{"path":"research/philosophy-of-the-unwritten-step.md","content":"# What philosophy says about links and premises\n\n**Date**: 2026-10-07 (late evening) · **Type**: a founder question, answered by reading across fifteen\ntraditions (63 lookups: 44 pages each put one question, and 19 web searches), by the\ncorpus's own earlier readings, and by two small checks on the evening's trial (18 model calls, each\nwith its expected outcomes written first). **Status**: every proposal is Claude's and **unruled**\n(ledger AD22 to AD29). Nothing is built. Four statements made earlier the same day are corrected\n(§ 13). It came ahead of the four open reviews because he asked.\n\nHis words: ***\"What does philosophy both analytical and otherwise have to bear on the links/premises\nquestions? Think deeply about this from many different angles.\"***\n\nThe questions meant are those of the day's three notes: whether a link between two claims is a\nreason ([how-far-a-premise-is-from-its-claim.md](how-far-a-premise-is-from-its-claim.md)), what it\nrests on ([what-a-link-rests-on.md](what-a-link-rests-on.md)), and whether what it rests on can be\nwritten out by machine and trusted ([writing-out-the-unwritten.md](writing-out-the-unwritten.md)).\n\n**Read depth, said first.** Almost every outside claim below comes from a fetch tool's small model\nanswering one question about one page. Claude did not read the pages. Each answer is kept as it\ncame back in [the folder](philosophy-of-the-unwritten-step/what-each-lookup-returned.md), with the\npages that turned out not to cover what was asked. § 15 lists the sources. Verify before citing\noutward.\n\n## 0. The short version\n\n- **What sits unwritten under a link is of four kinds, and only one of them is a missing premise.**\n  A fact about the case is a missing premise. The joining of two names is an act of judgment. The\n  rule is a licence for the step. And the rest is background, which no tradition thinks can be\n  written out whole. The trial's three-part form found the first three by trial and error. Four\n  traditions had drawn the same lines independently (§ 2).\n- **The rule is a licence and not a premise.** Lewis Carroll's regress of 1895 is the proof: write\n  the rule in as a premise and the step needs another rule. So the rule belongs in the slot the\n  graph has had since 28 September, the link's own relevance claim, and never as a second arrow into\n  the conclusion (§ 3).\n- **\"All of it written out\" has no end, and three separate arguments say why.** What can be had is\n  that any link can be written out on request. Mathematics, the one field that reached proof without\n  gaps, pays about four times the length for it and in practice settled on the same thing (§ 4).\n- **A step has a shape, and the reader built this evening reads only one.** His own example of 2011\n  runs from a sign to its cause. Put to the trial's blind reader it failed in all four askings, and\n  it passed only with the rule turned round (six calls, § 5).\n- **There is no one rule under a link.** Logic, induction, law, probability and pragmatics each hit\n  the same wall: one step falls under many rules of different breadth. So rules are kept in the\n  plural, with whose reading each is, and breadth is set by asking which changes of the case the\n  step survives (§ 6).\n- **One link can carry several arguments, and pruning in one order hid that.** Corrected with\n  twelve calls: of the thirty links, **17** have a written-out step in which every part is needed,\n  **5** are written around the link, **2** are unsettled and **6** could not be written out. The\n  evening's note said 15, 9 and 6, and this note said 18, 5, 1 and 6 until link 19 was read again\n  on 2026-10-08 (§ 7).\n- **A complete step is complete for some reader, and a complete step is not thereby a supporting\n  one** (§ 8, § 9).\n- **Philosophy has a second way of finding unwritten premises, by counterexample.** It adds nothing\n  unless a counterexample demands it, and it is the one route here that says something about a good\n  reason against a bad one. Untested (§ 10).\n- **People agree on steps and differ on the rules behind them.** A commission Toulmin served on, and\n  the law, both found it (⚠ narrowed 2026-10-08: true of bodies that must decide and share a tradition, while large publics show the reverse; [what-a-rule-rests-on.md](what-a-rule-rests-on.md) § 13.1). A graph that demands the rule before it accepts the step would break\n  agreements that work (§ 11).\n- **What philosophy does not give is a procedure.** Its two camps on the main question have\n  disagreed for two thousand years. The design below works under either (§ 14).\n\n## 1. Fifteen angles, one line each\n\n| Angle | What it says about a step and what it rests on | What it changes here |\n|---|---|---|\n| **Ancient logic** | The Stoics counted some arguments as valid though not by their form (*equal to the same, so equal to each other*). Alexander answered that they hold only on the strength of a universal premise. Aristotle fits premises to an audience, and counts the sign and the example as proofs beside the kind that runs from a rule. | The three-part form takes one side of the oldest dispute in logic. Signs and examples need forms of their own. |\n| **Medieval logic** | A step good by its content becomes good by its form when a premise is added: a necessary proposition where the step holds always, a contingent truth where it holds only as things now stand. | The trial's *rule* and *fact* are that split. |\n| **Indian logic** | The standard inference runs from a sign (smoke) to what it indicates (fire). Its explicit form states the general connection together with a familiar case. A reason is good when it is found in like cases and never in unlike ones. | A rule is shown with a case, and tested by like and unlike cases. |\n| **Peirce and Mill** | A rule, a case and a result can be arranged three ways, and only one is deduction. The rule a reasoner follows is a habit, judged by whether it leads from truths to truths. Mill: the conclusion is drawn *according to* the general proposition and not from it, and that proposition is a register of inferences already made. | A step records its shape. A rule's count across links is its register. |\n| **Carroll, Ryle, Toulmin** | A rule written in as a premise needs a further rule. A law is an inference ticket. A warrant authorises the move from grounds to claim, and has backing of its own. | The rule sits in the link's relevance slot. |\n| **Sellars and Brandom** | A step that is good by its content is not a gappy formal one. Stating the rule turns something done into something said, which can then be challenged. | A rule under an author's step is a commitment made by the step. |\n| **Kant and