{"path":"research/the-squirrel-and-the-strength-calculus.md","content":"# The squirrel and the strength calculus\n\n**Date**: 2026-10-08 · **Type**: a founder question, answered from the earlier rulings, the two\nnotes they rest on, the strength code, and one run of that code on the squirrel. **Status**: the\nrulings quoted are his. Every reading and proposal is Claude's and **unruled**. Nothing is built.\nThree statements in last night's philosophy note are corrected (§ 6).\n\nHis words: ***\"Doesn't the stuff about the squirrel smell rule relate quite strongly to the earlier\ndiscussions and rulings about how to weigh evidence in Deliberus, \"weakest rule\"/deduction/whether\nto weigh different parts as all-necessary to bear strength or separately for what they're worth?\"***\n\n## 0. The short version\n\n- **Yes, and more closely than last night's note knew.** The August rule was borrowed from this\n  very case. *The weakest part governs* is the old rule for the premises of one argument (linked\n  premises; Pollock's weakest link). The project applied it to the parts of a claim. For the\n  premises of one reason, the smell and the rule, the graph has no place: a reason is one arrow\n  from one claim.\n- **It is one question at three places** (§ 2): the parts of a claim (ruled), several reasons for a\n  claim (half ruled), and the premises inside one reason (the squirrel; open).\n- **September had already asked for what last night proposed.** Its literature review asks whether\n  links should record what kind of connection they are, *\"since which relevance number stays true\n  depends on it\"*. Last night's *a written-out step says which shape it has* is that record,\n  reached from philosophy with no knowledge of the question. His message joined them.\n- **Premise or licence now has a price.** If the rule is a second premise, the August reasoning\n  says the weaker of smell and rule governs. If it is the link's licence, the September rule\n  multiplies the smell's standing by how much the step carries. The numbers differ.\n- **Run on today's code** (§ 3): a rule drawn as a second arrow counts as a reason by itself. Drawn\n  under the link as required parts it is safe and nearly silent. The August design left the lift\n  from established parts waiting on a completeness check, and last night's check of a written-out\n  step is such a check.\n\n## 1. What was ruled, in his words\n\n| Date | His words | What it settled |\n|---|---|---|\n| 2026-08-31 | *\"Go with option C, both.\"* and, the same day, *\"lemme just bless it for now and we can always come back to revisit it in the future\"* | Untagged parts of a claim count as required: the weakest part governs. Provisional by his own word. |\n| 2026-09-17 | *\"Build the designed completion.\"* | A part caps its whole by how strongly it is *required*, and that can be argued in a requirement claim. |\n| 2026-09-19 | *\"But we will make do with what we've settled now on this issue.\"* | The cap stands for now; whether it can be attacked unfairly is open. |\n| 2026-09-21 | *\"Yes it should. We should expect good splits.\"* | A part a machine wrote caps its whole as a person's does. |\n| 2026-09-28 | *\"About the decision: your proposal is blessed, make it so.\"* | A link carries its supporter's own strength times the link's relevance. |\n| 2026-09-28 | *\"I want to make conscious choices about such crucial design and epistemic-calculus considerations\"* | The details of that calculus are his, one at a time. |\n| 2026-09-30 | *\"we'll go with your recommendations on this for now\"* | A refuted supporter adds nothing. |\n\n**Still his to choose, in the code's own words** (`deliberus/relevance.py`): how a link's two\nfactors combine, *\"product, as built, or weakest link\"*; what an unexamined link presumes; and a\nfixed point against the one pass run today.\n\n## 2. One question at three places\n\n*Do these count together, or each for what it is worth?*\n\n| Where | Example | Today | State |\n|---|---|---|---|\n| The parts of one claim | an expert's standing: her publications, her post, her field | The weakest part governs unless a part is tagged otherwise, and a required part caps its whole. | Ruled, 31 August and 17 September. |\n| Several reasons for one claim | three studies; three signs | Each link gives its supporter's standing times its relevance. Links add. Nothing discounts reasons that share an origin. | The link rule is ruled (28 September). How reasons combine is open: ledger Q22 and Q4, and questions 4 to 6 of the September review. |\n| The premises inside one reason | the smell and the rule | No place. A reason is one arrow from one claim. | Open: ledger AD22 and AD23. |\n\n**The tradition behind the August ruling is about the third row.