{"path":"research/philosophy-of-the-unwritten-step/what-each-lookup-returned.md","content":"# What each lookup returned, as it came back\n\n*Kept as it came back, 2026-10-07 at night, for [philosophy-of-the-unwritten-step.md](../philosophy-of-the-unwritten-step.md).\nEach entry is a page fetched and one question put to it, or a web search. **The answers were written by the\nfetch tool's own small model from the page, or by the search tool from its results. Claude did not read the\npages.** So every answer below is a summary at one remove, and a claim taken from it into the note carries\nthat read depth. Where an answer says a page does not cover something, the note does not cite that page for it.\nOne page could not be opened at its first address (the entry on medieval consequence) and one had been retired\n(scientific explanation); both were then read at their current addresses.*\n\n## 1. Page: https://plato.stanford.edu/entries/medieval-consequence/\n\n**Asked:** Answer in under 150 words, paraphrasing (no long quotations), and name the section(s) you rely on. (1) How do 14th-century logicians (Buridan, Pseudo-Scotus, Ockham, Burley) distinguish FORMAL from MATERIAL consequence? (2) What is the distinction between SIMPLE (absolute) consequence and consequence 'UT NUNC' (as-of-now)? (3) Does the entry say a material consequence can be reduced to a formal one by adding a premise, and if so what kind of premise is added in the simple case versus the ut-nunc case?\n\nThe server returned HTTP 404 Not Found.\n\nThe response body was not retrieved. If this URL requires authentication, use an authenticated tool (e.g. `gh` for GitHub, or an MCP-provided fetch tool) instead of WebFetch.\n\n## 2. Page: https://plato.stanford.edu/entries/logic-ancient/\n\n**Asked:** Answer in under 110 words, paraphrasing, and name the section. What does this entry say about Stoic 'unmethodically concluding arguments' (arguments that are valid but not in virtue of a recognised form, e.g. 'A is equal to B, B is equal to C, so A is equal to C')? Does it report a dispute with Peripatetics (e.g. Alexander of Aphrodisias) about whether such arguments need an added universal premise to be syllogistic? If the entry does not discuss this, say so plainly.\n\n# Response\n\nThe entry does not discuss Stoic \"unmethodically concluding arguments\" or disputes with Peripatetics about whether such arguments require added universal premises for syllogistic status.\n\n**Section:** \"5.4 Stoic Syllogistic\"\n\nThe section explains that Stoic syllogistics consisted of five indemonstrables and four inference rules (themata). While the Stoics acknowledged \"valid arguments that are not syllogisms,\" the entry states these \"could be somehow transformed into syllogisms\" through the themata system. However, it provides no discussion of unmethodical arguments or Peripatetic objections regarding additional premises.\n\n## 3. Page: https://plato.stanford.edu/entries/aristotle-rhetoric/\n\n**Asked:** Answer in under 170 words, paraphrasing, naming sections. (a) What is an enthymeme for Aristotle, and does the entry say it is DEFINED by having a missing/suppressed premise, or does it reject that as a later misreading? (b) What are sign-enthymemes, and how does a necessary sign (tekmerion) differ from a refutable sign? (c) What is 'example' (paradeigma) as the other kind of rhetorical proof, and how does it reason (part to part, like to like)? (d) In one line, what is a topos?\n\n# Enthymemes, Signs, and Rhetorical Proof\n\n**(a) Enthymeme Definition:** Section 6.1-6.4 clarifies that Aristotle defines enthymemes as deductive arguments (sullogismoi), NOT by missing premises. The entry rejects the traditional \"abbreviated syllogism\" reading as a later misinterpretation. Section 6.4 emphasizes: the brevity discussion concerns appropriate premise *selection* for audiences, \"not about logical incompleteness.\"\n\n**(b) Sign-Enthymemes:** Section 6.5 distinguishes two types. Non-necessary signs (type i and iii) can be refuted even if premises are true—they lack valid deductive form. Necessary signs or *tekmerion* (type ii, like fever indicating illness) cannot be refuted; they constitute valid deductions.\n\n**(c) Example (Paradeigma):** Section 5.3 describes examples as rhetorical induction. Unlike standard induction moving from many particulars to universals, rhetorical examples reason \"from one particular to a similar particular if both fall under the same genus\"—reasoning between analogous cases rather than upward to generals.\n\n**(d) Topos Definition:** Section 7.1 defines it succinctly: \"a heading under which many enthymemes fall\"—a general argumentative scheme generating multiple concrete arguments.\n\n## 4. Page: https://plato.stanford.edu/entries/aristotle-logic/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming sections. What does the entry say about (a) demonstration requiring premises that are 'immediate' (having no middle term / nothing prior), (b) the regress argument in Posterior Analytics I.3 and Aristotle's answer to it, and (c) the role of finding a 'middle term' in explanation or demonstration?\n\n# Aristotle's Logic: On Demonstrations and Middle Terms\n\n**(a) Immediate Premises:** Section 6.1 defines demonstration premises as \"immediate\" (_amesa_, \"without a middle\"). The entry notes interpreters debate this term's meaning—some read it as \"self-evident,\" though Aristotle emphasizes that immediate propositions have \"no other prior\" to them, linking priority to logical relations within his system.\n\n**(b) The Regress Problem:** Section 6.2 presents the challenge: if all scientific knowledge requires demonstration, and demonstration premises need demonstration, an infinite regress threatens. Aristotle rejects circular demonstration as incoherent (Section 6.3) and claims knowledge of first principles comes through _nous_ (insight), not demonstration, providing the necessary starting points.\n\n**(c) Middle Term's Explanatory Role:** The entry emphasizes that finding the middle term is central to syllogistic reasoning, though it doesn't explicitly detail explanation's connection to middle terms beyond their logical function in valid deductions.\n\n## 5. Page: https://plato.stanford.edu/entries/abduction/\n\n**Asked:** Answer in under 140 words, paraphrasing, naming sections. (a) How does the entry define abduction / inference to the best explanation, and how does it differ from deduction and induction? (b) Does it give Peirce's schema ('The surprising fact C is observed; but if A were true, C would be a matter of course; hence there is reason to suspect that A is true')? (c) Does it say abduction, read deductively, has the form of affirming the consequent, or that its goodness depends on comparison with rival explanations?\n\n# Abduction: Definition, Distinction, and Logical Form\n\n## (a) Definition and Distinction\n\nSection 1.1 defines abduction as reasoning to a hypothesis because it provides the **best explanation** of evidence, contrasting it with deduction (necessary inference) and induction (inference based purely on statistical data). The entry states that \"in abduction there is an implicit or explicit appeal to explanatory considerations, whereas in induction there is not.\"\n\n## (b) Peirce's Schema\n\nThe entry does **not** present Peirce's specific schema. Instead, it notes that the entry \"is exclusively concerned with abduction in the modern sense\" and references a separate supplement on Peirce's historical conception.\n\n## (c) Affirming the Consequent and Rival Comparisons\n\nThe entry **does not** discuss the logical form of affirming the consequent. However, Section 2 emphasizes that abduction's goodness fundamentally depends on comparative evaluation: it requires \"an absolute premise\" about whether a hypothesis is \"the best of the available potential explanations.\"\n\n## 6. Page: https://plato.stanford.edu/entries/peirce-logic/\n\n**Asked:** Answer in under 130 words, paraphrasing. Does this entry discuss (a) Peirce's notion of a 'leading principle' (or guiding principle) of an inference, and the distinction between a logical (formal) leading principle and a factual/material one; (b) Peirce's early classification of deduction, induction and hypothesis as the three ways of arranging Rule, Case and Result (the bean-bag example)? For each, say what the entry says and in which section, or say plainly that the entry does not cover it.\n\n# Analysis of Coverage\n\n**(a) Leading principle distinction:** The entry does **not** discuss Peirce's notion of a leading principle or the distinction between formal versus factual leading principles.\n\n**(b) Three-way classification (Rule, Case, Result):** The entry does **not** address Peirce's early classification of deduction, induction, and hypothesis as arrangements of Rule, Case, and Result, nor does it mention the bean-bag example.\n\nThe entry focuses exclusively on three dimensions of logical extension: (1) from monadic to polyadic logic, (2) from symbolic to diagrammatic representation, and (3) from bivalent to three-valued semantics. Neither topic falls within these primary concerns.\n\n## 7. Page: https://plato.stanford.edu/entries/bolzano-logic/\n\n**Asked:** Answer in under 140 words, paraphrasing, naming sections. (a) How does Bolzano define derivability (Ableitbarkeit) by means of 'variable ideas', and how does this differ from purely formal logical consequence (can non-logical ideas be held fixed, so that derivability is relative to a choice of which ideas vary)? (b) What is 'Abfolge' (the ground-consequence relation), and how does it differ from derivability?\n\n# Bolzano's Derivability and Grounding\n\n## (a) Derivability via Variable Ideas\n\nBolzano defines derivability (Ableitbarkeit) by designating certain ideas within propositions as \"variable\" and checking whether all substitutions making the premises true also make conclusions true. Crucially, this differs from formal logical consequence: derivability is **triadic**, involving premises, conclusions, and specified variable ideas. Non-logical ideas can indeed be held fixed while others vary, making derivability relative to this choice. As the text states, \"deducibility is a _triadic_ relation involving collections of premises, conclusions, and variable ideas.\" This allows contingent connections—e.g., [Harry Truman wasn't Buddhist] derives from [Harry Truman was a 20th-century US president]—not just necessary logical truths.\n\n## (b) Abfolge (Ground-Consequence Relation)\n\nAbfolge designates the \"objective connection among truths,\" fundamentally distinct from derivability. While derivability concerns truth-preservation under substitution, grounding involves explaining *why* truths hold. The text notes grounding is \"anti-transitive\" and \"anti-symmetrical,\" whereas derivability lacks these features. Grounding requires truth-value invariance and operates among true propositions exclusively, establishing hierarchical scientific organization—a relationship derivability alone cannot capture.\n\n## 8. Page: https://plato.stanford.edu/entries/sellars/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming the section. What does the entry say about Sellars's 'material rules of inference' (as opposed to formal rules), their role in the meaning of non-logical terms, and whether he treats material inferences such as 'it is raining, so the streets will be wet' as enthymemes with a suppressed premise or as good inferences in their own right? If the entry does not discuss the enthymeme question, say so.\n\n# Sellars on Material Inference\n\nIn the **Semantics** section (3.1), Sellars distinguishes formal inferences governed by syntactic rules from material inferences based on conceptual content alone. He argues that material inferences—like \"it is raining\" implying \"the street will be wet\"—are **not** mere enthymemes requiring suppressed premises. Instead, \"the web of material inferences an expression is involved in...determines its core meaning.\" These inferences constitute genuine rational transitions grounded in the meaning-constituting role of expressions, making material inference central to semantic understanding rather than derivative logical reasoning.\n\n## 9. Page: https://plato.stanford.edu/entries/ryle/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming sections. What does the entry say about (a) Ryle's regress argument against the 'intellectualist legend' (that intelligent performance must be preceded by considering a rule or proposition), and (b) Ryle's view of law-statements or hypothetical statements as 'inference tickets' or inference licences rather than as premises? If either is not covered, say so plainly.\n\n# Ryle on Intellectual Performance and Inference Tickets\n\n**(a) The Regress Argument (Section 7):**\n\nRyle argues that intelligent behavior cannot be explained by prior theoretical operations because those operations themselves require intelligence. This creates a vicious infinite regress. As he notes, \"there were reasoners before Aristotle\" and rules codify already-existing practices rather than enable them. Intelligent performance often requires merely satisfying criteria, not consulting rule-formulations beforehand.\n\n**(b) Inference Tickets (Section 9):**\n\nRyle characterizes dispositional statements and laws differently from fact-stating sentences. Laws function as \"inference ticket(s)\" that license movement between assertions and enable explanation, rather than describe occurrences. A dispositional sentence like \"Jones believes the earth is round\" similarly doesn't report what currently exists but rather what would satisfy it—an open-ended list of behaviors and mental acts.\n\n## 10. Page: https://en.wikisource.org/wiki/What_the_Tortoise_Said_to_Achilles\n\n**Asked:** In under 110 words and in your own words: what are the three propositions A, B and Z; what does the Tortoise accept and what does he refuse to accept; what is proposition C; and what happens each time Achilles writes the hypothetical down as a further premise? Give the year and the journal if the page states them.\n\n# Summary of \"What the Tortoise Said to Achilles\"\n\n**The Three Propositions:**\n- A: \"Things that are equal to the same are equal to each other\"\n- B: The two sides of a triangle are equal to the same\n- Z: The two sides of the triangle are equal to each other\n\n**The Tortoise's Position:**\nThe Tortoise accepts A and B but refuses to accept that Z logically follows from them without an additional premise.