Wittgenstein** | There is no rule for applying rules. Judgment can be practised and not taught, and practice is what ends the regress. | Joining two names is judgment. It can be stated. It cannot be derived. |\n| **Hermeneutics and critical theory** | Every statement answers a question. Understanding never makes all of its presuppositions plain. The background can be questioned only a piece at a time. | The standing property is that a link *can* be written out, a level at a time. |\n| **Practice** | Rules are abridgements of a practice. Scientists work from likeness to solved problems without agreed rules. | Some links rest on a like case and not on a rule. |\n| **Philosophy of science** | The covering-law form has three known failures: direction, an idle premise, and a generalization that is true by accident. Which generalization may be projected depends on its record. Hidden assumptions are found by counterexample. | Pruning; shape; a rule's record; the counterexample shown with the rule. |\n| **Relevance and sufficiency** | A premise must be used. An effect has several small sets of conditions that are each enough. An argument is a smallest set of premises that gives its claim. | Pruning looks for every such set. |\n| **Epistemology** | Implication is a relation between sentences, and inference is something a thinker does. A valid step can fail to pass support on. A defeater can attack the link and leave the conclusion alone. | A machine's link is a proposed implication. Complete is not supporting. A counterexample attacks the link. |\n| **Philosophy of language** | What is presupposed gets taken on quietly and is hard to deny. A hearer supplies the most accessible assumption and stops. Generic sentences have no settled truth conditions, and about kinds of people they suggest a nature. | Rules are shown as the question at issue. A machine's rule is the most accessible one. No bare generic about people. |\n| **Ethics and law** | An *ought* needs an *ought* among its grounds. A reason in one case can be none in another, and what lets it count differs from what it is. People agree on cases and differ on principles. A precedent's rule is settled by later cases. | The rule's kind routes the dispute. Agreement on a step without agreement on its rule is a state to show. |\n| **Mathematics** | Frege built his notation to keep the chain of inference free of gaps so that every presupposition would show. Formal proof now exists, at about four times the length of the informal one. Ordinary proofs leave gaps their readers can fill. | Expandable on request is the standard that works. |\n\n## 2. Four kinds of unwritten thing\n\n| | What it is | Who drew the line | Where it stops | Its home in the graph |\n|---|---|---|---|---|\n| **A fact about the case** | a further thing that has to be so, which no claim states | Pseudo-Scotus: the contingent truth added to a step that holds as things stand. Toulmin: more grounds. Rhetoric: the question of fact. | in evidence | a claim like any other; the evidence layer |\n| **A joining of names** | two wordings taken as one thing, or a thing taken as a case of a kind | Kant: subsuming under a rule, for which there is no rule. Wittgenstein. Rhetoric: the question of definition. | in practice, or in a ruling about a word | the concept layer |\n| **The rule** | what licenses going from this kind of claim to that kind | Stoics and Alexander; Peirce's guiding principle; Ryle's ticket; Toulmin's warrant; Hitchcock's covering generalization | in logic, in meaning, in experience, in a norm, or in something presupposed (§ 4) | the link's relevance claim |\n| **The background** | everything a reader must already be able to do and take for granted | Gadamer, Habermas, Dreyfus, Oakeshott, Polanyi | nowhere: it is questioned a piece at a time | none; whatever is asked about moves into the three rows above |\n\n**The trial found the first three rows by repair.** Its first form let a sentence about the case say\nthe whole step over again, so names were split from facts and both from the rule\n([writing-out-the-unwritten.md](writing-out-the-unwritten.md) § 8). The medieval split of\n*necessary* from *contingent* supplement, the three questions of classical rhetoric (did it happen,\nwhat is it called, was it right), Toulmin's grounds and warrant, and Kant's rule and its\napplication are four separate arrivals at the same lines.\n\n**A caution on that sentence.** Claude chose which traditions to read. Four that agree were found\nby someone looking for agreement.\n\n**Two further unwritten things belong to some steps only.** A step from a sign leaves unwritten\nwhat else would explain the sign (§ 5). And every step answers a question that is rarely written\nwith it: Collingwood and Gadamer both hold that a statement is understood only together with its\nquestion. Two people can accept one link as answers to two different questions.\n\n## 3. Premise or licence\n\n**Two camps, as old as logic.**\n\n- *Supply the premise.* A step that does not hold by its form is incomplete, and is made good by\n  adding what it left out. Alexander against the Stoics; Pseudo-Scotus on steps reduced to formal\n  ones; Hempel's covering laws in science.\n- *It was a licence all along.* The step is good as it stands, by a rule that is used and not\n  stated. The Stoics' own view of those arguments; Peirce's habit of mind; Mill; Ryle; Toulmin;\n  Sellars and Brandom, who deny that such a step is a formal one with a premise missing;\n  Hitchcock, whose covering generalization the evening's design borrowed.\n\n**Carroll's regress is why the second camp cannot be wholly wrong.** The Tortoise grants two\npremises and declines the conclusion. Achilles writes down *if those two, then the conclusion* as a\nthird premise. The Tortoise grants that too and still declines, and so on without end. Whatever\ntakes a reasoner from premises to conclusion cannot itself be one more premise.\n\n**Both camps grant what the design needs.** The rule can be stated. Stated, it can be asked for\nreasons. They differ on whether the step was defective before, and nothing here turns on that.\n\n**Three things do turn on the difference.**\n\n1. **Where the rule goes.** Drawn as a second premise, the rule becomes another arrow into the\n   conclusion, and that arrow needs a rule. The graph has had the other slot since 28 September: a\n   link has a relevance claim, attackable, joined to it by a link that passes no strength on\n   ([relevance-and-the-two-factors.md](relevance-and-the-two-factors.md)). No link has one yet. **The\n   rule, the facts and the joined names are that claim's grounds.** The link's weight then follows\n   them through the ordinary calculus, and nothing is counted twice.