** Linked premises *\"work together\nand fail together\"*, and Pollock's rule is that a deductive argument is as good as its weakest\npremise ([weakest-link-arithmetic-and-the-merge-hunch.md](weakest-link-arithmetic-and-the-merge-hunch.md)\n§ 0, § 1b, § 1d). The August note gave that rule to the first row. His sentence of 2011 states the\nsquirrel in the third: the conclusion argued *from* the smell *\"along with\"* the rule.\n\n## 3. The squirrel, run through the code\n\nEvery number is from `compute_claim_badge`, the function behind the badge on a claim page, fed by\nhand with each arrangement ([the script](the-squirrel-and-the-strength-calculus/squirrel_strength_run.py),\n[its output](the-squirrel-and-the-strength-calculus/squirrel_strength_run.json)). No stored graph\nand no model. The first claim stands at 0.9. A link is presumed half relevant, as an extracted link\nis. The badge reads *unsettled* below 0.52.\n\n| How the step is drawn | The conclusion | Reads as |\n|---|---|---|\n| Nothing written: the bare link, as today | 0.519 | unsettled |\n| The rule as a second arrow | 0.569 | supported |\n| The same, when the squirrel does **not** smell | 0.519 | unsettled |\n| Three written sentences as separate supports of the link's relevance claim | 0.530 | supported |\n| Three written sentences as required parts of that claim, all established | 0.520 | unsettled |\n| The same parts, each certain | 0.520 | supported, by a hair |\n| The rule refuted, parts untagged | 0.519 | unsettled |\n| The rule refuted, parts tagged required | 0.503 | unsettled |\n| A rival explanation, established, as an attack on the relevance claim | 0.518 | unsettled |\n| One reason at its very best: a certain first claim, relevance 1 | 0.600 | supported |\n| A far link with its middle claim written in | 0.500 | unsettled |\n\n1. **A rule drawn beside the reason is counted as a reason.** It lifts the conclusion as far with\n   no smell as the smell did alone, and together they more than triple the lift. This is the error\n   the August ruling removed for parts.\n2. **Separate supports make writing pay.** The trial's writer wrote 3.6 added sentences a step\n   where a reader needed 1.2. Under addition the surplus raises the link.\n3. **Required parts are safe and nearly silent.** A whole built only from required parts cannot\n   rise above 0.511, however certain each part is. So writing a step out can lower a link and can\n   hardly raise it: all risk for the one who writes. The project wants the opposite.\n4. **Two shapes already on record show here too.** One reason alone tops out at 0.600, and support\n   fades across a written-in middle claim. Both follow from an impact that is second-order near\n   zero ([the September review](strength-calculus-literature/bayesian-and-informal-logic.md)\n   § 2.7; its question 6 asks whether that is intended).\n\n## 4. What the earlier work holds, and what the squirrel joins\n\n**Premise or licence has a price.** Last night's AD22 said the rule is the link's licence. The\nSeptember review shows that the product is the exact update, and no approximation, when relevance\nmeans how much likelier the conclusion is with the first claim than without it (§ 0, § 2.1). For\njointly needed premises its table says no per-link number exists (*\"not separable\"*, § 2.2) and\npoints to the August note, where the weakest governs. So the two readings of the rule fall under\ntwo rulings. As a licence: the product between first claim and licence, and the weakest part only\namong the licence's own grounds. As a premise: the weaker of the two. With a well-established\nsmell and a doubtful rule these give different strengths.\n\n**\"Not separable\" is what yesterday afternoon measured.** Where a first claim needs a rule to bear\nat all, its bearing has no value until the rule is named. Four ways of asking a machine *is this a\nreason for that* failed that day ([what-a-link-rests-on.md](what-a-link-rests-on.md)).\n\n**The shape is the record September asked for.** The review's table (§ 2.2) gives each kind of\nconnection its own portable number and ends: *\"the structure has to be recorded somewhere\"*.\n\n| Last night's shape | The review's row | What the number is | How several combine |\n|---|---|---|---|\n| from a rule and a case | jointly necessary parts | none per premise | the weakest governs |\n| from a sign to its cause | signs that the conclusion explains | how much likelier the sign is with the cause than without | they add, and a rival that explains them counts against all at once |\n| from a case to a like case | not in the review | the likeness, in what matters | open; the strength code already files the questions about likeness under the link's relevance ([what-a-rule-rests-on.md](what-a-rule-rests-on.md) § 7) |\n| from cases to a rule (a fourth shape, added the same day: [what-a-rule-rests-on.md](what-a-rule-rests-on.md) § 6) | not in the review | that things of the kind are alike in this respect | open |\n\nThe squirrel is the second row. **For a sign, the weakest written sentence is not its force.