\n\n**Proposition C:**\nC states: \"If A and B are true, Z must be true.\" It's the hypothetical linking the premises to the conclusion.\n\n**The Pattern:**\nEach time Achilles writes down a hypothetical as a new premise, the Tortoise refuses to accept the final conclusion unless Achilles also accepts *another* hypothetical explaining why this new premise leads to Z. This creates infinite regression—new premises demand new connecting hypotheticals endlessly.\n\n**Publication Details:**\nThe work appeared in 1895, though the page doesn't specify the journal name.\n\n## 11. Page: https://plato.stanford.edu/entries/logic-normative/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming the section. Summarise Gilbert Harman's distinction between implication (a relation among propositions, the subject of logic) and inference or reasoning (a change in view by a thinker), and his main objections to the idea that logical rules are rules of reasoning (e.g. clutter avoidance, that one may respond to an implication by giving up a premise).\n\n# Harman's Challenge to Logic's Normativity\n\nIn **Section 3: Harman's Challenge**, Harman distinguishes between two enterprises: deductive logic (studying static relations among propositions) versus theories of reasoning (normative accounts of how agents should form and revise beliefs). He argues these differ fundamentally because \"logical principles are not directly rules of belief revision.\"\n\nHarman raises four main objections to treating logic as normative for reasoning:\n\n1. **Belief Revision**: Following logical implications may be irrational when conclusions conflict with evidence; rational agents should revise premises instead.\n\n2. **Clutter Avoidance**: Agents with limited cognitive resources cannot reasonably derive every logical consequence, as most would be useless.\n\n3. **Excessive Demands**: Some logical truths require proofs too complex for ordinary agents to verify.\n\n4. **Preface Paradox**: Situations exist where inconsistency appears rationally required, contradicting logical norms.\n\nHarman's core insight is that logical implication differs from practical reasoning guidance.\n\n## 12. Page: https://plato.stanford.edu/entries/rule-following/\n\n**Asked:** Answer in under 120 words, paraphrasing, naming the section. Summarise the regress of interpretations in Wittgenstein's rule-following considerations (Philosophical Investigations around sections 198 to 201): why can a rule, or an interpretation of a rule, not by itself fix how it is to be applied, and what does Wittgenstein say stops the regress?\n\n# The Regress of Interpretations in Rule-Following\n\nAccording to the Stanford Encyclopedia article's discussion in **Section 5 (Non-Reductionism)**, Wittgenstein identifies why rules cannot self-apply: any rule requires interpretation to guide action, yet that interpretation itself becomes another rule needing interpretation, generating infinite regress.\n\nThe article notes that Miller argues interpretation isn't necessary: \"in applying a rule R in a particular case there need be no _further_ inferential step\" beyond the rule itself. Wittgenstein stops the regress through **training and practice**. The article explains that \"what puts an agent in a position to follow a rule is her having been trained into a practice or custom of following rules.\"\n\nThus, shared communal practices—not further rules—terminate the regress.\n\n## 13. Page: https://plato.stanford.edu/entries/kant-judgment/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming sections. (a) Does the entry discuss Kant's claim (Critique of Pure Reason A132-134/B171-174) that the power of judgment, the capacity to subsume particulars under rules, cannot itself be guided by further rules, on pain of regress, so that it is a talent that can be practised but not taught? (b) Does it explain the distinction between determining (determinative) judgment, where the universal is given, and reflecting (reflective) judgment, where only the particular is given and the universal must be found? If not covered, say so plainly.\n\n# Analysis of Entry Coverage\n\n**(a) On judgment as unguided by rules:**\nNo, the entry does not discuss Kant's claim that the power of judgment cannot be guided by further rules without regress, making it unteachable. Section 1.1 mentions judgment as \"the faculty of subsuming under rules\" but does not address the regress problem or the untouchability thesis that Kant articulates in those specific passages.\n\n**(b) On determining versus reflecting judgment:**\nNo, the entry does not explain this distinction. While Section 2 classifies \"kinds of judgments,\" it focuses on logical forms and propositional content. The difference between determining judgment (where universals guide subsumption of particulars) and reflecting judgment (where particulars must find their universals) receives no treatment. The supplementary document on \"Kinds of Use\" is referenced but its contents remain inaccessible in the provided text.\n\n## 14. Page: https://plato.stanford.edu/entries/consequence-medieval/\n\n**Asked:** Answer in under 160 words, paraphrasing (no long quotations), and name the section(s). (1) How do 14th-century logicians (Buridan, Pseudo-Scotus, Ockham, Burley) distinguish FORMAL from MATERIAL consequence? (2) What is the distinction between SIMPLE (absolute) consequence and consequence 'UT NUNC' (as-of-now)? (3) Does the entry say a material consequence can be reduced to a formal one by adding a premise, and what kind of premise is added in the simple case (a necessary proposition?) versus the ut-nunc case (a contingently true one?)\n\n# Medieval Consequence Distinctions\n\n**(1) Formal vs. Material Consequence (Section 3.2-3.4):**\n\nLogicians disagreed fundamentally. Buridan's Parisian approach defined formal consequence through substitutivity—valid \"in all terms retaining a similar form.\" British authors like Lavenham instead emphasized epistemic containment: \"the consequent necessarily belongs to the understanding of the antecedent.\" Ockham's earlier account used intrinsic/extrinsic middles. Burley recovered natural/accidental distinctions, arguing natural consequences hold \"through an intrinsic topic\" when antecedent includes consequent.\n\n**(2) Simple vs. Ut Nunc (Section 3.2):**\n\nBurley distinguished temporal scope: simple consequence \"holds for every time,\" while ut nunc consequence \"holds for a determinate time\" only—exemplified by \"Every man runs; therefore Socrates runs,\" valid only when Socrates remains human.\n\n**(3) Reduction Through Added Premises (Section 3.3):**\n\nYes. Pseudo-Scotus formulated this explicitly: simple consequences require necessary premises; ut nunc consequences require contingently true premises holding at the consequence's temporal reference point.\n\n## 15. Page: https://plato.stanford.edu/entries/aristotle-rhetoric/\n\n**Asked:** Answer in under 120 words, paraphrasing. In the section on the brevity of the enthymeme (around 6.4): does Aristotle say that a premise may be left unstated when the audience already knows it (the example of Dorieus winning a crown contest at the Olympic games)? What exactly does the entry reject: (i) that speakers may omit known premises, or (ii) that an enthymeme is BY DEFINITION an incomplete or abbreviated syllogism? State both answers plainly.\n\n# Enthymeme Brevity and Premise Omission\n\nThe entry **rejects interpretation (ii)**: that enthymemes are *defined by* incompleteness. The text states: \"This is not to say that the enthymeme is defined by incompleteness and brevity.\"\n\nRegarding interpretation (i), the entry does **not clearly address** whether speakers may omit premises the audience knows. The section focuses on refuting the definition-based incompleteness view, explaining instead that enthymeme premises are \"adjusted to the intellectual capacities of the public audience.\" However, it provides no explicit example about omitting known premises like an Olympic victory reference.\n\n## 16. Page: https://plato.stanford.edu/entries/abduction/peirce.html\n\n**Asked:** Answer in under 150 words, paraphrasing. (a) Does this supplement give Peirce's schema for abduction (the surprising fact C is observed; if A were true C would be a matter of course; hence there is reason to suspect A)? (b) Does it describe Peirce's early view of hypothesis, deduction and induction as different arrangements of a Rule, a Case and a Result (the beans example), and if so state which two yield which in each of the three? (c) Does it say abduction for Peirce belongs to the context of discovery (generating hypotheses) rather than justification?\n\n# Analysis of the Supplement\n\n**(a) Yes.** The text explicitly presents Peirce's abductive schema: \"The surprising fact, _C_, is observed. But if _A_ were true, _C_ would be a matter of course. Hence, there is reason to suspect that _A_ is true.\"\n\n**(b) No.** The supplement does not discuss Peirce's early triadic arrangement of Rule, Case, and Result, nor does it mention the beans example commonly used to illustrate deduction, induction, and abduction as different logical operations.\n\n**(c) Yes.** The text clearly states that for Peirce, \"abduction had its proper place in the context of discovery, the stage of inquiry in which we try to generate theories which may then later be assessed,\" distinguishing this from the modern view that places abduction in the \"context of justification.\"\n\n## 17. Page: https://en.wikisource.org/wiki/The_Fixation_of_Belief\n\n**Asked:** In under 110 words and in your own words: what does Peirce say here about the 'guiding principle' of inference: what is it, is it a habit of mind, and how does he say a guiding principle is judged good or bad (true or false)? Does he give an example (e.g. about a rotating copper disk and a magnet)? Give the year of publication if the page states it.\n\n# Peirce on Guiding Principles of Inference\n\nPublished in **1877**, Peirce explains that a guiding principle is \"some habit of mind\" determining which inference we draw from given premises. A principle is judged good when it \"produces true conclusions from true premisses\" and bad otherwise.\n\nHe illustrates this with copper: observing that a rotating copper disk stops between magnet poles, we infer this happens with every copper disk. The guiding principle—\"what is true of one piece of copper is true of another\"—proves safer for copper than other substances like brass, showing how principles vary in reliability depending on the subject matter.\n\n## 18. Page: https://plato.stanford.edu/entries/transmission-justification-warrant/\n\n**Asked:** Answer in under 140 words, paraphrasing, naming sections. Explain 'transmission failure': how can a deductively valid argument with justified premises fail to transmit justification to its conclusion? What structural condition do Crispin Wright and others say causes it (e.g. the justification for a premise depends on already having justification for the conclusion)? Mention one standard example (Moore's proof, or the zebra/cleverly disguised mule case).\n\n# Transmission Failure in Epistemic Justification\n\n**Transmission failure** (Section 3) occurs when a deductively valid argument's premises are justified, yet this justification doesn't transmit to the conclusion. Even with knowledge of the logical entailment, the conclusion isn't justified *in virtue of* the premises and their connection.\n\n**The Information-Dependence Template** (Section 3.2) identifies a key structural cause: justification for a premise depends on collateral information that itself requires independent justification for believing the conclusion. As Wright states, \"whether e justifies p depends on what one has by way of collateral information, i\" and failure occurs when needed elements of that background information are entailed by the conclusion.\n\n**The Twins Example** illustrates this perfectly: evidence that \"this girl looks like Jessica\" justifies \"this girl is Jessica\" only if you already independently justify that \"this girl is not Jocelyn.\" The argument cannot transmit its justification because obtaining the premise's justification presupposes the conclusion's independent justification.\n\n## 19. Page: https://plato.stanford.edu/entries/reasoning-defeasible/\n\n**Asked:** Answer in under 120 words, paraphrasing, naming the section. Explain John Pollock's distinction between rebutting defeaters and undercutting defeaters, and what a 'prima facie reason' is. Give his standard example for an undercutting defeater if the entry has one (e.g. an object looking red under red light).\n\n# Pollock's Defeaters and Prima Facie Reasons\n\nIn the \"History\" section (1.1), John Pollock distinguishes two defeater types. A **prima facie reason** is a belief supporting another proposition, though defeasibly rather than conclusively.\n\n**Rebutting defeaters** provide independent reasons for believing the conclusion's negation. **Undercutting defeaters** challenge whether the original premises actually support the conclusion in the given circumstances—they undermine the inferential link itself.\n\nPollock's classic example: \"an elephant appearing pink undercuts the inference that it actually is pink if you know your color vision becomes unreliable around pink elephants.\" The appearance still exists, but the defeater questions whether appearances reliably indicate reality here, rather than directly contradicting the color claim.\n\n## 20. Page: https://plato.stanford.edu/entries/logic-relevance/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming sections. (a) What is the variable-sharing criterion of relevance? (b) Does the entry describe the idea, from Anderson and Belnap's natural deduction systems, that a premise must actually be USED in deriving the conclusion, tracked by indices or subscripts on hypotheses? (c) Which classically valid inferences do relevance logicians reject as fallacies of relevance?\n\n# Relevance Logic: Three Key Aspects\n\n**(a) Variable-Sharing Criterion**\nThe variable-sharing principle (\"Semantics for Relevant Implication\" section) requires that formulas of the form A→B cannot be proven unless A and B share \"at least one propositional variable\" in common. This formal constraint ensures theorems remain topically connected.