\n   ⚠ **Corrected 2026-10-08:** *grounds* was left unspecified, and it matters. Run on the strength\n   code, written sentences drawn as separate supports add, so writing more raises a link. Drawn as\n   required parts nothing is counted twice, and an established step moves the conclusion by one\n   thousandth ([the-squirrel-and-the-strength-calculus.md](the-squirrel-and-the-strength-calculus.md) § 3).\n2. **The regress stays, and stays askable.** That the rule supports the relevance claim is again a\n   step with a rule. The traditions that faced this say the same thing in different words: a step\n   stands until somebody asks why with a reason for asking (Brandom's default and challenge; the\n   corpus has this in [what-counts-as-evidence/philosophy-of-evidence.md](what-counts-as-evidence/philosophy-of-evidence.md)\n   § 7). The graph should make each further step askable. It should not claim to have reached the\n   end.\n3. **Whose the rule is.** In the second camp's terms, an author who makes a step is *committed* to\n   a licence for it, whether or not they could state one. That is a third standing beside *asserted\n   by* and *nobody's* (§ 11). A link a machine draws commits nobody: in Harman's terms it proposes\n   an implication between two sentences, and no thinker has inferred anything.\n\n**The evening's own data fits.** On five links the machine's rule brought the reader to the second\nclaim with no help from the first (§ 7). Such a sentence licenses nothing between the two claims.\nIt is the second claim over again in general form. The check *is the first claim needed* is the\ncheck that a written sentence works as a licence for this step.\n\n## 4. Can all of it be written out\n\nHis aim of 2011, every premise made explicit, has a direct ancestor. Frege's preface of 1879 says he\nkept the chain of inference free of gaps so that nothing intuitive could enter unnoticed. Leibniz\nhoped for the same (the corpus has that lineage in\n[fractal-priors-for-success.md](fractal-priors-for-success.md)). In mathematics it worked.\n\n**Three regresses say it cannot be finished elsewhere, and each ends in something that is not a\nsentence.**\n\n| The regress | Who | Where it ends |\n|---|---|---|\n| Every premise needs a premise | Aristotle, *Posterior Analytics* | in premises with nothing prior, grasped and not proved |\n| Every rule written as a premise needs a rule | Carroll | in rules that are followed and not stated |\n| Every rule needs a rule for applying it | Kant; Wittgenstein | in judgment and training |\n\n**And the background is not a list.** Gadamer: the situation one understands from can never be made\nfully transparent. Habermas: the shared background can be put in question a piece at a time and\nnever all at once. Dreyfus made the same objection to the first programmes that tried to write\ncommon sense down as rules and facts. Leibniz held that for any truth that could have been\notherwise the analysis runs on without end.\n\n**What mathematics settled on.** A formal proof runs to about four times the length of the proof a\nmathematician writes (the de Bruijn factor, reported between three and six). Ordinary proofs leave\ngaps on purpose where the reader can fill them (Fallis counts three kinds). On one account of what\nmakes such a proof rigorous, it shows that a full derivation exists without being one (Azzouni).\n\n**So the property to hold is that any link can be written out when asked, with the first level\nwritten eagerly.** That is his ruling of 25 August (*do eagerly, show on contest*) and the canon\nline that nothing is permanently atomic, with their grounds. It also says what the 34 against 2,139\nof this evening's note should be measured against: the target is a way to produce any step asked\nfor, with a known error. A count of written premises that approaches the count of claims is no\ntarget.\n\n⚠ *2026-10-10: the founder asked for more than this the same week, and had ruled more on\n25 August: the descent worked out eagerly at every level, into a stage the default map does not\nshow. What stays capped is how deep the machine builds on its own sentences. A chain's end is a\nreading and is not a named kind set by the machine:\n[the-chain-inside-a-link.md](the-chain-inside-a-link.md) § 1, § 4.3 (ledger AG2, unruled).\n**He ruled on the cap the same day (ledger AG6): the machine may and should write deeper steps,\nand the small tasks that write them are quality-controlled like the others. So with no measured\nerror the cap does not hold the writing back; it is what the measuring is for:\n[quality-control-for-deeper-steps.md](quality-control-for-deeper-steps.md).***\n\n**Where a chain under a rule stops has a kind**, as a horizon does:\n\n- a rule of logic, which cannot be argued for without being used;\n- a rule that belongs to what the words mean, or that makes one thing count as another (*moving the\n  ball over the line counts as a goal*);\n- a generalization from experience;\n- a norm;\n- something presupposed that is neither true nor false. Collingwood's term is an absolute\n  presupposition. The corpus knows it as a hinge\n  ([the-load-bearing-unsaid.md](the-load-bearing-unsaid.md)).\n\nRead by Claude, of the nineteen rules the trial kept about seven are of the second kind, eight of\nthe third and four of the fourth. Several of the seven say that one thing *constitutes* another,\nwhich is a joining of names in the dress of a rule.\n\n## 5. A step has a shape\n\n**Peirce, 1878.** A rule, a case and a result. From the rule and the case to the result is\ndeduction. From the case and the result to the rule is induction. From the rule and the result to\nthe case he called hypothesis, later abduction.\n\n**His example of 2011 is the third.** *Dead squirrels smell of decomposition* is the rule. *The\nsquirrel smells of decomposition* is the result. *The squirrel is dead* is the case. Aristotle would\ncall it an argument from a sign of the refutable kind. The standard inference of Indian logic, from\nsmoke to fire, has the same shape, and that tradition's explicit form sets a rule and a familiar\ncase side by side. As a deduction the squirrel affirms the consequent. The rule that would make it\none is the converse: *squirrels that smell of decomposition are dead*.\n\n**Put to the trial's blind reader** ([the script, with the outcomes written first](philosophy-of-the-unwritten-step/squirrel_check.py);\n[its answers](philosophy-of-the-unwritten-step/squirrel_check.json)):\n\n| Statements | The four claims include | Claim first | Rule first |\n|---|---|---|---|\n| his two sentences | nothing that explains the smell | none | none |\n| his two sentences | a rival: *it has rolled in something that was rotting* | none | none |\n| his first sentence and the converse rule | the same rival | *the squirrel is dead* | *the squirrel is dead* |\n\nThe reader named the fault itself in three of the four refusals.