** A\nweak law with no rival makes a strong sign: if only a few dead squirrels smelled, and nothing else\nsmelled so, the smell would still nearly settle it. A sure law with many rivals makes a weak sign.\nSo the all-necessary rule fits the first shape only, and a sign is weighed for what it is worth.\n\n**The lift's gate now has a measurement.** The August note says three well-established parts lift\ntheir whole only to 0.507 because nothing checks that the parts are all there is, and proposes\nthat the lift wait on such a check (§ 7, § 9d: *\"the lift and the cap share one gate\"*). Last\nnight's check asks a reader who does not know the intended conclusion whether the written\nsentences reach it, and whether each is needed. That is a completeness check, for a step. It also\nhas the form of the tradition's test for linked premises: take one away and see whether the rest\nstill carry the conclusion. The August note records the objection to such tests, that they need a\njudgment of support before the structure is known (§ 1d); here the reader's yes or no is that\njudgment. It is a machine's reading, it fits the first shape only, and no person has read a step.\n\n## 5. What this suggests (unruled; refinements of AD22 and AD23, no new ledger rows)\n\n1. **For a step from a rule and a case, what is written under the link is filed as required parts\n   of that link's relevance claim, never as further arrows or as separate supports.** Under the\n   weakest-part rule a repeated sentence is free, so a writer that over-writes cannot raise a link.\n2. **One record, not three.** The step's shape (AD23), the kind of connection (the review's\n   question 4) and typed combinations (Q22) are the same record at two levels.\n3. **For a step of the first shape that passes the check, the link's relevance follows its weakest\n   written part upward as well as downward**, raised and never total. This is the August design,\n   first usable here.\n4. **A sign keeps its two numbers** (the conclusion with the sign, and without; proposed\n   29 September), with *what else would leave this sign* as the place a rival attaches.\n5. **Three tests before anything is built**: the same weight however many sentences a step is\n   written in; the same weight wherever a fact is filed; and a far link against the same link with\n   its middle claim written in.\n\n## 6. Corrected with this note\n\n| Where | What it said | What is so |\n|---|---|---|\n| [philosophy-of-the-unwritten-step.md](philosophy-of-the-unwritten-step.md) § 3; ledger AD22 | With the written sentences as the relevance claim's grounds, *the link's weight then follows them through the ordinary calculus, and nothing is counted twice* | *Grounds* was not specified. As separate supports they add. As required parts nothing is counted twice, and the weight barely follows (§ 3). |\n| the same note, § 9 | *How strongly A supports B is the chance of B given A* | That is one of two numbers. The September review: relevance needs the chance of B with A and without. |\n| the same note, § 9 | The product the graph uses *is an approximation* | A link's contribution is the exact update when relevance means that contrast (the review, § 0). What departs from it is the number put in for relevance, and the curve applied to the sum afterwards (§ 2.7). |\n\n## 7. Read, and not checked\n\n- **Read by Claude for this note**: the August note § 0 to § 1f and its passages on the lift; the\n  September review § 0, § 2.1, § 2.2, § 2.5 to § 2.7 and § 6; `relevance.py` whole; the strength\n  functions in `support_semantics.py` and `qbaf.py`. A helper read nine notes and the strength\n  modules in full; [its report](the-squirrel-and-the-strength-calculus/strength-rulings-and-code-as-read-2026-10-08.md)\n  is kept whole. Nothing outside the corpus was read.\n- **Not verified**: the helper reports that the code reads `support_interpretation` where several\n  notes say `support_semantics`, and that the ledger row for the August ruling still reads\n  *awaiting founder confirm*.\n- **The run fed the badge function by hand.** No link in the graph has a relevance claim, so the\n  stored route was not exercised.\n\n## Cross-references\n\n[weakest-link-arithmetic-and-the-merge-hunch.md](weakest-link-arithmetic-and-the-merge-hunch.md) ·\n[what-the-necessary-default-changes.md](what-the-necessary-default-changes.md) ·\n[relevance-and-the-two-factors.md](relevance-and-the-two-factors.md) ·\n[strength-calculus-literature/bayesian-and-informal-logic.md](strength-calculus-literature/bayesian-and-informal-logic.md) ·\n[what-counts-as-evidence.md](what-counts-as-evidence.md) ·\n[philosophy-of-the-unwritten-step.md](philosophy-of-the-unwritten-step.md) ·\n[writing-out-the-unwritten.md](writing-out-the-unwritten.md) ·\n[what-a-link-rests-on.md](what-a-link-rests-on.md).\n"}