\n\n**(b) Index-Tracking in Natural Deduction**\nYes, the \"Proof Theory\" section extensively discusses Anderson and Belnap's system. Subscripted indices on hypotheses track which premises are \"really used\" in deriving conclusions. When discharging assumptions to prove implications, \"the number of the hypothesis must really occur\" in the resulting consequent's subscript.\n\n**(c) Rejected Inferences**\nRelevance logicians reject classical inferences exhibiting \"fallacies of relevance,\" including disjunctive syllogism and ex falso quodlibet (explosion). They also invalidate theses like p→(q→q) and (p∧¬p)→q, where antecedents seem irrelevant to consequents.\n\n## 21. Page: https://plato.stanford.edu/entries/causation-regularity/\n\n**Asked:** Answer in under 120 words, paraphrasing, naming the section. Define J. L. Mackie's INUS condition. Does the entry say that an effect typically has several alternative minimal sufficient conditions (a disjunction of conjunctions), so that no one minimal sufficient condition is unique or necessary?\n\n# Mackie's INUS Condition (Section 1.3)\n\nAn INUS condition is an \"insufficient but non-redundant part of an unnecessary but sufficient condition\" for an effect. In Mackie's framework, multiple distinct factor clusters can each suffice to produce the same outcome—none individually necessary.\n\nYes, the entry confirms this explicitly. It states that \"one and the same effect can have _many_ causes understood as sufficient and necessary totalities.\" The entry illustrates how a house fire might result from various sufficient but unnecessary combinations: short-circuit plus oxygen, arson plus petrol, or a burning tree falling on it. Each cluster is minimally sufficient; their disjunction represents the complete causal picture relative to a specific causal field.\n\n## 22. Page: https://plato.stanford.edu/entries/scientific-explanation/\n\n**Asked:** Answer in under 190 words, paraphrasing, naming sections. (a) State the Deductive-Nomological (covering-law) model: what must the explanans contain? (b) Describe the standard counterexamples: explanatory asymmetry (flagpole and shadow), explanatory irrelevance (the hexed salt, or the man taking birth-control pills), and the difficulty of distinguishing laws from accidental generalizations. (c) Does the entry report Scriven's view that singular causal explanations can be given without citing a law (the ink-stain or knocked-over ink example) and the notion that laws play a justifying role rather than being part of the explanation?\n\nI cannot provide the requested information about the Deductive-Nomological model, counterexamples, or Scriven's views on scientific explanation.\n\nThe webpage content you've provided is a **retirement notice** from the Stanford Encyclopedia of Philosophy. It states that the original \"Scientific Explanation\" entry has been retired and replaced with a new version titled **\"20th Century Theories of Scientific Explanation\"** (available at a different URL).\n\nThe page contains only navigational elements and a redirect notice—it does not include the actual philosophical content discussing the covering-law model, flagpole/shadow examples, hexed salt counterexamples, or Scriven's theoretical contributions.\n\nTo answer your questions about these specific philosophical concepts and arguments, you would need to access the actual entry at the redirected URL or consult the related entry on \"Causal Approaches to Scientific Explanation\" mentioned in the notice.\n\n## 23. Page: https://plato.stanford.edu/entries/goodman/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming the section. Explain Goodman's new riddle of induction (the predicate 'grue') and why it shows that the same evidence fits incompatible generalizations. Then explain his proposed answer: projectibility decided by the entrenchment of predicates, i.e. their record of past actual projections.\n\n# Goodman's New Riddle of Induction (Section 5.3-5.4)\n\nGoodman's riddle demonstrates that identical evidence supports incompatible predictions. All emeralds examined before time *t* are green, confirming \"all emeralds are green.\" Yet this same evidence equally confirms \"all emeralds are grue\"—defined as green-if-examined-before-*t*, blue-otherwise. Both hypotheses fit past observations identically but predict opposite colors for future emeralds.\n\nThe puzzle reveals that predicate choice matters for induction; some predicates are lawlike while others aren't. Goodman's solution invokes **projectibility**, determined by predicate **entrenchment**—their historical frequency in successful past projections. \"Green\" has far greater entrenchment than \"grue\" because scientists have repeatedly projected hypotheses using \"green.\" When competing hypotheses match empirically, the one employing better-entrenched predicates overrides alternatives, explaining why we favor green over grue.\n\n## 24. Page: https://plato.stanford.edu/entries/generics/\n\n**Asked:** Answer in under 170 words, paraphrasing, naming sections. (a) Why do generic sentences ('ducks lay eggs', 'mosquitoes carry the West Nile virus', 'ravens are black') resist analysis as 'all' or 'most' statements? (b) What is Leslie's view that generics express a cognitively default mode of generalization? (c) What does the entry say about generics about social kinds, essentialization and prejudice (Leslie, Haslanger, Rhodes)?\n\n# Generic Generalizations: Key Insights\n\n**(a) Why Generics Resist Quantifier Analysis**\n\nGenerics like \"ducks lay eggs\" cannot be reduced to universal or majority statements. As the entry notes, \"ducks lay eggs\" is true despite only female ducks laying eggs, yet \"ducks are female\" is false. Similarly, \"mosquitoes carry West Nile virus\" is accepted though fewer than 1% carry it, while \"humans are right-handed\" is rejected despite over 90% being right-handed. Generics thus operate independently from quantificational determiners.\n\n**(b) Leslie's Default Generalization Hypothesis**\n\nIn section 4.1, the entry explains that Leslie and colleagues propose generics express \"cognitively fundamental, default generalizations\" acquired early in development. Unlike quantified statements requiring cognitive sophistication, generics represent our basic way of conceptualizing kinds—explaining why languages lack dedicated generic operators and why people default to generic interpretations of quantified statements.\n\n**(c) Generics, Essentialism, and Social Prejudice**\n\nSection 5.1 details how generic language about social groups fosters essentialism. Haslanger argues statements like \"women are submissive\" suggest intrinsic group natures rather than social circumstances. Research shows generic language rapidly essentializes novel groups and reinforces harmful stereotypes, while Rhodes demonstrates action-focused language (\"do science\") better engages underrepresented children than identity-focused language (\"be scientists\").\n\n## 25. Page: https://plato.stanford.edu/entries/conditionals/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming sections. State Adams's thesis (or 'the Thesis') connecting the acceptability or probability of an indicative conditional with the conditional probability of the consequent given the antecedent. Then state what Lewis's triviality result shows about whether there can be a proposition whose probability always equals that conditional probability. Also: why can the material conditional 'A ⊃ B' be highly probable while the conditional probability of B given A is low?\n\n# Adams's Thesis and Lewis's Triviality Result\n\n**Adams's Thesis** (§3.1): Your degree of belief that \"if A, B\" should equal your conditional probability of B given A: bp(B if A) = bp_A(B).\n\n**Lewis's Triviality Result** (§3.1): No proposition exists whose probability consistently matches conditional probability across all belief distributions. Conditional probability doesn't measure truth-probability of any single proposition.\n\n**Why Material Conditional Differs** (§3.1, §4.4): The material conditional A ⊃ B can be highly probable when bp_A(B) is low because bp(A ⊃ B) = bp(~A) + bp(A)·bp_A(B). When the antecedent is improbable, ~A contributes significantly to the material conditional's overall probability, independent of the consequent's likelihood given the antecedent's truth.\n\n## 26. Page: https://plato.stanford.edu/entries/moral-particularism/\n\n**Asked:** Answer in under 150 words, paraphrasing, naming sections. Explain (a) Dancy's holism in the theory of reasons: that a feature which is a reason in one case may be no reason, or an opposite reason, in another; (b) his distinction between favourers, enablers (and disablers), and intensifiers (and attenuators), with his promise example if given; (c) what the particularist concludes about whether moral thought needs general principles.\n\n# Moral Particularism: Dancy's Key Contributions\n\n## (a) Holism of Reasons\n\nSection 3 presents Dancy's core doctrine: features functioning as reasons possess \"variable relevance.\" A consideration that constitutes a reason in one case may provide no reason in another, or even count against the action. For instance, a drug-induced appearance of red might normally justify believing something is red, but when one knows the drug reverses colors, that same appearance becomes reason to believe the opposite.\n\n## (b) Reason Types\n\nWhile the article doesn't explicitly name \"enablers\" and \"intensifiers,\" it discusses how \"not made under duress\" functions as an enabling condition rather than itself counting in favor—a feature whose absence prevents the promise-fact from serving as a reason.\n\n## (c) Conclusion About Principles\n\nSection 3 concludes that \"moral thought does not have a distinctive structure.\" The particularist denies that moral rationality depends on principles. Experienced judges develop familiarity with how features contribute differently across contexts, rather than following invariant rules, making principles unnecessary for moral competence.\n\n## 27. Page: https://plato.stanford.edu/entries/legal-reas-prec/\n\n**Asked:** Answer in under 180 words, paraphrasing, naming sections. (a) What is the ratio decidendi of a case, and why is identifying it problematic: can the facts of a case be characterised at different levels of generality, yielding different rules? (b) What is 'distinguishing', and what does it show about whether a precedent lays down a fixed rule? (c) How does the entry describe analogical reasoning from a precedent as different from applying a rule? (d) Does it mention that judges may agree on an outcome while disagreeing about the rationale?\n\n# Legal Reasoning: Precedent and Analogy Analysis\n\n**(a) Ratio Decidendi and Generality Problems**\n\nThe ratio decidendi (section 2) represents \"the proposition of law for which the case is authority.\" Identifying it is problematic because facts can be characterized at varying abstraction levels. The entry illustrates this through a product liability case: was the relevant vehicle of harm a \"beverage,\" \"consumable,\" or \"article for human use\"? Each characterization yields different rules with different scope, making precise identification difficult without additional contextual guidance.\n\n**(b) Distinguishing and Rule-Making**\n\nDistinguishing (section 2.1.2) occurs when later courts avoid following a precedent despite facts falling within its stated ratio, by identifying factual differences. This demonstrates that precedents don't truly establish fixed rules, since lower courts can narrow rulings while preserving the original outcome—a power inconsistent with traditional rule-based approaches.\n\n**(c) Analogical Reasoning vs. Rule Application**\n\nAnalogical reasoning (section 4) differs fundamentally from rule application: analogies provide non-binding, variable-strength arguments grounded in underlying justifications, while rules presumptively settle cases. Analogies must be \"considered along with other reasons,\" whereas rules operate categorically.\n\n**(d) Disagreement on Rationale**\n\nThe entry doesn't explicitly address whether judges may agree on outcomes while disagreeing about rationales.\n\n## 28. Page: https://plato.stanford.edu/entries/lakatos/\n\n**Asked:** Answer in under 160 words, paraphrasing, naming sections. Summarise Lakatos's 'Proofs and Refutations': (a) the difference between local counterexamples (to a lemma) and global counterexamples (to the conjecture); (b) 'hidden lemmas' and the method of lemma-incorporation, where a counterexample exposes an unstated assumption that is then built into the theorem as a condition; (c) monster-barring and exception-barring as inferior responses.\n\n# Lakatos's \"Proofs and Refutations\": Counterexamples and Mathematical Growth\n\n**Section 3.1** explains Lakatos's framework for mathematical development through counterexample analysis.\n\n**(a) Local vs. Global Counterexamples:**\nGlobal counterexamples refute a conclusion without refuting premises, revealing hidden logical gaps. Local counterexamples refute specific premises while leaving conclusions intact. Together they expose unstated assumptions requiring incorporation.\n\n**(b) Hidden Lemmas and Lemma-Incorporation:**\nWhen counterexamples strike, mathematicians unearth \"hidden lemmas\"—tacit premises the original proof presupposed. Rather than abandoning work, they integrate these into refined theorems as explicit conditions. This generates what Lakatos terms \"proof-generated definitions.\"\n\n**(c) Monster-Barring vs. Lemma-Incorporation:**\nMonster-barring excludes problematic cases through definitional stipulation (dismissing picture-frames as \"non-normal\" polyhedra). This inferior method merely restricts content. Lemma-incorporation proves superior by discovering deeper relationships governing all cases, advancing genuine mathematical understanding through systematic concept-refinement.\n\n## 29. Page: https://plato.stanford.edu/entries/collingwood/\n\n**Asked:** Answer in under 140 words, paraphrasing, naming sections. Summarise Collingwood's 'logic of question and answer' (a statement's meaning and truth are relative to the question it answers) and his distinction between relative and absolute presuppositions. Are absolute presuppositions true or false, and can they be verified?