\n\n**Three things follow.**\n\n1. **The reader built this evening is a deductive reader.** That was not known. It means the\n   three-part form and its check fit steps of the first shape only.\n2. **The writer turned every link into the first shape, since the task said the second claim is\n   what follows.** For a step from evidence to what explains it, that means writing the converse\n   generalization. Such a sentence is usually a generic (*squirrels that smell so are dead*), and it\n   is seldom the sentence a person would give as their reason. That would be the law that runs the\n   other way, together with *nothing else here explains it*.\n3. **Generics are a poor place to put the weight.** Their truth conditions are unsettled: *ducks lay\n   eggs* is true though most ducks do not. And about kinds of people they suggest that the trait\n   belongs to the kind's nature (Haslanger). The evening's form moves the question of a link's\n   worth onto one generic sentence.\n\n**So a written-out step says which shape it has.**\n\n| Shape | What is written | What stays to be asked |\n|---|---|---|\n| from a rule and a case | the three-part form of this evening | is the rule true |\n| from a sign to what it indicates | the law that runs from the thing indicated to the sign | what else would produce the sign here |\n| from a case to a like case | the earlier case, and the respect in which the two are alike | are they alike in what matters |\n\nThe patterns the graph already classifies have the second and third shapes among them, each with\nstanding questions about rivals and likeness. This is a further reason to treat writing a step out\nand naming its pattern as one act.\n\nBolzano kept the two directions apart in 1837. One relation holds when the truth of some sentences\nguarantees another under every admissible change of terms. A second holds when one truth is the\nground of another. The first can run from a sign to its cause. The second never does. The graph's\nsupport links are of the first kind.\n\n## 6. Which rule\n\n**One problem, met in five fields.**\n\n- **Logic.** For Bolzano, whether one sentence can be derived from others is relative to which of\n  their ideas are allowed to vary. Hold more fixed and more follows. A rule under a step is a choice\n  of what to vary. Hitchcock's covering generalization follows Bolzano here.\n- **Induction.** Goodman: the same observations fit *all emeralds are green* and a rival built to\n  fit them equally. What marks the one to project is no feature of its form. It is the record of\n  its terms in past projections, which he called entrenchment.\n- **Law.** The rule a case stands for is not given with the case. The same facts can be described as\n  about a beverage, a consumable, or any article for human use, and each gives a rule of different\n  reach. Later courts settle it, and may narrow it by distinguishing.\n- **Probability.** How likely the conclusion is, given the case, depends on which class the case is\n  counted in. The corpus has this as the reference class problem.\n- **Pragmatics.** A hearer supplies the most accessible assumption that makes the remark relevant,\n  and stops there. That is a fair account of what the trial's writer did. Its rule is the nearest\n  one to hand. Nothing makes it the author's.\n\n**Consequences.**\n\n- **Rules are plural, and each has a reader.** The trial already found that two writings agree on\n  one rule, or one containing the other, on 23 of 27. That counts where two readings overlap. It\n  does not show a single rule there to be found.\n- **Breadth is set by variation.** Bolzano's device, turned into closed questions: *would the step\n  still hold if this term were that one?* Each answer fixes one idea or lets it vary. The rule is\n  then read off the pattern of answers. Indian logic states the same test as a condition on any\n  good reason: present in like cases, absent from unlike ones. Two readers who answer differently\n  have a located disagreement about a link they both accept. Untested here.\n- **A rule's count across links is its record, and a record is conservative.** Goodman's answer is\n  the principled reading of *what recurs is offered*. It also means that an assumption shared by\n  everybody recurs most.\n- **Agreement on a step does not wait for a rule.** § 11.\n- **Added 2026-10-10: a default among the plural rules.** A library with a prover asks for the\n  widest rule that can be proved. With no prover the proposal is that a group of links prompts the\n  rule, which starts no wider than they need and widens as far as a stated mechanism reaches\n  ([alien-proofs-and-the-library.md](alien-proofs-and-the-library.md) § 4.6; ledger AF1, unruled).\n\n## 7. One link, several arguments\n\nMackie: an effect has several alternative sets of conditions, each enough and none necessary, and a\ncause is a part of one such set that the set cannot do without. In formal argumentation an\nargument is a smallest consistent set of premises that gives its claim, and one claim has many.\nRelevance logic adds that a premise counts only if it is used, and tracks use step by step.\n\n**The evening's pruning is that test of use.** It left each added sentence out and kept it only if\nthe reader then failed. But it tried the sentences in one order: names, then facts, then the rule.\nA fixed order finds one small set where there may be several.\n\n**The trial's own readings show there were several** (counted with no model call): on 16 of the 24\npruned links the step without the rule had been enough, and on 12 of those the pruning kept the\nrule. Those twelve have two ways of being complete. (The step without the rule was asked in one\norder only.)\n\n**Rechecked for the links reported as written around**\n([the script, with its expectation written first](philosophy-of-the-unwritten-step/first_claim_recheck.py);\n[answers](philosophy-of-the-unwritten-step/first_claim_recheck.json)). Nine links had been reported\nso: in the set that survived pruning, the reader reached the second claim without the first. On six\nof the nine the step without the rule had also been enough. For those six the reader was given the\ncase sentences alone, with no rule and no first claim, in both orders:\n\n| Link | Read by hand as | Case sentences alone | So |\n|---|---|---|---|\n| 2 | several steps | not enough, both orders | the first claim is needed on that route |\n| 6 | one further claim | not enough, both orders | the first claim is needed on that route |\n| 19 | one step | not enough, both orders | unsettled: see below |\n| 10 | several steps | enough, both orders | written around on both routes |\n| 30 | one further claim | enough, both orders | written around on both routes |\n| 29 | one further claim | enough in one order only | unsettled |\n\nExpected beforehand: not enough on at least three of the six. It held, at exactly three.