each independence fact written down\n  as a claim (two tests are independent; two witnesses did not confer) moves the number one step\n  from the default toward what probability would say. Where every such fact has been recorded, R2's\n  rules and R1's agree; where none has, R2 reads as R4. The disagreement between Pollock and the\n  founder is about where on that dial a graph sits today, not about the dial. ⚠ *2026-10-15:\n  \"limit\" read as an asymptote the graph never reaches; the better word is* target, *reached one\n  claim at a time: a claim whose start is a reference-class claim, whose rivals sit in a stored\n  partition and whose reasons' independence the keeper has read, reads as R1 today under these\n  rules. What R1 requires, item by item, and what a stranger can be promised:\n  `the-number-in-the-world-and-the-repertoire.md` § 1, § 3.*\n- *Not R3*: the bands stay, but a number computed cardinally is declared cardinal.\n\n## 5. What the pick changes, in order\n\n1. **The argument channel's rule**: maximum over links of (standing × relevance), in place of the\n   sum. Ledger Q37, proposed, unruled.\n2. **The lift is a claim.** Two independent reasons justify more only through a further claim that\n   says so (*two independent positive tests make the diagnosis more likely than either*), whose\n   parts are the two reasons tagged necessary (so its own standing is the weaker of them), whose link\n   carries a relevance above either test's, and which anyone may attack. Under the maximum the\n   members cannot double count once the joint link stands (Prakken's second principle for free).\n   The typing pass of Q22 proposes such claims; Q4's origin channels are its ground.\n3. **Chains**: a chain under a link combines by the weakest step (Pollock's serial rule), so\n   writing out a step cannot raise a link and lowers it only where a step is shown weaker. That is\n   invariance (§ 1) by construction, where the product of relevances along a chain is not (0.9 ×\n   0.9 < 0.9). The machine's step stays a claim that moves no strength until somebody argues it\n   (AG12); the arithmetic applies to steps people have taken up. Closing question 1, as recommended.\n4. **The base**: 0.5 stays as the neutral point of a signed offset and is read as *nothing\n   examined*, never as *even odds*. Honest starting values (Q35's path) are the first step toward\n   the limit and change nothing in the default.\n5. **The display**: unchanged; the third state *nothing stands (N checked)* (Q34) is R2's own\n   vocabulary.\n\n## 6. The specification: the eight cases\n\nThe audit note § 13 lists eight discriminating cases. Under the pick, each has a required answer,\nwhich is what any arithmetic is tested against before it ships:\n\n1. *Two independent arguments for one claim*: reads as the better one; a joint claim lifts it.\n2. *Two linked premises, one false, conclusion true*: the argument falls (weakest step); the claim\n   keeps whatever other reasons it has; nothing counts against it (Q34).\n3. *A conjunction split faithfully*: the whole reads as its weakest part (ruled).\n4. *A disjunction or conditional whose embedded propositions are not both asserted*: the embedded\n   sentences are parts of what is said, not reasons; the rebuild check decides the cut.\n5. *The same evidence copied into fourteen arguments, against fourteen distinct observations from\n   one instrument*: both read as one reason until a claim about the instrument's independence is\n   written (Q4); then the second lifts and the first does not.\n6. *The same argument with and without a redundant intermediate step*: identical numbers\n   (invariance; the weakest-step rule).\n7. *A newly exposed substantive assumption*: may lower the claim, since it is a step shown weaker;\n   may never raise it.\n8. *A very credible statement of a probabilistic rule supporting its instance defeasibly*: the\n   rule's standing is high, the link's relevance carries the defeasibility; the product keeps them\n   apart (Q33).\n\nToday's code fails the sixth (measured) and gives the first and fifth the sum's answer.\n\n## 7. Two things asked about in the same reply\n\n**Ledger Q37** is a row in the ruling ledger (`session26-open-rulings.md`, Arc Q), proposed on\n2026-10-14 and unruled: *on the reasons channel the default with nothing further said is the best\nreason, and a lift above it is a claim with the lifted reasons as its required parts.* It is § 5's\nitems 1 and 2, with § 4's reasons, and it carries the outside reader's line (depends on the\nseparability floor, B2; extends the weakest-part default, B10).\n\n**The inflation fear** named in the same reply is this: closing question 2 asks him to read the 39\nparts people attached and sort each as a part, a reason, a need or debris, and the replay in\n`checks-on-machines-and-people.md` § 11 found 24 of them to be reasons their claim rests on, stored\nas parts because the page's box asks *What's underneath?* **Refiling** those 24 would move them\nfrom the parts channel to the argument channel. Under the code as built, the parts channel cannot\ninflate a claim (the weakest part governs, so a sixth part never raises a whole) while the argument\nchannel can (every link adds energy), so refiling 24 reasons would **raise 24 claims' numbers with\nno new evidence**, which is what *inflate* means here: a number rising from how the same material\nis filed rather than from anything newly recorded. Under Q37 the argument channel cannot inflate\neither (the maximum), so the refiling becomes strength-neutral or lowering, and his sorting can be\ndone on what each sentence *is* without the arithmetic leaning on the answer.\n\n## 8. Open after this\n\nClosing question 1a is his: which reading, and whether the default-and-limit framing is how he\nwants it stated. Then Q37; then the chain rule (closing question 1); then the starting values\n(Q35). The eight cases above are the acceptance test for whatever he rules, and `scripts/` holds\nno runner for them yet.\n"}