\n\n# Collingwood's Logic of Question and Answer\n\n## Question-Answer Logic (Section 2.2)\n\nCollingwood argues that meaning depends on context within the \"logic of question and answer.\" A statement functions either as a proposition (answering questions with truth-values) or as a presupposition (generating questions without truth-values). The same statement can shift roles depending on its function in logical discourse.\n\n## Presupposition Types (Section 2.2)\n\n**Relative presuppositions** are provisional assumptions that future research might overthrow—like a doctor's assumption that aspirin treats fever.\n\n**Absolute presuppositions** are foundational assumptions enabling inquiry itself, such as the uniformity of nature for empirical science or \"causes as manipulable\" for medicine.\n\n## Truth and Verification (Section 2.2)\n\nCollingwood denies absolute presuppositions have truth-values. As he states, \"logical efficacy\" depends not on being true or false but on enabling questioning. Verification demands are \"nonsense questions\" because presuppositions function through being presupposed, not through correspondence to reality.\n\n## 30. Page: https://plato.stanford.edu/entries/gadamer/\n\n**Asked:** Answer in under 140 words, paraphrasing, naming sections. Summarise (a) Gadamer's rehabilitation of prejudice (fore-judgment, Vorurteil) as a condition of understanding; (b) the role of question and answer in understanding a text; (c) the fusion of horizons. Does the entry say understanding can never make all its presuppositions explicit?\n\n# Gadamer's Key Concepts\n\n**(a) Rehabilitation of Prejudice**\nSection 3.1 describes how Gadamer reframes prejudgment (Vorurteil) positively. Rather than blocking understanding, our pre-judgments actually enable it by opening us to what requires interpretation. These anticipatory structures allow preliminary grasping of meaning, and can themselves be revised through dialogue.\n\n**(b) Question and Answer**\nThe entry emphasizes dialogue's centrality, drawing from Platonic dialectic. Understanding prioritizes questioning: our prejudices become evident through questioning in dialogue, allowing problematic assumptions to surface and be examined.\n\n**(c) Fusion of Horizons**\nSection 3.2 explains how understanding involves negotiating between oneself and interpretive partners, establishing shared frameworks. This \"fusion\" integrates the unfamiliar with the familiar, creating new meaning contexts.\n\n**Explicit Presuppositions**\nYes—section 3.2 explicitly states that hermeneutic situations \"can never be made completely transparent to us\" because our historical tradition constitutively shapes understanding itself.\n\n## 31. Page: https://plato.stanford.edu/entries/habermas/\n\n**Asked:** Answer in under 140 words, paraphrasing, naming sections. (a) What does the entry say about validity claims (truth, rightness, sincerity) raised in speech acts, and about discourse as the redemption of a claim once it is challenged? (b) What does it say about the lifeworld as a background of shared, unproblematic assumptions, and whether that background can be made explicit all at once or only piecemeal?\n\n# Habermas on Validity Claims and the Lifeworld\n\n**(a) Validity Claims and Discourse**\n\nIn \"Habermas's Pragmatic Theory of Meaning\" (§2.1), the entry explains that every speech act simultaneously raises three equiprimordial validity claims: to truth, rightness, and sincerity. When a hearer challenges one of these claims, speakers must shift from action to discourse—a \"reflective form of agreement-oriented action\" (§3.1). Discourse functions as the mechanism for \"redeeming\" contested validity claims through argumentation governed by specific rules ensuring \"the unforced force of the better argument.\"\n\n**(b) The Lifeworld as Background**\n\nUnder \"Lifeworld\" (§2.3.1), Habermas characterizes it as \"a background stock of cultural knowledge that is 'always already' familiar to agents,\" enabling mutual understanding. Critically, this background possesses a \"peculiar half transcendence\"—it resists complete objectification. Agents can only problematize portions piecemeal; the entire lifeworld cannot be made fully explicit simultaneously.\n\n## 32. Search: Stanford Encyclopedia \"20th Century Theories of Scientific Explanation\" deductive-nomological flagpole hexed salt Scriven ink\n\nWeb search results for query: \"Stanford Encyclopedia \"20th Century Theories of Scientific Explanation\" deductive-nomological flagpole hexed salt Scriven ink\"\n\nLinks: [{\"title\":\"20th Century Theories of Scientific Explanation (Stanford Encyclopedia of Philosophy)\",\"url\":\"https://plato.stanford.edu/entries/scientific-explanation-20th/\"},{\"title\":\"20th Century Theories of Scientific Explanation (Stanford Encyclopedia of Philosophy)\",\"url\":\"https://seop.illc.uva.nl/entries/scientific-explanation-20th/\"},{\"title\":\"Causal Approaches to Scientific Explanation (Stanford Encyclopedia of Philosophy)\",\"url\":\"https://plato.stanford.edu/entries/causal-explanation-science/\"},{\"title\":\"20th Century Theories of Scientific Explanation > Notes (Stanford Encyclopedia of Philosophy)\",\"url\":\"https://plato.stanford.edu/entries/scientific-explanation-20th/notes.html\"},{\"title\":\"Deductive-nomological model\",\"url\":\"https://en.wikipedia.org/wiki/Deductive-nomological_model\"},{\"title\":\"Explanation\",\"url\":\"https://en.wikipedia.org/wiki/Explanation\"},{\"title\":\"From Observation to Insight: Mechanistic World Models and the Quest for Autonomous Discovery\",\"url\":\"https://arxiv.org/pdf/2607.12474\"},{\"title\":\"Explanations from contemporary quantum theories: some ontological characteristics\",\"url\":\"https://arxiv.org/pdf/1103.0879\"},{\"title\":\"Scientific Explanation and Natural Language: A Unified Epistemological-Linguistic Perspective for Explainable AI\",\"url\":\"https://arxiv.org/pdf/2205.01809\"}]\n\nGreat! The search found relevant results from the Stanford Encyclopedia of Philosophy on \"20th Century Theories of Scientific Explanation\" that include several of the examples and concepts you mentioned:\n\nThe discussion begins with Michael Scriven (1962) advancing a singular causal explanation involving an inkwell as a counterexample to the deductive-nomological (DN) model.\n\nThe article discusses hexed salt in the context of the Causal Mechanical Model, examining whether both birth control pills and hexed salt constitute causal processes.\n\nThe flagpole-and-shadow example illustrates a classic criticism of the DN account, where given the angle of the sun, the height of a flagpole and the length of its shadow can each be logically deduced from the other, yet only the former explains the latter.\n\nThe search results confirm that these examples and discussions are indeed found in the Stanford Encyclopedia's article on 20th century theories of scientific explanation, demonstrating how counterexamples like the inkwell, flagpole-shadow, and hexed salt are used to critique and refine theories of scientific explanation.\n\n## 33. Search: Peirce 1878 \"Deduction, Induction, and Hypothesis\" beans \"Rule\" \"Case\" \"Result\" \"These beans are from this bag\" text\n\nWeb search results for query: \"Peirce 1878 \"Deduction, Induction, and Hypothesis\" beans \"Rule\" \"Case\" \"Result\" \"These beans are from this bag\" text\"\n\nLinks: [{\"title\":\"Abduction or the logic of surprise* JAIME NUBIOLA\",\"url\":\"https://www.unav.es/users/AbductionLogicSurprise.pdf\"},{\"title\":\"Peirce, Charles S. (1878). Deduction, Induction, and Hypothesis\",\"url\":\"http://www.commens.org/bibliography/journal_article/peirce-charles-s-1878-deduction-induction-and-hypothesis\"},{\"title\":\"JCCC Honors Journal Volume 10 Issue 1 Fall 2018 Article 2\",\"url\":\"https://files01.core.ac.uk/download/pdf/303928168.pdf\"},{\"title\":\"AN EXPLORER UPON UNTRODDEN GROUND: PEIRCE ON ABDUCTION Stathis Psillos\",\"url\":\"http://users.uoa.gr/~psillos/PapersI/11-Peirce-Abduction.pdf\"},{\"title\":\"Untitled Document\",\"url\":\"https://www.pucsp.br/~lbraga/epap_peir1.htm\"},{\"title\":\"(PDF) Peirce’s Abduction\",\"url\":\"https://www.researchgate.net/publication/375914374_Peirce's_Abduction\"},{\"title\":\"Popular Science Monthly/Volume 13/August 1878/Illustrations of the Logic of Science VI - Wikisource, the free online library\",\"url\":\"https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_13/August_1878/Illustrations_of_the_Logic_of_Science_VI\"},{\"title\":\"Probabilistic Abduction - AMISTAD Lab\",\"url\":\"https://www.cs.hmc.edu/~montanez/projects/probabilistic-abduction.html\"},{\"title\":\"Assessing LLMs' mathematical abilities requires understanding the various mechanisms of mathematical creativity\",\"url\":\"https://arxiv.org/pdf/2608.16118\"}]\n\nThe web search has successfully retrieved results containing the text and examples you were looking for from Peirce's 1878 paper \"Deduction, Induction, and Hypothesis.\"\n\nHere are some key findings:\n\nIn 1878, in the series Illustrations of the Logic of Science, Peirce published in Popular Science Monthly his paper 'Deduction, Induction and Hypothesis,' which contains a classic exposition of the three modes of inference.\n\nThe search results include Peirce's famous bean example with the Rule, Case, and Result structure:\n\n**Deduction:**\nRule.—All the beans from this bag are white. Case.—These beans are from this bag. Result.—These beans are white.\n\n**Induction:**\nCase.—These beans are from this bag. Result.—These beans are white. Rule.—All the beans from this bag are white.\n\n**Hypothesis:**\nRule.—All the beans from this bag are white. Result.—These beans are white.\n\nThe search results also include the original Wikisource text from the Popular Science Monthly (Volume 13, August 1878), which appears to be the most direct source of the original publication.\n\n## 34. Search: Kant \"peculiar talent which can be practised only, and cannot be taught\" judgment rules for applying rules regress A133 B172\n\nWeb search results for query: \"Kant \"peculiar talent which can be practised only, and cannot be taught\" judgment rules for applying rules regress A133 B172\"\n\nLinks: [{\"title\":\"1 Preparing the Particular: Kant on the Imagination’s Role in Judgment\",\"url\":\"https://philarchive.org/archive/DUNPTP-2\"},{\"title\":\"KANT ON MORAL FEELING AND PRACTICAL JUDGMENT NICHOLAS DUNN Introduction\",\"url\":\"https://philarchive.org/archive/DUNKOM\"},{\"title\":\"Reflective Judgment, Determinative Judgment, and the ...\",\"url\":\"https://openscholarship.wustl.edu/cgi/viewcontent.cgi?article=1078&context=law_jurisprudence\"},{\"title\":\"1 Reflections of Reason: Kant on Practical Judgement ...\",\"url\":\"https://philarchive.org/archive/DUNROR-2\"},{\"title\":\"THE SEMIOTICS OF THE SCHEMA1\",\"url\":\"https://www.luisradford.ca/pub/65_kantpiaget2.pdf\"},{\"title\":\"© Copyright 2007 by Social Theory and Practice, Vol. 33, No. 3 (July 2007) 1\",\"url\":\"https://philarchive.org/archive/DECACF\"},{\"title\":\"What is orientation in judgment?: an essay on Kant’s theory of Urteilskraft\",\"url\":\"https://philarchive.org/archive/DUNWIO\"},{\"title\":\"KANT’S THEORY OF TASTE A Reading of the Critique of Aesthetic Judgment\",\"url\":\"https://catdir.loc.gov/catdir/samples/cam031/00034261.pdf\"},{\"title\":\"What is Orientation in Judgment?: an Essay on Kant’s theory of Urteilskraft\",\"url\":\"https://static1.squarespace.com/static/5b2ff87012b13f027dd9863a/t/5cab67d0eb39311ed751cd89/1554737107255/Preface.pdf\"}]\n\nI've found relevant search results about Kant's discussion of judgment at A133/B172. Here's what the sources reveal:\n\nKant defines the power of judgment 'in general' as 'the faculty of subsuming under rules, i.e., of determining whether something stands under a given rule or not' at A133/B172.\n\nThe key issue Kant addresses involves a regress problem: the task of distinguishing whether something stands under a certain rule or not cannot be governed by a rule, on pain of regress: this rule would require another rule ad infinitum. Something must stop the regress to secure the possibility of making judgements whatsoever.\n\nKant's solution to this regress is remarkable. He calls judgment 'a special talent that cannot be taught but only practiced.' More specifically, \"can be practised only, and cannot be taught.\" A 'sharpened' power of judgment is a skill that can only be acquired through experience.\n\nThe philosophical significance is that judgment provides a straightforward way of understanding Kant's solution to the regress problem generated by discursive rules: it can only be stopped by non-discursive means. In other words, judgment does not follow rules but creates them in the very act of judging itself.\n\n## 35. Search: Brandom \"Articulating Reasons\" material inference enthymeme \"formalist\" suppressed premise conditional \"making explicit\" inferential commitment\n\nWeb search results for query: \"Brandom \"Articulating Reasons\" material inference enthymeme \"formalist\" suppressed premise conditional \"making explicit\" inferential commitment\"\n\nLinks: [{\"title\":\"Mimetic Rationality and Material Inference : Adorno and Brandom\",\"url\":\"https://www.cairn.info/revue-internationale-de-philosophie-2004-1-page-7.htm\"},{\"title\":\"Brandom’s inferentialist Theory and the Meaning Entitlement Connection\",\"url\":\"https://philarchive.org/archive/MARBIT-2v6\"},{\"title\":\"An Exploration of Robert Brandom's Articulating Reasons\",\"url\":\"https://www.janbransen.nl/wp-content/uploads/2021/04/Normativity-as-the-Key-to-Objectivity-An-Exploration-of-Robert-Brandom-s-Articulating-Reasons.pdf\"},{\"title\":\"1 Brandom’s inferentialist Theory and the Meaning Entitlement Connection\",\"url\":\"https://philarchive.org/archive/MARBIT-2v5\"},{\"title\":\"Jh\",\"url\":\"https://pages.jh.edu/rrynasi1/HealeySeminar/literature/Brandom2000ArticulatingReasons.pdf\"},{\"title\":\"Articulating Reasons\",\"url\":\"https://sites.pitt.edu/~rbrandom/Courses/2022%20Phil%20of%20Language/Reasons%20texts/Brandom_-_Articulating_Reasons.pdf\"},{\"title\":\"No knowledge but discursive: Brandom on meaning, inference and normativity\",\"url\":\"https://link.springer.com/article/10.1007/s11229-025-05266-2\"},{\"title\":\"Reasons: Three Essays on their Logic, Pragmatics, and Semantics Robert Brandom\",\"url\":\"https://sites.pitt.edu/~rbrandom/Texts/Reason%20TELPA%2021-8-26%20g.pdf\"},{\"title\":\"Material inference\",\"url\":\"https://en.wikipedia.org/wiki/Material_inference\"}]\n\nBased on the search results, here are the key findings regarding Brandom's treatment of material inference, enthymemes, and the formalist position in *Articulating Reasons*:\n\n## Material Inference vs. Enthymematic Analysis\n\nMaterial inferences like \"It is raining, therefore the streets will be wet\" are not formally valid yet appear plausible, leading formalists to treat them as enthymemes with a suppressed premise that can be reconstructed as a conditional detachment. However, for Brandom's broad inferentialism, a material inference doesn't involve any implicit suppressed premise.