\n\n⚠ **Link 19 is unsettled, found 2026-10-08.** Its row was first read as *the first claim is needed\non that route*. But pruning had kept one sentence for link 19, a fact, with no rule, and the reader\nhad taken that fact alone as enough for the second claim in both orders. The recheck gave the\nreader the same fact with the link's two naming sentences, and it answered *none* in both orders. A\nset of sentences cannot be enough when a larger set holding it is not. So the reader contradicted\nitself, and by the rule applied to link 29 the link is unsettled. Links 2 and 6 are not touched:\nwhat pruning kept for them was the rule, which is not among the case sentences. The contradiction\nalso shows what § 8 says in general: *enough* is a reading, made on one asking.\n\n**Where the thirty end up, corrected.**\n\n| | Evening's note | Corrected |\n|---|---|---|\n| Plain: nothing needed adding | 2 | 2 |\n| A written-out step in which every part is needed, the first claim among them | 13 | **15** |\n| Written around on every route tried | 9 | **5** |\n| Unsettled: the reader's answers disagree | | **2** |\n| Not written out to the reader's satisfaction | 6 | 6 |\n\nSo **17 of 30** have a step that uses the link's first claim, where the evening's note said 15 and\nthis note first said 18. The five\nwritten around are all links the hand reading called far (four *one further claim*, one *several\nsteps*). *The reader needed 1.2 added sentences* stands as a count for that one order of leaving\nout, and says nothing about which sentences.\n\n**What changes.** Pruning looks for every small set that is enough. A link counts as a reason when\nat least one such set needs its first claim. A link with two such sets carries two arguments, which\nis worth showing. Not run: the pruning in the reverse order over all 24, about 170 calls.\n\n**On drawing a written-around link as a chain.** Support does not pass along a chain in general. It\ndoes when the middle claim *screens off* the first from the last (Shogenji 2003). The written-around\ntest is that condition for this reader. So the chain is owed its first half: does the first claim\nsupport the machine's sentence. Without that, the sentence is only another argument for the second\nclaim.\n\n## 8. Complete for whom\n\nAristotle's premises are chosen for an audience, and in dialectic a premise is whatever the\nanswerer grants. Carroll's Tortoise is a reader who grants nothing unwritten, and for him no step is\never complete. Every reader between those two brings a practice.\n\nThe trial's reader joined names without being told to, and let some holes pass. It also refused a\nplain case of affirming the consequent (§ 5). *Enough* described that reader.\n\n- **A step is recorded as complete for a named reader**: which model, which version, when.\n- **Three readers are worth choosing on purpose.** A stranger, who brings as little as possible:\n  the project's own test. An opponent, told to resist: the dialectical tradition's reader, and the\n  natural partner of a writer that never refuses. And the author, who alone can say *that is what I\n  rely on*.\n- **What a reader adds silently cannot be seen by that reader.** It takes a reader of another kind.\n  This is the corpus's own principle, never ask a mind to audit its own frame, applied to\n  completeness.\n\n**A correction in passing.** [the-load-bearing-unsaid.md](the-load-bearing-unsaid.md) says\nAristotle's enthymeme is a syllogism with a premise deliberately left out. The Stanford entry on the\n*Rhetoric* reports that Aristotle does not define the enthymeme by a missing premise: it is a\ndeduction whose premises suit a public audience, and the *truncated syllogism* reading is later.\nThat doc's point about the audience supplying what is shared stands. Marked there.\n\n## 9. Complete is not supporting\n\nThe evening's note said that once everything is written in, whether a step bears *has become\nwhether its written premises are true*. Too quick, on three counts.\n\n- **A valid step with true premises can fail to pass support on.** This happens when one could only\n  come to accept a premise by already accepting the conclusion (Wright's failure of transmission).\n  Hitchcock's fourth test for a covering generalization, that it can be known apart from the\n  conclusion, is the same guard. The trial's checks catch the crude form: a rule that is the second\n  claim over again.\n- **A rule's standing is not the link's strength.** How strongly A supports B is the chance of B\n  given A. Lewis showed that no one sentence has that as its own probability in general, and the\n  plain *if A then B* can be near certain merely because A is unlikely. The product the graph uses\n  since 28 September (the supporter's strength times the link's relevance) is an approximation, and\n  the reference class problem of § 6 is why.\n  ⚠ **Corrected 2026-10-08:** two things here disagree with the September literature review. How\n  strongly A supports B needs two numbers, the chance of B with A and without it; the chance of B\n  given A alone says whether A would be enough. And a link's contribution as built is the exact\n  update when relevance means that contrast: what is uncertain is the number put in for relevance\n  ([the-squirrel-and-the-strength-calculus.md](the-squirrel-and-the-strength-calculus.md) § 4, § 6).\n- **Not everything a step needs is a premise of it.** Dancy separates what favours a conclusion\n  from what lets the favourer count (a promise, and its not having been given under duress), and\n  from what makes it count for more. Pollock's undercutting defeater is the denial of an enabler: it\n  attacks the link and leaves the conclusion alone. The trial's *facts* mix a further premise with\n  such conditions. A generic rule's list of *unless* is open, and the pattern's standing questions\n  are that list.\n\n**And one routing rule.** On the standard reading of Hume, no conclusion about what ought to be\nfollows from premises about what is. So when a link runs from a factual claim to a claim of value,\nthe rule under it is a claim of value, and its dispute belongs to the weighing layer. Words that\ndescribe and judge at once (*murder*, *cruel*) carry the judgment into the joining of names. That\nis where a persuasive definition does its work\n([prime-real-estate-words.md](prime-real-estate-words.md)).\n\n## 10. A second way: by refutation\n\nThe evening's writer is charitable. It adds whatever lets the step go through. Told to write a\nrule, it wrote one for 29 links of 30.