\n\n## Formalist Arguments and Brandom's Response\n\nFormalist approaches to logic treat \"good inference\" as \"formally valid inference,\" but inferences of the form \"A, therefore B\" are incomprehensible or invalid from this perspective, prompting logicians to treat them as enthymemes in which a missing premise is available and presupposed.\n\n## Making Explicit vs. Material Validity\n\nMaterial inferences are valid not because of their logical form, but because of their contents. Brandom's view is that the possibility of supplementing material inferences with an enthymematic premise does not indicate the priority of formal over material inference since it leaves the question of formalism unexplained.\n\n## Inferential Commitments\n\nAccording to Brandom's conceptual role semantics, grasping a concept involves a commitment to drawing certain inferences, which is a consequence of the inferentialist thesis that meaning is given by justification through assertibility conditions, with inferential commitments stemming from a material notion of inference.\n\n## 36. Search: Sunstein \"incompletely theorized agreements\" agree on outcome without agreeing on the general theory or reasons Harvard Law Review 1995\n\nWeb search results for query: \"Sunstein \"incompletely theorized agreements\" agree on outcome without agreeing on the general theory or reasons Harvard Law Review 1995\"\n\nLinks: [{\"title\":\"Incompletely Theorized Agreements by Cass R. Sunstein :: SSRN\",\"url\":\"https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2995488\"},{\"title\":\"Articles & Essays by Cass R. Sunstein\",\"url\":\"https://home.uchicago.edu/~csunstei/articles-essays.html\"},{\"title\":\"Incompletely Theorized Agreements - Harvard Law School\",\"url\":\"https://hls.harvard.edu/bibliography/incompletely-theorized-agreements/\"},{\"title\":\"1 Incomplete Ideal Theory1 Amy Berg\",\"url\":\"https://philarchive.org/archive/BERIIT\"},{\"title\":\"University of Chicago Law School University of Chicago Law School\",\"url\":\"https://chicagounbound.uchicago.edu/cgi/viewcontent.cgi?article=12308&amp=&context=journal_articles\"},{\"title\":\"226 HARVARD LAW REVIEW [Vol. 126:176\",\"url\":\"https://harvardlawreview.org/wp-content/uploads/2012/11/vol126_united_states_v_jones.pdf\"},{\"title\":\"Bridging the gap: the case for an ‘Incompletely Theorized Agreement’ on AI policy\",\"url\":\"https://link.springer.com/article/10.1007/s43681-020-00037-w\"},{\"title\":\"Incompletely Theorized Agreements in Constitutional Law\",\"url\":\"https://chicagounbound.uchicago.edu/cgi/viewcontent.cgi?article=1149&context=public_law_and_legal_theory\"},{\"title\":\"Legal Theory Lexicon 037: Overlapping Consensus & Incompletely Theorized Agreements\",\"url\":\"https://legaltheorylexicon.com/2004/05/legal_theory_le_1-8/\"},{\"title\":\"Articles & Essays by Cass R. Sunstein:\",\"url\":\"https://home.uchicago.edu/%7Ecsunstei/articles-essays.html\"}]\n\nBased on the search results, I found the article you're looking for. Cass R. Sunstein's \"Incompletely Theorized Agreements\" was published in Harvard Law Review, Vol. 108, No. 7, p. 1733 in 1995.\n\nThe concept describes a legal strategy where participants in legal controversies try to produce incompletely theorized agreements on particular outcomes by agreeing on the result and on relatively narrow or low-level explanations for it, without needing to agree on fundamental principle. More specifically, they do not offer larger or more abstract explanations than are necessary to decide the case, and when they disagree on an abstraction, they move to a level of greater particularity.\n\nThe distinctive feature of this account is that it emphasizes agreement on (relative) particulars rather than on (relative) abstractions, which is an important source of social stability and an important way for diverse people to demonstrate mutual respect in law and liberal democracy.\n\n## 37. Search: Toulmin \"The Tyranny of Principles\" National Commission for the Protection of Human Subjects agreed on cases disagreed on principles reasons\n\nWeb search results for query: \"Toulmin \"The Tyranny of Principles\" National Commission for the Protection of Human Subjects agreed on cases disagreed on principles reasons\"\n\nLinks: [{\"title\":\"Jonsen Et Toulmin, The Abuse of Casuistry\",\"url\":\"https://www.scribd.com/document/728139093/Jonsen-Et-Toulmin-The-Abuse-of-Casuistry\"},{\"title\":\"The Value of Consensus\",\"url\":\"https://nap.nationalacademies.org/read/4771/chapter/14\"},{\"title\":\"A Critical Extension of Toulman's Tyranny of Principles by R.J. Lambert on Prezi\",\"url\":\"https://prezi.com/dxrt-dlxdztr/a-critical-extension-of-toulmans-tyranny-of-principles/\"},{\"title\":\"PATF: Toulmin, Stephen - The Tyranny of Principles\",\"url\":\"http://ofd-patf.blogspot.com/2010/06/toulmin-stephen-tyranny-of-principles.html\"},{\"title\":\"The tyranny of principles.\",\"url\":\"https://www.semanticscholar.org/paper/The-tyranny-of-principles.-Toulmin/bef701dcbb99c248f5583056bc77c02447112080\"},{\"title\":\"Toulmin and the Turn to Tolstoy\",\"url\":\"https://lawliberty.org/toulmin-and-the-turn-to-tolstoy/\"},{\"title\":\"(PDF) Lecture 9: The Work of Stephen Toulmin\",\"url\":\"https://www.researchgate.net/publication/356866740_Lecture_9_The_Work_of_Stephen_Toulmin\"},{\"title\":\"Stephen Toulmin, The Tyranny of Principle - PDF Free Download\",\"url\":\"https://idoc.tips/stephen-toulmin-the-tyranny-of-principle-pdf-free.html\"},{\"title\":\"Doc MWI 23 Belmont%20Report\",\"url\":\"https://clinregs.niaid.nih.gov/sites/default/files/documents/malawi/Doc_MWI-23_Belmont%20Report.pdf\"}]\n\nBased on the search results, here's what I found about Toulmin's \"The Tyranny of Principles\" and the National Commission for the Protection of Human Subjects:\n\n## The Commission's Experience\n\nToulmin collaborated in the work of the National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research from 1975 to 1978, which was set up by the United States Congress in 1974.\n\n## Agreement on Cases, Disagreement on Principles\n\nAlthough commissioners were usually in agreement about their recommendations—\"even about quite detailed recommendations\"—the consensus did not extend to the arguments or principles supporting these recommendations, with Toulmin noting: \"They could agree; they could agree what they were agreeing about; but, apparently, they could not agree why they agreed about it.\"\n\n## The Reasons for This Phenomenon\n\nToulmin took part in the US Congress task force for determining the ethical treatment of human test subjects in medical research, along with scientists and other moral leaders, and was struck with how much agreement they could reach, yet when asked about the principles that underwrote their conclusions, each member gave different reasons.\n\nThis observation became central to Toulmin's critique of the revival of a tyrannical absolutism in recent discussions about social and personal ethics.\n\n## 38. Search: Walton Krabbe \"Commitment in Dialogue\" \"dark-side commitments\" veiled implicit commitments brought to light maieutic\n\nWeb search results for query: \"Walton Krabbe \"Commitment in Dialogue\" \"dark-side commitments\" veiled implicit commitments brought to light maieutic\"\n\nLinks: [{\"title\":\"93 Dialogue and Interpersonal Communication:\",\"url\":\"https://dialnet.unirioja.es/descarga/articulo/3963420.pdf\"},{\"title\":\"(PDF) Commitment, Types of Dialogue, and Fallacies\",\"url\":\"https://www.researchgate.net/publication/237542685_Commitment_Types_of_Dialogue_and_Fallacies\"},{\"title\":\"Douglas Walton, Commitment, Types of Dialogue, and Fallacies - PhilPapers\",\"url\":\"https://philpapers.org/rec/WALCTO-2\"},{\"title\":\"(PDF) Dialectical Relevance and Dialogical Context in Walton’s Pragmatic Theory\",\"url\":\"https://www.researchgate.net/publication/228176081_Dialectical_Relevance_and_Dialogical_Context_in_Walton's_Pragmatic_Theory\"},{\"title\":\"Commitment, Types of Dialogue, and Fallacies\",\"url\":\"http://ojs.uwindsor.ca/ojs/leddy/index.php/informal_logic/article/view/2532\"},{\"title\":\"Commitment, Types of Dialogue and Fallacies\",\"url\":\"https://www.academia.edu/14227219/Commitment_Types_of_Dialogue_and_Fallacies\"},{\"title\":\"Commitment in Dialogue\",\"url\":\"https://www.sunypress.edu/p-2174-commitment-in-dialogue.aspx\"},{\"title\":\"INFORMAL LOGIC XIY.2&3, Spring & Fall 1993\",\"url\":\"https://informallogic.ca/index.php/informal_logic/article/download/2532/1973\"},{\"title\":\"The Place of Emotion in Argument 0271008334, 0271008539 - DOKUMEN.PUB\",\"url\":\"https://dokumen.pub/the-place-of-emotion-in-argument-0271008334-0271008539.html\"}]\n\nI found relevant information about Walton and Krabbe's work on commitment in dialogue. Here are the key findings:\n\n## Commitment in Dialogue\n\nDouglas Walton and Erik C. W. Krabbe published \"Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning\" in 1995 with State University of New York Press.\n\n## Dark-Side Commitments\n\nWalton and Krabbe divided commitment sets into two subsets: a light side of overt, expressed, explicit commitments, and a dark side of commitments that are only partially apparent or plausibly surmised by one or more of the participants in the dialogue.\n\nThe dark side set is said to be \"dark,\" meaning that it is not known to be one participant's commitment by the other participant (or even, in some cases, by the holder himself).\n\n## Veiled and Implicit Commitments\n\nIn much everyday argumentation, commitments are often veiled, or only partly apparent to all the participants in a discussion. These are described as \"veiled\" or \"deeper\" commitments that the arguer is only aware of as \"gut feelings.\"\n\n## Maieutic Function\n\nA dialogue has a maieutic function in that it can reveal fallacies and hidden commitments in one's argument. The dark-side commitments are expressed as explicit commitments and defended and sharpened in the fires of argument.\n\n## 39. Search: Stoic \"unmethodically concluding\" arguments amethodos perainontes Alexander of Aphrodisias added universal premise equal to the same\n\nWeb search results for query: \"Stoic \"unmethodically concluding\" arguments amethodos perainontes Alexander of Aphrodisias added universal premise equal to the same\"\n\nLinks: [{\"title\":\"(PDF) Alexander of Aphrodisias on Aristotle's Theory of the Stoic Indemonstrables\",\"url\":\"https://www.researchgate.net/publication/278729133_Alexander_of_Aphrodisias_on_Aristotle's_Theory_of_the_Stoic_Indemonstrables\"},{\"title\":\"Alexander of Aphrodisias - On Aristotle Topics 1\",\"url\":\"https://www.scribd.com/document/702339787/Alexander-of-Aphrodisias-on-Aristotle-topics-1\"},{\"title\":\"Cambridge Companions Online © Cambridge University Press, 2006 susanne bobzien\",\"url\":\"https://philarchive.org/archive/BOBSL\"},{\"title\":\"Alexander of Aphrodisias’ Lazy Arguments against Stoic Determinism\",\"url\":\"https://ojs.utlib.ee/index.php/spe/article/download/22849/17337/31930\"},{\"title\":\"Alexander of Aphrodisias' Lazy Arguments against Stoic Determinism\",\"url\":\"https://www.researchgate.net/publication/395079913_Alexander_of_Aphrodisias'_Lazy_Arguments_against_Stoic_Determinism\"},{\"title\":\"Alexander of Aphrodisias on Aristotle's theory of the Stoic ...\",\"url\":\"https://philarchive.org/archive/BOBAOA\"},{\"title\":\"Susanne Bobzien, Alexander of Aphrodisias on Aristotle's Theory of the Stoic Indemonstrables - PhilArchive\",\"url\":\"https://philarchive.org/rec/BOBAOA\"},{\"title\":\"Alexander of Aphrodisias and the problem of instrumentality’ of logic. Notes on in A. Pr. 2, 22-33\",\"url\":\"https://revistas.udea.edu.co/index.php/estudios_de_filosofia/article/view/11623?articlesBySimilarityPage=39\"},{\"title\":\"Alexander of Aphrodisias: On Aristotle Topics 2 (Ancient Commentators on Aristotle) 2020018997, 2020018998, 9781350151284, 9781350151291, 9781350151307, 9781350195028, 1350151289 - DOKUMEN.PUB\",\"url\":\"https://dokumen.pub/alexander-of-aphrodisias-on-aristotle-topics-2-ancient-commentators-on-aristotle-2020018997-2020018998-9781350151284-9781350151291-9781350151307-9781350195028-1350151289.html\"}]\n\nI found relevant information about your query. Based on the search results:\n\nThe Stoics distinguished arguments named 'unmethodically concluding' (amethodōs perainontes), which were a type of valid argument but not formal syllogisms. \n\nThe arguments that the Stoics say 'conclude unmethodically' work such that if A equals B and similarly C equals B, it has not thereby been syllogistically proved that A equals C since the necessity of this is not 'through the suppositions': the conclusion only follows from the suppositions on the strength of the truth of the universal that Things equal to the same thing are also equal to one.\n\nThis illustrates a key aspect of Alexander of Aphrodisias's analysis: he recognized that while such arguments reach valid conclusions, they require an added universal premise (like \"things equal to the same thing are also equal to one another\") to make the logical connection explicit, which is why they don't count as formal syllogisms without this additional universal principle.\n\nThese aren't syllogisms - they are neither indemonstrables nor can they be reduced to one, since they contain no non-simple assertible as component.\n\n## 40. Search: de Bruijn factor formalization ratio informal proof length \"about four\" Wiedijk\n\nWeb search results for query: \"de Bruijn factor formalization ratio informal proof length \"about four\" Wiedijk\"\n\nLinks: [{\"title\":\"Formal proof\",\"url\":\"https://www.cs.ru.nl/~freek/pubs/notices.pdf\"},{\"title\":\"The De Bruijn Factor\",\"url\":\"https://www.researchgate.net/publication/2384941_The_De_Bruijn_Factor\"},{\"title\":\"Formalising Ordinal Partition Relations Using Isabelle/HOL\",\"url\":\"https://arxiv.org/pdf/2011.13218\"},{\"title\":\"Irrationality and Transcendence Criteria for Infinite Series ...\",\"url\":\"https://arxiv.org/pdf/2101.05257\"},{\"title\":\"The De Bruijn Factor Freek Wiedijk\",\"url\":\"https://www.cs.ru.nl/~freek/factor/factor.pdf\"},{\"title\":\"[PDF] Formal proof -- getting started\",\"url\":\"https://www.semanticscholar.org/paper/Formal-proof-getting-started-Wiedijk/472ee7cc568c6e8e0124d9f84db206745b43f6ec\"},{\"title\":\"Univalent Foundations and the UniMath Library\",\"url\":\"https://arxiv.org/pdf/1710.02723\"},{\"title\":\"De Bruijn factor\",\"url\":\"https://en.wikipedia.org/wiki/De_Bruijn_factor\"},{\"title\":\"A Formalisation of a Special Case of the Union-Closed Conjecture in Isabelle/HOL\",\"url\":\"https://arxiv.org/pdf/2609.20876\"}]\n\nHere are the search results for your query about the de Bruijn factor, formalization ratio, and Wiedijk's work:\n\n## Key Findings:\n\nUsing current technology, a formalization will be roughly four times the size of a corresponding informal LaTeX proof (this ratio is called the de Bruijn factor).\n\nFor three specific examples this factor turns out to be approximately equal to four, according to Wiedijk's research.\n\n**Definition and Purpose:**\nThe de Bruijn factor is defined as the ratio of the size of the formal mathematics to the size of the corresponding mathematical exposition. It can be regarded as measuring the cost of formalization.\n\n**Origins:**\nIt was created by the Dutch computer-proof pioneer Nicolaas Govert de Bruijn, and Freek Wiedijk refined the definition to use the compressed size of the formal proof over the compressed size of the informal proof. He called this the \"intrinsic de Bruijn Factor\".\n\n**Measurement Variations:**\nWiedijk and others report de Bruijn factors in the range of 3-6, though this can vary significantly depending on the type of mathematics and level of detail involved.\n\n## 41. Search: Shogenji \"A condition for transitivity in probabilistic support\" screening off confirmation not transitive\n\nWeb search results for query: \"Shogenji \"A condition for transitivity in probabilistic support\" screening off confirmation not transitive\"\n\nLinks: [{\"title\":\"[PDF] A weaker condition for transitivity in probabilistic support\",\"url\":\"https://www.semanticscholar.org/paper/A-weaker-condition-for-transitivity-in-support-Roche/d9227cfe0e3015ed1859f14831b923db6644ff69\"},{\"title\":\"Confirmation, Transitivity, and Moore: The Screening-Off Approach\",\"url\":\"https://philarchive.org/archive/ROCCTA-3\"},{\"title\":\"(PDF) A condition for transitivity in high probability\",\"url\":\"https://www.researchgate.net/publication/314119852_A_condition_for_transitivity_in_high_probability\"},{\"title\":\"Hesse’s Condition for Transitivity of Probabilistic Support: A Friendly Reminder\",\"url\":\"https://link.springer.com/article/10.1007/s10670-023-00724-0\"},{\"title\":\"(PDF) Confirmation, transitivity, and Moore: The Screening-Off Approach\",\"url\":\"https://www.researchgate.net/publication/257637223_Confirmation_transitivity_and_Moore_The_Screening-Off_Approach\"},{\"title\":\"A New Condition for Transitivity of Probabilistic Support\",\"url\":\"https://link.springer.com/article/10.1007/s10670-020-00349-7\"},{\"title\":\"Tomoji Shogenji, Mediated Confirmation - PhilPapers\",\"url\":\"https://philpapers.org/rec/SHOMC-3\"},{\"title\":\"Bayesian Confirmation and Justifications\",\"url\":\"https://www.researchgate.net/publication/335596802_Bayesian_Confirmation_and_Justifications\"},{\"title\":\"s11229 021 03165 w\",\"url\":\"https://link.springer.com/article/10.1007/s11229-021-03165-w\"}]\n\nBased on the search results, here's what I found regarding Shogenji's work on transitivity in probabilistic support:\n\nIt is well known that the probabilistic relation of confirmation is not transitive in that even if E confirms H1 and H1 confirms H2, E may not confirm H2.\n\nShogenji showed that screening off is a sufficient constraint for the transitivity of probabilistic support. More specifically, probabilistic support is transitive provided the intermediary proposition screens off the original evidence with respect to the hypothesis in question.\n\nThe probabilistic support relation is known to violate transitivity, but philosophers have identified various conditions under which it does not, most notably screening-off and weak screening-off.\n\nThe search results reference Shogenji's seminal 2003 paper titled \"A Condition for Transitivity in Probabilistic Support\" published in the British Journal for the Philosophy of Science, which established that the screening-off condition is sufficient to restore transitivity in probabilistic support relations. Subsequent work by Roche and others has explored weaker versions of this screening-off condition while still maintaining transitivity.\n\n## 42. Search: Besnard Hunter logic-based argumentation \"an argument is a pair\" minimal consistent subset entails claim definition\n\nWeb search results for query: \"Besnard Hunter logic-based argumentation \"an argument is a pair\" minimal consistent subset entails claim definition\"\n\nLinks: [{\"title\":\"1 A Review of Argumentation Based on Deductive Arguments\",\"url\":\"http://www0.cs.ucl.ac.uk/staff/a.hunter/papers/hofachapter.pdf\"},{\"title\":\"A Logic-Based Theory of Deductive Arguments\",\"url\":\"https://www.researchgate.net/publication/222543439_A_Logic-Based_Theory_of_Deductive_Arguments\"},{\"title\":\"(PDF) Base Logics in Argumentation.\",\"url\":\"https://www.researchgate.net/publication/221651006_Base_Logics_in_Argumentation\"},{\"title\":\"A logic-based theory of deductive arguments\",\"url\":\"https://www2.fiit.stuba.sk/~kvasnicka/CognitiveScience/8.prednaska/BesnardHunter_AI.pdf\"},{\"title\":\"(PDF) Practical First-Order Argumentation.\",\"url\":\"https://www.researchgate.net/publication/221603790_Practical_First-Order_Argumentation\"},{\"title\":\"Using Enthymemes to Fill the Gap between Logical Argumentation and Revision of Abstract Argumentation Frameworks\",\"url\":\"https://arxiv.org/pdf/1603.08789\"},{\"title\":\"Algorithms for Effective Argumentation in Classical Propositional Logic: A Connection Graph Approach\",\"url\":\"https://link.springer.com/chapter/10.1007/978-3-540-77684-0_19\"},{\"title\":\"Identifying the Class of Maxi-Consistent Operators in Argumentation\",\"url\":\"https://arxiv.org/pdf/1402.0573\"},{\"title\":\"Dialectical Reconciliation via Structured Argumentative Dialogues\",\"url\":\"https://arxiv.org/pdf/2306.14694\"}]\n\nBased on the search results, I can provide you with the definition of an argument according to Besnard and Hunter's logic-based argumentation framework:\n\nIn the Besnard-Hunter framework, an argument is simply a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item.\n\nMore formally, a deductive argument built from a belief base Δ is a pair ⟨Φ, α⟩, where Φ is called the support and α the claim, such that: Φ ⊆ Δ, Φ does not entail contradiction, Φ entails α, and Φ is minimal with respect to subset inclusion among the sets of formulae which satisfy these conditions.\n\nIn other words, an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item (which is a formula). The key components are:\n\n1. **Support (Φ)**: A set of premises from the knowledge base\n2. **Claim (α)**: The conclusion being argued for\n3. **Consistency**: The support must be consistent (cannot derive a contradiction)\n4. **Entailment**: The support must entail the claim\n5. **Minimality**: There should be no proper subset of the support that still entails the claim\n\n## 43. Page: https://plato.stanford.edu/entries/presupposition/\n\n**Asked:** Answer in under 140 words, paraphrasing, naming sections. (a) What is presupposition accommodation (Lewis 1979; Stalnaker's common ground): what happens when a speaker says something that presupposes P and P is not yet common ground? (b) Does the entry say presupposed or not-at-issue content is harder to deny or challenge directly than asserted content, and does it mention the 'Hey, wait a minute!' test (von Fintel / Shanon)?\n\n# Presupposition Accommodation and Denial\n\n## (a) Accommodation (Section 5)\n\nWhen a speaker utters a sentence whose presupposition P is not yet established in the common ground, accommodation occurs. As Karttunen (1974) explains, \"the listener is entitled and expected to extend it as required.\" Lewis (1979) formalized this: hearers adjust their context to make the speaker's presuppositions true, allowing conversation to proceed smoothly despite unsatisfied presuppositions.\n\n## (b) Denying Presupposed Content\n\nThe encyclopedia does **not** explicitly state whether presupposed content is harder to deny than asserted content, nor does it mention the 'Hey, wait a minute!' test or von Fintel/Shanon. \n\nThe entry does note that unembedded presuppositions are typically \"not cancellable\" (Section 1.3), distinguishing them from implicatures. However, this addresses projection behavior rather than direct challengeability.\n\n## 44. Page: https://plato.stanford.edu/entries/frame-problem/\n\n**Asked:** Answer in under 130 words, paraphrasing, naming sections. What does the entry say about (a) the frame problem in its wider epistemological sense: how a reasoner determines what is relevant and what stays the same without considering everything, and (b) Dreyfus's argument that human know-how and common-sense background cannot be captured as a body of explicit rules and facts?\n\n# Frame Problem: Epistemology and Dreyfus\n\n**(a) Epistemological Frame Problem:**\n\nSection 3 explains that the core challenge is how a reasoner determines which beliefs require revision after an action. The difficulty lies in establishing relevance boundaries. As the text notes, \"relevance is dependent on context,\" making it impossible to specify a priori which propositions matter. This creates a potential infinite regress: determining what's relevant requires understanding the broader context, which itself needs contextual grounding. The problem persists even with access to complete information.\n\n**(b) Dreyfus's Critique:**\n\nDreyfus argues (Section 5) that classical AI's assumption of explicit representational rules cannot capture human competence. He contends that human intelligence operates through \"background familiarity with how things behave\" rather than encoded rules. Modern robotics attempts merely \"finesse rather than solve\" this problem because they respond only to fixed features, not dynamic context. Dreyfus advocates instead for neurodynamical approaches involving \"attractors\" shaped by experience—neither representations nor associations.\n\n## 45. Page: https://plato.stanford.edu/entries/thomas-kuhn/\n\n**Asked:** Answer in under 110 words, paraphrasing, naming the section. What does the entry say about exemplars (paradigms as shared examples) and Kuhn's claim that scientists are guided by perceived similarity to exemplary problem-solutions rather than by explicit rules, so that science can proceed without agreed rules?\n\n# Exemplars and Scientific Guidance (Section 3)\n\nIn \"The Concept of a Paradigm,\" Kuhn argues that scientists navigate research through familiarity with exemplary problem-solutions rather than applying codified methodological rules. He contends that paradigm-as-exemplars function through perceived resemblance: \"similarity to the exemplar\" guides scientists' work. This approach explains how scientific communities maintain coherence without explicit algorithmic procedures. Kuhn rejected the traditional distinction between discovery and justification contexts, proposing instead that training with exemplars enables researchers to recognize and solve novel puzzles through analogical reasoning—a naturalistic cognitive process rather than rule-governed rationality.\n\n## 46. Page: https://plato.stanford.edu/entries/oakeshott/\n\n**Asked:** Answer in under 110 words, paraphrasing, naming the section. Summarise Oakeshott's distinction between technical knowledge (formulable in rules, learnt from a book) and practical knowledge (existing only in use, not formulable in rules) in 'Rationalism in Politics', and what he says the rationalist gets wrong about rules and practice.\n\n# Section 3: Rationality and Rationalism\n\nOakeshott distinguishes technical knowledge—easily learned rules applicable without experience—from traditional knowledge, which is \"knowing how\" rather than \"knowing that,\" acquired through engagement and requiring judgment.\n\nThe rationalist erroneously believes correct decisions emerge from applying rules or calculating consequences. However, Oakeshott argues that rules themselves derive from practical experience and represent \"abridgments\" of customs and traditions. Using rules skillfully demands judgment transcending the instructions provided. Rationalists mistake abstracted knowledge for something independent of practice, fundamentally misunderstanding how rules actually function in real situations.\n\n## 47. Page: https://plato.stanford.edu/entries/mill/\n\n**Asked:** Answer in under 120 words, paraphrasing, naming the section. What does the entry say about Mill's account of the syllogism in A System of Logic: the charge that the syllogism begs the question, his claim that all inference is from particulars to particulars, and his view that a general proposition is a register or memorandum of past inferences and a formula for making more?\n\n# Mill's Account of the Syllogism\n\nIn the \"Philosophy of Language and Logic\" section (3.1), the entry explains that Mill argues syllogistic reasoning cannot produce new knowledge. He contends that \"nothing ever was, or can be proved by syllogism which was not known\" beforehand.\n\nMill claims the conclusion must already be contained within the premises for validity. Using the example \"All men are mortal; Socrates is a man; therefore, Socrates is mortal,\" he suggests the first premise already includes the conclusion's claim.