\n\nLakatos described the other method in the history of one theorem. A counterexample to a proof shows\nthat the proof used something it never stated, a hidden lemma. The good response states that lemma\nand builds it into the theorem as a condition. The poor responses exclude the offending case by\nredefinition (he called it monster-barring) or list it as an exception.\n\n**As a way of writing a link out:**\n\n1. Ask for a situation in which the first claim holds and the second fails.\n2. Check the situation with closed questions: does the first claim hold in it, does the second\n   fail.\n3. Name what the situation has that the step assumed away. That is the unwritten premise.\n4. Write it in, and ask again.\n\n**What it would give that the charitable way does not.**\n\n- Nothing is added unless a counterexample demands it, so there is nothing to prune.\n- The counterexample is a concrete thing anybody can attack.\n- It says something about a good reason against a bad one without a verdict on the rule: was no\n  counterexample found, was one found and its condition built in, or could the step be saved only\n  by excluding that one case.\n\n**By hand, as an illustration and not a result.** The squirrel: a live squirrel that has rolled in\ncarrion. Unwritten premise: nothing else made it smell. Link 20 of the trial, which the hand reading\ncalled not a reason: its written rule says acts that differ only in how they are classed do not\ndiffer in justice. A prison sentence and a kidnapping are alike as physical acts, are classed\ndifferently, and differ in justice; so are a fine and a robbery. So that rule is false as written,\nand what the link needs is narrower: something about a state classing its own act. That narrower\nsentence is what the two texts in fact dispute. The charitable way put a false rule on the page and\nno check objected.\n\n⚠ *2026-10-08: this paragraph first gave killing in self-defence as the counterexample. That one is\nweak, since self-defence differs from murder in more than how it is classed. The case above is the\nfirst text's own. Van den Haag writes that imprisonment is not thought to legitimize kidnapping, nor\nfines robbery, and the graph holds that claim from the same source (`claim_aafcefb51964`, beside\n`claim_098ef998cfb6`: the physical likeness of a crime and its punishment is morally and legally\nirrelevant). So the rule the machine wrote under his claim is one his own text denies. The look\ninto both texts for a written sentence was run only for the fifteen links between the two\nconsciousness texts; it would have found this.*\n\n**In the graph a counterexample is an attack on the link's relevance claim**, Pollock's undercutter,\nand the slot exists. The corpus has the pattern for a neighbouring case: an analogy is proposed\ntogether with its strongest counter-analogy ([the-analogy-daemon.md](the-analogy-daemon.md)).\n\n**The catch.** Generic rules allow exceptions, so one counterexample does not refute one. What\nmatters is how ordinary the counterexample is, and that is a judgment of degree, which no model\nhere has read steadily. The counterexample is the valuable object. A rating of it is not. Untested.\n\n## 11. Whose sentence, and how it is shown\n\n**Agreement on the step, difference on the rule.** Toulmin served from 1975 to 1978 on a United\nStates commission on research with human subjects. Its members agreed on detailed recommendations,\nand in his words *\"they could not agree why they agreed about it\"*. Sunstein describes the same in\ncourts: people settle on an outcome and a narrow reason for it and leave the theory open, and when\nthey disagree on an abstraction they move to something more particular. He counts this a source of\nstability.\n\nFor the convergence wager this is evidence about *where* agreement sits. On Toulmin's showing it\nsits at the level of the step, and comes apart at the level of the stated rule. That is consistent\nwith the corpus's own picture of disagreement living in the middle, and it is a warning: asking for\nthe rule can turn a working agreement into a dispute. The corpus has the general form in\n[the-load-bearing-unsaid.md](the-load-bearing-unsaid.md).\n\n**⚠ Checked 2026-10-08, and narrowed.** Toulmin's account is one member's testimony. Jonsen, his\nco-author and a fellow member, said in 1998 that Congress's mandate was to identify principles, and\nthat *\"The Commissioners believed, as principalists, they worked as casuists.\"* Sunstein lists the\nreverse pattern first: agreement on a general principle with sharp disagreement about cases. In\nlarge publics that reverse is the measured one (Prothro and Grigg 1960). So where agreement sits\ndepends on the body: a small one that must decide can meet at the step, and a large public meets at\na principle's words and parts at its cases. The two proposals below stand as they were. Reading:\n[what-a-rule-rests-on.md](what-a-rule-rests-on.md) § 13.1.\n\n- **A link can be held by people who give different rules, and the graph shows that as a state.**\n- **A rule is never required before a step is accepted.**\n\n**The standing of a rule under an author's own step.** Walton and Krabbe distinguish the commitments\na speaker has stated from those on the *dark side*, which the speaker may not be aware of and which\ndialogue brings to light. Brought to light, a commitment can be owned, replaced or given up. So:\n\n- the rule is marked **committed by the step, not asserted**;\n- the author's moves are three: *that is what I rely on*, *I rely on something else, namely…*, and\n  *then I withdraw the step*;\n- nobody else can make those moves for the author. This is the consent ruling applied to rules.\n  The third move is what Socratic questioning usually produces.\n\nThe psychology the corpus already carries applies: reasons are often found after the fact, so what\nan author says they relied on is itself a reconstruction. *Needed for the step* is what the checks\ntest. *Used by the author* is known only from the text or from the author. A written sentence\nshould say which of the two it claims to be. The outside reading of this afternoon has that\ndistinction from Ennis.\n\n**How a rule is shown.**\n\n- **As the question at issue.** What is presupposed gets taken on by the hearer without a decision\n  (Lewis called it accommodation). Asserted content can be denied directly. Presupposed content\n  cannot, and needs something like *hey, wait a minute*. A line under a link reading *this rests on\n  R* is presupposition-shaped. *Does R hold?* with a move beside it is at issue. This is the\n  mechanism behind proposal AD17.\n- **No bare generic about a kind of people.** Such a rule is written with its scope (*in the cases\n  this text describes*, *for most*) or goes to a person first.\n- **The warning the corpus already carries stands.** Turning what goes without saying into\n  something arguable is not neutral (Bourdieu).\n\n## 12. What this changes (proposals, all unruled; ledger AD22 to AD29)\n\n| | Proposal |\n|---|---|\n| AD22 | **What a step needs is drawn as the grounds of that link's relevance claim, and not as further arrows into the conclusion.** The rule is a licence: written in as a premise it needs another rule. The facts and the joined names are grounds of the same claim, and the names also go to the concept layer. The regress is not closed. Each further step can be asked for, and stands until somebody asks with a reason. Refines AD13 and AD18. |\n| AD23 | **A written-out step records its shape: from a rule and a case; from a sign to what it indicates; from a case to a like case.** The three-part form and the blind reader fit the first only. Until the other two have checks of their own, such links are marked by shape and not forced into the form of a rule. |\n| AD24 | **A step is complete for a named reader, and three readers are chosen on purpose: a stranger, an opponent, the author.** |\n| AD25 | **A link carries rules in the plural, each with whose reading it is, and a rule's breadth is set by asking which changes of the case the step survives.** A rule's count across links is its record, and is read as conservative. |\n| AD26 | **Pruning looks for every small set of sentences that is enough, and a link counts as a reason when at least one such set needs its first claim.** Corrects AD15 and AD16: 17 with such a step, 5 written around, 2 unsettled, 6 not written out. |\n| AD27 | **Every written-out rule is shown with the strongest counterexample found against it, as an attack on the link's relevance claim.** A repair that only excludes that one case is marked as such. Untested. |\n| AD28 | **A rule under an author's own step is marked *committed by the step, not asserted*; the author may own it, replace it or withdraw the step; and agreement on a step with different rules is shown as a state.** A rule is shown as the question at issue, and a rule about a kind of people never as a bare generic. |\n| AD29 | **The standing property is that any link can be written out on request, the first level eagerly, and each chain under a rule ends in a named kind of stop.** *All of it written* is not a target. Refines AD8 and AD19. |\n\n**Told as pictures, 2026-10-08.** Each proposal has a spoken name in the ledger (*the toll bridge*\nfor AD22, and so on), with two examples and what it would open. The table, and six thoughts that\ncame from telling them, are in\n[what-the-walkthroughs-and-the-reviews-are-for.md](what-the-walkthroughs-and-the-reviews-are-for.md)\n§ 6 and § 7.\n\n**Considered, and not proposed.**\n\n- *Choosing a camp.* The licence view and the supply-the-premise view both survive. The design\n  holds under either: the rule is stated, as one camp wants, and sits in the licence's place, as\n  the other does.\n- *A fixed list of rule kinds as a schema.* The five stops of § 4 are a reading of where chains end.\n  By the corpus's own test a borrowed category earns its place by yielding a move, and a kind here\n  yields one only as a routing hint.\n- *Formal logic for the check.* As in the evening's note.\n- *Dropping the three-part form.* It is the right form for one shape, and the only one with any\n  measurement.\n\n**Read against the strength rulings, 2026-10-08** (the founder's question). AD22 and AD23 meet the\nAugust weakest-part ruling and the September link rule. AD23's shape is the record the September\nreview asked links to carry, and AD22 needs *grounds* specified before it can be built:\n[the-squirrel-and-the-strength-calculus.md](the-squirrel-and-the-strength-calculus.md).\n\n**Read against induction and analogy, 2026-10-08** (the founder's thought that a rule rests on cases and\ncases on likeness). § 5's table has three shapes and the graph holds a fourth, from cases to a rule: the\nkind stored as *example*, 84 links between claims taken from texts against 37 for analogy and precedent\ntogether. It is Peirce's induction, which § 5 quotes and does not list. Likeness also sits twice inside\nthe first shape: behind the rule, and in what ties this case to it. And § 6's *which rule* has a sixth\nfield, since choosing which earlier cases count as alike is the same choice.\n[what-a-rule-rests-on.md](what-a-rule-rests-on.md) § 5 to § 7.\n\n## 13. Corrected with this note\n\n| Where | What it said | What is so |\n|---|---|---|\n| [writing-out-the-unwritten.md](writing-out-the-unwritten.md) § 0, § 8b, § 9.4; ledger AD16; the walkthrough; the to-do list; the session record; `CLAUDE.md` | 15 of the thirty pass every check, 9 are written around, 6 could not be written out | 17, 5, 2 unsettled, 6 (18, 5, 1 and 6 until link 19 was read again, § 7). The pruning tried one order (§ 7) |\n| the same note § 8b; ledger AD15 | the reader needed 1.2 added sentences and could do without 37 of 42 joined names | a count for one order of leaving out. On 12 of 24 links the case sentences and the rule could each stand in for the other |\n| the same note § 1 | with everything written in, whether a step bears has become whether its premises are true | also whether they can be accepted without the conclusion, and a rule's standing is not the link's strength (§ 9) |\n| the same note § 1, § 6 | his 2011 example is a written-out step of the three-part form | it is written out as a step from a sign. The trial's reader refuses it as he wrote it (§ 5) |\n| [the-load-bearing-unsaid.md](the-load-bearing-unsaid.md) | Aristotle's enthymeme has a premise deliberately left out | not his definition, on the Stanford entry's reading (§ 8) |\n\n## 14. What philosophy does not give\n\n- **No procedure.** Each tradition that met this built a practice around it: dialectic, the\n  commentary, the law report, the referee, the proof assistant. The corpus says the same of every\n  field that met the sameness problem.\n- **No verdict between the camps.**\n- **No measure.** Nothing read here says how often a written-out step is right. That is still the\n  thirty links, one family of models, and no person's reading.\n- **A selection.** Fifteen angles were chosen by one reader looking for bearing on one design. Not\n  read: phenomenology beyond Gadamer, Chinese and Islamic logic, speech-act theory beyond one rule\n  of Searle's, formal epistemology beyond four results, and the feminist epistemology that the\n  corpus's conviction about positions rests on.\n\n## 15. What was read, and how far\n\n**By Claude, in full, this session**: the day's three notes; the trial's files; the 24 pruned steps.