\n\nHowever, the entry notes this position depends on \"equating the meaning of a universal statement with a conjunction of singular statements\"—a problematic equation. While challenging to defend rigorously, Mill's broader argument succeeds in demonstrating that linguistic reflection alone cannot advance genuine knowledge about the world.\n\n## 48. Page: https://plato.stanford.edu/entries/leibniz-modal/\n\n**Asked:** Answer in under 100 words, paraphrasing, naming the section. Explain Leibniz's infinite-analysis account of contingency: that in a necessary truth the analysis of the concepts terminates in an identity after finitely many steps, whereas in a contingent truth the analysis continues to infinity and only God sees the connection.\n\n# Leibniz's Infinite-Analysis Account of Contingency\n\n**Section 2: The Nature of Modality**\n\nIn necessary truths, conceptual analysis reaches completion, reducing to identities. For contingency, analysis proceeds infinitely—the predicate never fully reduces to the subject. As Leibniz explains, \"in contingent propositions one continues the analysis to infinity through reasons for reasons, so that one never has a complete demonstration.\" Only God comprehends this infinite chain instantly. This infinite regress distinguishes contingent truths from necessary ones, grounding Leibniz's account of modal distinctions without requiring possible-worlds semantics explicitly.\n\n## 49. Page: https://plato.stanford.edu/entries/hume-moral/\n\n**Asked:** Answer in under 90 words, paraphrasing, naming the section. What does the entry say about Hume's is-ought passage (Treatise 3.1.1): what is its standard reading about deriving an evaluative or 'ought' conclusion from purely factual 'is' premises, and are there alternative readings?\n\n# Hume's Is-Ought Passage (Section 5)\n\nThe standard twentieth-century interpretation holds that Hume establishes a logical principle: no evaluative conclusion can validly follow from purely factual premises alone. This reading treats it as \"Hume's Law.\"\n\nHowever, alternative interpretations exist. Some cognitivist scholars argue Hume merely shows that \"demonstrative reason\" cannot discover moral properties, leaving probable reasoning open. Others suggest the passage addresses how we originally discover virtue and vice—requiring sentiment's input, not just reason alone.\n\n## 50. Page: https://plato.stanford.edu/entries/scientific-explanation-20th/\n\n**Asked:** Answer in under 190 words, paraphrasing, naming sections. (a) State the Deductive-Nomological model: what must the explanans contain and what relation must it bear to the explanandum? (b) Describe the counterexamples: explanatory asymmetry (flagpole and shadow) and explanatory irrelevance (the hexed salt, or the man taking birth-control pills). (c) What does the entry say about distinguishing laws from accidentally true generalizations? (d) What was Scriven's objection with the inkwell/ink-stain example, and does the entry describe his 'role-justifying grounds' idea: that a law may justify an explanation without being part of it?\n\n# Scientific Explanation: DN Model and Counterexamples\n\n## (a) The Deductive-Nomological Model (Section 2.1)\n\nThe DN model requires that the explanans must contain at least one \"law of nature\" as an essential premise. The model demands that \"the explanandum must be a logical consequence of the explanans\" and \"the sentences constituting the explanans must be true.\" The explanation takes the form of a sound deductive argument where the phenomenon follows as a conclusion from the premises.\n\n## (b) Two Key Counterexamples (Section 2.5)\n\n**Explanatory Asymmetry**: One can derive a flagpole's shadow length from its height using light propagation laws (explanatory), but deriving the height from shadow length using identical laws seems non-explanatory, despite satisfying DN criteria.\n\n**Explanatory Irrelevance**: A male taking birth control pills regularly failing to become pregnant meets DN criteria (with a lawlike generalization), yet this explanation seems defective because the pill-taking is causally irrelevant to male pregnancy prevention.\n\n## (c) Distinguishing Laws from Accidents (Section 2.2)\n\nThe entry notes this remains \"highly recalcitrant.\" While \"all gases expand when heated\" is a law, \"all 1964 Greensbury School Board members are bald\" is merely accidentally true. However, no principled, universally accepted criterion has been established for making this distinction.\n\n## (d) Scriven's Inkwell Objection (Section 2.4)\n\nScriven claimed \"The knee impact caused the inkwell to tip\" explains the tipping without explicit laws, challenging DN necessity. The entry does not discuss his \"role-justifying grounds\" concept.\n\n## 51. Search: Mill System of Logic \"All inference is from particulars to particulars\" \"general propositions are merely registers of such inferences already made, and short formulae for making more\"\n\nWeb search results for query: \"Mill System of Logic \"All inference is from particulars to particulars\" \"general propositions are merely registers of such inferences already made, and short formulae for making more\"\"\n\nLinks: [{\"title\":\"Mill’s System of Logic: Selected Works vol. VII\",\"url\":\"https://oll.libertyfund.org/pages/mill-s-system-of-logic-selected-works-vol-vii\"},{\"title\":\"Mill on the Syllogism\",\"url\":\"https://www.logicmuseum.com/hypothetical/millonenumeration.htm\"},{\"title\":\"A System of Logic, Ratiocinative and Inductive/Chapter 11 - Wikisource, the free online library\",\"url\":\"https://en.wikisource.org/wiki/A_System_of_Logic,_Ratiocinative_and_Inductive/Chapter_11\"},{\"title\":\"Logic and theory of representation\",\"url\":\"https://arxiv.org/pdf/2307.10629\"},{\"title\":\"A System of Logic\",\"url\":\"https://en.wikipedia.org/wiki/A_System_of_Logic\"},{\"title\":\"General Logic-Systems that Determine Significant Collections of Consequence Operators\",\"url\":\"https://arxiv.org/pdf/math/0603573\"},{\"title\":\"apps.dtic.mil\",\"url\":\"https://apps.dtic.mil/sti/pdfs/ADA134747.pdf\"},{\"title\":\"Jump to ratings and reviews\",\"url\":\"https://www.goodreads.com/book/show/1347804\"},{\"title\":\"www.cambridge.org\",\"url\":\"https://www.cambridge.org/core/books/cambridge-companion-to-mill/mill-on-language-and-logic/E373155D5BBB8C48ADD6D7450CD4EC19\"}]\n\nPerfect! I found the exact quote you're searching for. Here are the search results:\n\nThe quote \"All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formulae for making more: The major premise of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula: the real logical antecedent, or premise, being the particular facts from which the general proposition was collected by induction\" appears in Mill's *System of Logic*.\n\nThis represents Mill's single most important thesis for his logic of experience—that all inference is from particulars to particulars. This argument underlies his theory of induction, with the view that no reasoning from generals to particulars can prove anything, since from a general principle we cannot infer any particulars but those which the principle itself assumes as known.\n\nThe text is available in full at multiple sources, including the Online Library of Liberty and Wikisource versions of *A System of Logic, Ratiocinative and Inductive*.\n\n## 52. Search: Dancy \"Ethics Without Principles\" favourers enablers disablers intensifiers attenuators distinction promise \"not given under duress\"\n\nWeb search results for query: \"Dancy \"Ethics Without Principles\" favourers enablers disablers intensifiers attenuators distinction promise \"not given under duress\"\"\n\nLinks: [{\"title\":\"(PDF) Moral particularism and the real world\",\"url\":\"https://www.researchgate.net/publication/46117477_Moral_particularism_and_the_real_world\"},{\"title\":\"(PDF) Ethics Without Principles\",\"url\":\"https://www.academia.edu/9794528/Ethics_Without_Principles\"},{\"title\":\"Ethics without Principles\",\"url\":\"https://ndpr.nd.edu/reviews/ethics-without-principles/\"},{\"title\":\"Ethics without Principles\",\"url\":\"https://masters.ecampus.com/ethics-without-principles-dancy-jonathan/bk/9780199297689\"},{\"title\":\"Ethics without principles - 3:16\",\"url\":\"https://www.3-16am.co.uk/articles/ethics-without-principles\"},{\"title\":\"Review of Jonathan Dancy, Ethics without Principles\",\"url\":\"https://www.fehige.info/pdf/TLS_Dancy.pdf\"},{\"title\":\"ETHICS WITHOUT PRINCIPLES PAPER by Jonathan Dancy\",\"url\":\"https://www.goodreads.com/book/show/1029137.Ethics_Without_Principles\"},{\"title\":\"Ethics without Principles - Paperback - Jonathan Dancy - Oxford University Press\",\"url\":\"https://global.oup.com/academic/product/ethics-without-principles-9780199297689\"},{\"title\":\"Ethics Without Principles: Jonathan Dancy: 9780199270026\",\"url\":\"https://www.booksamillion.com/p/Ethics-Without-Principles/Jonathan-Dancy/9780199270026\"}]\n\nNow let me search specifically for information about promises and \"not given under duress\" in relation to Dancy's work:\n\nLinks: [{\"title\":\"Moral Particularism (Stanford Encyclopedia of Philosophy)\",\"url\":\"https://plato.stanford.edu/entries/moral-particularism/\"},{\"title\":\"Jonathan Dancy, Ethics without principles - PhilPapers\",\"url\":\"https://philpapers.org/rec/DANEWP\"},{\"title\":\"Ethics without Principles\",\"url\":\"https://ndpr.nd.edu/reviews/ethics-without-principles/\"},{\"title\":\"(PDF) Ethics Without Principles\",\"url\":\"https://www.academia.edu/9794528/Ethics_Without_Principles\"},{\"title\":\"Ethics without principles : Dancy, Jonathan : Free Download, Borrow, and Streaming : Internet Archive\",\"url\":\"https://archive.org/details/ethicswithoutpri0000danc\"},{\"title\":\"Ethics Without Principles\",\"url\":\"https://www.researchgate.net/publication/287181150_Ethics_Without_Principles\"},{\"title\":\"Argument Models\",\"url\":\"https://link.springer.com/chapter/10.1007/978-3-031-92990-8_3\"},{\"title\":\"Ethics Without Principles - Jonathan Dancy - Google Books\",\"url\":\"https://books.google.com/books/about/Ethics_Without_Principles.html?id=ys69fEWwz2AC\"},{\"title\":\"Jonathan Dancy\",\"url\":\"https://en.wikipedia.org/wiki/Jonathan_Dancy\"},{\"title\":\"The Principle-Based Method of Practical Ethics\",\"url\":\"https://link.springer.com/article/10.1007/s10728-015-0295-x\"}]\n\nBased on my search results, I found relevant information about Dancy's *Ethics Without Principles* and the distinctions you asked about.\n\n## Key Distinctions in Dancy's Framework\n\nDancy's 2004 book *Ethics without Principles* makes much of a distinction between reasons, enablers, disablers, intensifiers, and attenuators. Dancy used the distinction between favourers and enablers to stop a certain form of anti-particularist argument.\n\n## The Promise and \"Not Given Under Duress\" Example\n\nDancy uses promises as a key example to illustrate these distinctions. That a promise was not made under duress functions as an enabling condition, one in whose absence the first feature (that I promised) would not serve as a reason for action.\n\nMore specifically, Dancy distinguishes between the conditions of the reason: If I promised to do it then I have a reason to do it, unless the promise was made under duress or I am not capable of doing it, and the conditions of the inference: If I promised to do it then you can conclude that I must do it, unless there is a more compelling reason not to do it.\n\nIn other words, whether a promise was \"not given under duress\" is an **enabling condition** (or \"enabler\")—it's a necessary background condition that must obtain for the promise itself to count as a reason for action, but it doesn't itself count as a favoring reason.\n\n## 53. Search: Boghossian \"What is inference?\" \"taking condition\" inferring requires taking premises to support conclusion regress Carroll\n\nWeb search results for query: \"Boghossian \"What is inference?\" \"taking condition\" inferring requires taking premises to support conclusion regress Carroll\"\n\nLinks: [{\"title\":\"1 Inference as Consciousness of Necessity Eric Marcus Auburn University\",\"url\":\"https://philarchive.org/archive/MARIAC-13v1\"},{\"title\":\"Inference and the taking condition - Kietzmann - 2018 - Ratio - Wiley Online Library\",\"url\":\"https://onlinelibrary.wiley.com/doi/abs/10.1111/rati.12195\"},{\"title\":\"Inference and the taking condition\",\"url\":\"https://www.researchgate.net/publication/323591411_Inference_and_the_taking_condition\"},{\"title\":\"[논문]Inference and the taking condition\",\"url\":\"https://scienceon.kisti.re.kr/srch/selectPORSrchArticle.do?cn=NART86687538\"},{\"title\":\"Comment on Paul Boghossian, “What Is Inference”\",\"url\":\"https://www.researchgate.net/publication/257637381_Comment_on_Paul_Boghossian_What_Is_Inference\"},{\"title\":\"Comment on Paul Boghossian, “What is inference”\",\"url\":\"https://link.springer.com/article/10.1007/s11098-012-9892-9\"},{\"title\":\"s12136 023 00548 1\",\"url\":\"https://link.springer.com/10.1007/s12136-023-00548-1\"},{\"title\":\"s11229 017 1535 4\",\"url\":\"https://link.springer.com/doi/10.1007/s11229-017-1535-4\"},{\"title\":\"s11098 018 1142 3\",\"url\":\"https://link.springer.com/10.1007/s11098-018-1142-3\"}]\n\nBased on the web search results, I found relevant information about Boghossian's work on inference and the \"Taking Condition.\" Here's what the search revealed:\n\nBoghossian's Taking Condition states that inferring necessarily involves the thinker taking his premises to support his conclusion and drawing his conclusion because of that fact.\n\nCarroll's \"What the Tortoise Said to Achilles\" presents the idea that there is a psychological gap between accepting the premises of a simple inference and accepting the conclusion, and once we attempt to fill the gap with an additional thought, the regress is off and running; the addition is never enough.\n\nThe Taking Condition has been criticized: if taking is interpreted as believing, it seems to lead to a vicious regress and to overintellectualize the act of inferring.\n\nThe regresses discussed are structurally similar to Lewis Carroll's famous regress, which involves quantitative extravagance with no explanatory power.