\n**By Claude, by search within the file**: the corpus's\n[philosophy-of-evidence.md](what-counts-as-evidence/philosophy-of-evidence.md),\n[the-load-bearing-unsaid.md](the-load-bearing-unsaid.md),\n[relevance-and-the-two-factors.md](relevance-and-the-two-factors.md), and this afternoon's helper\nreport on argumentation theory (for Hitchcock, Toulmin's warrants, Ennis and the pragma-dialectical\n*logical minimum*).\n\n**Outside**, 2026-10-07, each a page put one question, or a web search, the answer written by the\ntool's own model and kept [as it came back](philosophy-of-the-unwritten-step/what-each-lookup-returned.md):\n\n| Used for | Source | Kind |\n|---|---|---|\n| Stoic arguments and Alexander's reply | a web search (Bobzien's papers among the results) | search summary |\n| Formal and material consequence; simple and as-of-now; reduction by an added premise | Stanford Encyclopedia, *Medieval Theories of Consequence* | page, one question |\n| Enthymeme, sign, example, topos | Stanford Encyclopedia, *Aristotle's Rhetoric* | page, two questions |\n| Immediate premises; the regress | Stanford Encyclopedia, *Aristotle's Logic* | page |\n| Five-membered argument; the triple condition; sign inference | Stanford Encyclopedia, *Logic in Classical Indian Philosophy* | page |\n| Rule, case, result | a web search returning Peirce's 1878 paper on Wikisource | search summary |\n| Guiding principle as habit | Peirce, *The Fixation of Belief* (1877), Wikisource | page |\n| Abduction; Peirce's schema | Stanford Encyclopedia, *Abduction* and its supplement on Peirce | pages |\n| *According to the formula* | a web search returning Mill's *System of Logic* | search summary, quotation matched |\n| The Tortoise | Carroll's text of 1895, Wikisource | page |\n| Inference tickets; the regress of knowing how | Stanford Encyclopedia, *Gilbert Ryle* | page |\n| Grounds, warrant, backing | Wikipedia, *Toulmin method*; the afternoon's helper report | page; helper |\n| Material inference | Stanford Encyclopedia, *Wilfrid Sellars*; a web search on Brandom | page; search summary |\n| No rule for applying rules | a web search (papers on Kant's power of judgment) | search summary |\n| The regress of interpretations | Stanford Encyclopedia, *Rule-Following and Intentionality* | page |\n| Question and answer; absolute presuppositions | Stanford Encyclopedia, *Collingwood* | page |\n| Prejudice; never fully transparent | Stanford Encyclopedia, *Gadamer* | page |\n| Lifeworld; validity claims | Stanford Encyclopedia, *Habermas* | page |\n| Rules as abridgements; exemplars; the background | Stanford Encyclopedia, *Oakeshott*, *Thomas Kuhn*, *The Frame Problem* | pages |\n| Covering laws and their failures; the inkwell | Stanford Encyclopedia, *20th Century Theories of Scientific Explanation* | page |\n| Grue and entrenchment | Stanford Encyclopedia, *Nelson Goodman* | page |\n| Hidden lemmas | Stanford Encyclopedia, *Imre Lakatos* | page |\n| Derivability and ground | Stanford Encyclopedia, *Bolzano's Logic*; a web search on Hitchcock | page; search summary |\n| A premise must be used | Stanford Encyclopedia, *Relevance Logic* | page |\n| Several sufficient sets | the Stanford Encyclopedia entry on regularity theories of causation | page |\n| An argument as a smallest set | a web search (Besnard and Hunter) | search summary |\n| Screening off | a web search (Shogenji 2003; Roche) | search summary |\n| Implication and inference | Stanford Encyclopedia, *The Normative Status of Logic* | page |\n| The taking condition | a web search | search summary; not used in the argument |\n| Transmission failure | Stanford Encyclopedia, *Transmission of Justification and Warrant* | page |\n| Rebutting and undercutting | Stanford Encyclopedia, *Defeasible Reasoning* | page |\n| Conditionals and probability | Stanford Encyclopedia, *Indicative Conditionals* | page |\n| Accommodation; *hey, wait a minute* | Stanford Encyclopedia, *Presupposition*; a web search | page; search summary |\n| Implicated premises | Wikipedia, *Relevance theory* | page |\n| Generics | Stanford Encyclopedia, *Generic Generalizations* | page |\n| Is and ought | Stanford Encyclopedia, *Hume's Moral Philosophy* | page |\n| Favourers and enablers | Stanford Encyclopedia, *Moral Particularism*; a web search | page; search summary |\n| Ratio; levels of generality; distinguishing | Stanford Encyclopedia, *Precedent and Analogy in Legal Reasoning* | page |\n| The commission | a web search on Toulmin's *The Tyranny of Principles* | search summary, quotation as returned |\n| Incompletely theorized agreements | a web search (Sunstein, *Harvard Law Review* 1995) | search summary |\n| Dark-side commitments | a web search (Walton and Krabbe 1995) | search summary |\n| Counts as | a web search (Searle) | search summary |\n| The three questions of rhetoric | Wikipedia, *Stasis (argumentation theory)* | page |\n| Gapless inference | a web search (Frege's preface of 1879) | search summary |\n| Infinite analysis | Stanford Encyclopedia, *Leibniz's Modal Metaphysics* | page |\n| Four times the length | a web search (Wiedijk on the de Bruijn factor) | search summary |\n| Gaps in proofs; proofs as indicating derivations | a web search (Fallis; Azzouni) | search summary |\n\n**Pages that did not cover what was asked**, so nothing here leans on them for it: the Stanford\nentries on ancient logic (Stoic arguments of this kind), on Peirce's deductive logic (guiding\nprinciples; rule, case, result), on Kant's theory of judgment (the regress), on Frege's logic (his\naim), on presupposition (the *hey, wait a minute* test), and on Mill (the sentence quoted).\n\n**From the corpus and not looked up again**: default and challenge; the reference class problem;\nBourdieu's doxa; hinges; Mercier and Sperber on reasons found after the fact; Dancy as a limit on\nthe ontology; the stranger test.\n\n**Model calls**: 18 on the keeper's plan (6 for the squirrel, 12 for the recheck), about one dollar\nat API list prices. No money was paid.\n\n## Cross-references\n\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[how-far-a-premise-is-from-its-claim.md](how-far-a-premise-is-from-its-claim.md) ·\n[relevance-and-the-two-factors.md](relevance-and-the-two-factors.md) (the relevance claim) ·\n[what-counts-as-evidence/philosophy-of-evidence.md](what-counts-as-evidence/philosophy-of-evidence.md)\n(default and challenge) · [the-load-bearing-unsaid.md](the-load-bearing-unsaid.md) ·\n[the-analogy-daemon.md](the-analogy-daemon.md) (a proposal with its counter attached) ·\n[what-belongs-in-the-ontology.md](what-belongs-in-the-ontology.md) (what a schema may bake in) ·\n[prime-real-estate-words.md](prime-real-estate-words.md) ·\n[walton-argument-schemes.md](walton-argument-schemes.md) (the patterns and their questions) ·\n[scheme-bounded-decomposition-and-evidence-as-subgraph.md](scheme-bounded-decomposition-and-evidence-as-subgraph.md).\n"}