\n\nThe search results show that Boghossian's Taking Condition is a central concept in the debate about what constitutes inference, particularly in relation to Carroll's classic regress problem and the question of how reasoners can satisfy the Taking Condition without engendering an infinite regress.\n\n## 54. Search: \"Hey, wait a minute\" test presupposition von Fintel not-at-issue content harder to challenge directly than asserted content\n\nWeb search results for query: \"\"Hey, wait a minute\" test presupposition von Fintel not-at-issue content harder to challenge directly than asserted content\"\n\nLinks: [{\"title\":\"Only, Presupposition and Implicature\",\"url\":\"https://www.asc.ohio-state.edu/roberts.21/only.pdf\"},{\"title\":\"Testimony by Presupposition\",\"url\":\"https://link.springer.com/article/10.1007/s10670-022-00623-w\"},{\"title\":\"Persuasive presuppositions - ScienceDirect\",\"url\":\"https://www.sciencedirect.com/science/article/pii/S0378216623000978\"},{\"title\":\"Backgrounding and accommodation of presuppositions: an experimental approach\",\"url\":\"https://semanticsarchive.net/sub2012/CumminsAmaralKatsos.pdf\"},{\"title\":\"\\\"No, they did not\\\": Dialogue response dynamics in pre-trained language models\",\"url\":\"https://arxiv.org/pdf/2210.02526\"},{\"title\":\"The projection problem of presuppositions Clemens Mayr\",\"url\":\"https://eggschool.org/wp-content/uploads/2016/06/Egg_presupposition_1-1.pdf\"},{\"title\":\"Would you Believe it? The King of France is Back! ( ...\",\"url\":\"https://web.mit.edu/fintel/fintel-2004-kof.pdf\"},{\"title\":\"Studying meaning 1 Relationships of meaning (1) a. Today is Wednesday.\",\"url\":\"https://mitcho.com/nus/sem2019/handout01.pdf\"},{\"title\":\"To appear in Comments welcome! Anne Bezuidenhout and Marga Reimer (eds.)\",\"url\":\"https://semanticsarchive.net/Archive/zAzNjllO/von.fintel.kof.pdf\"},{\"title\":\"3.4: Presupposition - Social Sci LibreTexts\",\"url\":\"https://socialsci.libretexts.org/Bookshelves/Linguistics/Analyzing_Meaning_-_An_Introduction_to_Semantics_and_Pragmatics_(Kroeger)/03:_Truth_and_inference/3.04:_Presupposition\"}]\n\nI've found comprehensive information about the \"Hey, wait a minute\" test and its relationship to presuppositions and not-at-issue content. Here's what the research shows:\n\n## The \"Hey, wait a minute\" Test\n\nThe test, attributed to Shannon (1976) by von Fintel (2004), consists of a dialog in which a target utterance is followed by an interjection by another speaker, beginning with \"Hey, wait a minute!\" and then taking issue with the suspected presupposition.\n\n## Not-at-Issue Content and Challenge\n\nThe underlying observation is that while we can directly deny or call into question the at-issue content of an utterance, we cannot do so with the presupposed content, so to avoid letting it slip by we must call a halt to the conversational proceedings.\n\nAny content that is not at issue can be objected to with \"Hey, wait a minute\", whether this is a linguistically triggered presupposition or merely a prior commitment of the speaker. This suggests the test detects a broader category than just presuppositions.\n\n## Difficulty Challenging Not-at-Issue Content\n\nA more natural way to object to not-at-issue content is pausing the dialogue to question a side comment or assumption, which is highlighted in the \"peripherality test\" using phrases like \"Hey, wait a minute\" to make targeting not-at-issue content more acceptable.\n\nThe research confirms that not-at-issue content (including presuppositions and conventional implicatures) is harder to challenge directly than asserted content, which is why special discourse moves like \"Hey, wait a minute\" are needed.\n\n## 55. Search: Hitchcock \"non-logical consequence\" covering generalization Bolzano substitution variable enthymematic arguments not missing premises\n\nWeb search results for query: \"Hitchcock \"non-logical consequence\" covering generalization Bolzano substitution variable enthymematic arguments not missing premises\"\n\nLinks: [{\"title\":\"VI1.2&3, Spring&Fall1985 Informal Logic Enthymematic Arguments DAVID HITCHCOCK\",\"url\":\"https://ojs.uwindsor.ca/index.php/informal_logic/article/download/2707/2148\"},{\"title\":\"Non-logical consequence David Hitchcock McMaster University\",\"url\":\"https://www.humanities.mcmaster.ca/~hitchckd/non-logicalconsequence.pdf\"},{\"title\":\"Reasoning by Analogy: A General Theory\",\"url\":\"https://link.springer.com/chapter/10.1007/978-3-319-53562-3_12\"},{\"title\":\"(PDF) Smook on Logical and Extralogical Constants\",\"url\":\"https://www.researchgate.net/publication/315863963_Smook_on_Logical_and_Extralogical_Constants\"},{\"title\":\"Bolzano’s Logic (Stanford Encyclopedia of Philosophy)\",\"url\":\"https://plato.stanford.edu/entries/bolzano-logic/\"},{\"title\":\"Evaluating Inferences: the Nature and Role of Warrants 287\",\"url\":\"https://informallogic.ca/index.php/informal_logic/article/download/455/424\"},{\"title\":\"Enthymematic Arguments\",\"url\":\"https://www.researchgate.net/publication/315875905_Enthymematic_Arguments\"},{\"title\":\"Definability and Interpolation in Philosophy\",\"url\":\"https://arxiv.org/pdf/2602.07907\"},{\"title\":\"(PDF) Enthymematic Arguments\",\"url\":\"https://www.researchgate.net/publication/315862067_Enthymematic_Arguments\"}]\n\nI found relevant search results on your query. Here's what the sources reveal:\n\nBolzano accommodated not only logical consequence but also enthymematic consequence, by allowing substitution in his framework. In a substitutional conception of logical consequence, the logical terms are those not subject to substitution when searching for a substitutional counter-example—i.e. a parallel argument with true premises and an untrue conclusion, obtained by uniform substitution on the original argument's extra-logical terms.\n\nRegarding Hitchcock's treatment of non-logical consequence: Hitchcock offers reasons why the \"assumption\" of an enthymematic argument must generalize over a content expression occurring in both premises and conclusion, and unless there is a repeated content expression common to premises and conclusion, the premises will not be \"topically relevant\" to the conclusion and the argument will be a non-sequitur.\n\nImportantly, many inferences can only be declared valid if they are interpreted as enthymematic, requiring supplementation in the form of \"tacit\" premises, which suggests that Hitchcock's approach to enthymematic arguments does not necessarily treat them as having \"missing premises\" in the traditional sense.\n\nFollowing Bolzano, Hitchcock rules out trivial cases in which there is no counter-example because no substitution could make the premises true or no substitution could make the conclusion false.\n\n## 56. Search: Searle constitutive rules \"X counts as Y in context C\" regulative rules institutional facts definition\n\nWeb search results for query: \"Searle constitutive rules \"X counts as Y in context C\" regulative rules institutional facts definition\"\n\nLinks: [{\"title\":\"Rules and Games\",\"url\":\"https://link.springer.com/article/10.1007/s11406-018-0050-2\"},{\"title\":\"(PDF) Searle's theory of institutional facts: A program of critical revision\",\"url\":\"https://www.researchgate.net/publication/286306083_Searle's_theory_of_institutional_facts_A_program_of_critical_revision\"},{\"title\":\"Constitutive Rules in Context by Corrado Roversi :: SSRN\",\"url\":\"https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1518414_code1398111.pdf?abstractid=1518414&mirid=1\"},{\"title\":\"How to Understand Rule-Constituted Kinds Manuel García-Carpintero1\",\"url\":\"https://www.ub.edu/grc_logos/wp-content/uploads/files_publication/user125/1691076685-ConstitutiveVsRegulativeNorms_rpp.pdf\"},{\"title\":\"Governing Governance: A Formal Framework for Analysing Institutional Design and Enactment Governance\",\"url\":\"https://arxiv.org/pdf/1704.06654\"},{\"title\":\"What if Pinocchio Were a Reinforcement Learning Agent: A Normative End-to-End Pipeline\",\"url\":\"https://arxiv.org/pdf/2603.16651\"},{\"title\":\"Revisiting Constitutive Rules\",\"url\":\"https://www.slideshare.net/GiovanniSileno/revisiting-constitutive-rules\"},{\"title\":\"Social ontology\",\"url\":\"https://en.wikipedia.org/wiki/Social_ontology\"},{\"title\":\"Article - Constitutive Rules in Context\",\"url\":\"https://biblioscout.net/article/10.25162/arsp-2010-0018\"}]\n\nI've found comprehensive information about Searle's theory of constitutive rules, regulative rules, and institutional facts. Here's what the search results reveal:\n\n## Constitutive Rules: \"X counts as Y in context C\"\n\nConstitutive rules often have the form: X counts as Y in context C. In this form, X stands for some natural phenomenon, such as moving a round object into a basket, and Y gives some \"institutional\" description of X: in this case, scoring points.\n\n## Relationship to Institutional Facts\n\nInstitutional facts are constituted by collectively shared acceptance analyzable into a hierarchy of acceptance units of the form X counts as Y in context C, where the Y element is a status function assigned to the X element. These institutional facts describe a social reality ascribed by the institution, giving an institutional interpretation of the brute (actual) reality.\n\n## Regulative Rules\n\nRegulative rules take the form: Do X or If Y do X. The regulative typically takes the form of an imperative, \"Drive on the right!\", for example; the constitutive rules take the form \"X counts as Y\" or \"X counts as Y in context C\".\n\n## Key Distinction\n\nConstitutive norms describe how rules bring certain social or institutional realities into existence by defining what actions, statuses, or roles count as within a given context, and Searle characterizes them as a way to build institutional facts from brute facts.\n\n## 57. Page: https://en.wikipedia.org/wiki/Stasis_(argumentation_theory)\n\n**Asked:** In under 110 words: list the four stases of classical stasis theory (Hermagoras; conjecture or fact, definition, quality, translation or procedure/jurisdiction) with a one-line gloss of the question each asks. Say who is credited with the doctrine.\n\n# The Four Stases of Classical Stasis Theory\n\n**Cicero** is credited with developing stasis theory as a procedure for rhetorical invention. The four types are:\n\n1. **Conjectural (Fact)**: \"Is/was it?\" — addresses whether something occurred\n2. **Definitional (Definition)**: \"What is/what is its meaning?\" — clarifies the nature of the issue\n3. **Qualitative (Quality)**: \"How good or bad is/was it?\" — evaluates significance and justification\n4. **Translative (Procedure)**: \"Is/was this appropriate process or place to handle the matter?\" — determines jurisdiction and proper venue\n\nEach stasis guides speakers toward building effective arguments by systematically questioning different dimensions of a dispute.\n\n## 58. Page: https://en.wikipedia.org/wiki/Relevance_theory\n\n**Asked:** In under 110 words: what does the article say about 'implicated premises' and 'implicated conclusions' in relevance theory (Sperber and Wilson), and about the hearer following a path of least effort in supplying contextual assumptions until expectations of relevance are satisfied?\n\n# Relevance Theory: Implied Meanings and Efficient Processing\n\nThe article discusses how hearers derive **implicated premises** from their cognitive environment and draw **implicated conclusions** based on utterances. These inferences go beyond explicit content.\n\nRegarding the processing strategy, the text states: \"Follow a path of least effort in computing cognitive effects: test interpretive hypotheses in order of accessibility, and stop when your expectations of relevance are satisfied.\"\n\nThis means listeners don't exhaustively analyze all possible meanings. Instead, they examine interpretations sequentially by how easily they come to mind, halting once they've found one meeting their relevance expectations. This efficient mechanism prevents excessive cognitive burden while enabling successful communication, as addressees assume speakers have crafted utterances optimally for comprehension.\n\n## 59. Search: Fallis \"Intentional gaps in mathematical proofs\" inferential gaps enthymematic gaps untraversed gaps informal proofs formal derivation Azzouni derivation-indicator\n\nWeb search results for query: \"Fallis \"Intentional gaps in mathematical proofs\" inferential gaps enthymematic gaps untraversed gaps informal proofs formal derivation Azzouni derivation-indicator\"\n\nLinks: [{\"title\":\"Intentional Gaps In Mathematical Proofs\",\"url\":\"https://www.researchgate.net/publication/227068791_Intentional_Gaps_In_Mathematical_Proofs\"},{\"title\":\"Vrije Universiteit Brussel Acceptable Gaps in Mathematical Proofs\",\"url\":\"https://cris.vub.be/ws/portalfiles/portal/109272934/Line_Edslev_Andersen._Acceptable_Gaps_in_Mathematical_Proofs.pdf\"},{\"title\":\"Deep Disagreement in Mathematics\",\"url\":\"https://arxiv.org/pdf/2210.16488\"},{\"title\":\"LAGUNAS EXPRESIVAS EN LA DEMOSTRACIÓN ...\",\"url\":\"https://critica.filosoficas.unam.mx/index.php/critica/article/download/1695/1389\"},{\"title\":\"Non-Deductive Methods in Mathematics (Stanford Encyclopedia of Philosophy/Fall 2009 Edition)\",\"url\":\"https://plato.stanford.edu/archives/fall2009/entries/mathematics-nondeductive/\"},{\"title\":\"Acceptable gaps in mathematical proofs\",\"url\":\"https://www.researchgate.net/publication/324503223_Acceptable_gaps_in_mathematical_proofs\"},{\"title\":\"Towards a New Epistemology of Mathematics\",\"url\":\"https://link.springer.com/article/10.1007/s10670-008-9101-6\"},{\"title\":\"Right for the wrong reasons: common bad arguments for the correct answer to the Monty Hall Problem\",\"url\":\"https://link.springer.com/article/10.1007/s11229-025-05389-6\"},{\"title\":\"MATHEMATICAL RIGOR AND PROOF\",\"url\":\"https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/abs/mathematical-rigor-and-proof/045E9F382FDA2BD0E74C57CE7B619466\"}]\n\nNow let me search for information about Azzouni and derivation-indicator in relation to this work:\n\nLinks: [{\"title\":\"Formal Proofs in Mathematical Practice\",\"url\":\"https://link.springer.com/rwe/10.1007/978-3-031-40846-5_35\"},{\"title\":\"The Derivation-Indicator View of Mathematical Practice\",\"url\":\"https://www.researchgate.net/publication/31368291_The_Derivation-Indicator_View_of_Mathematical_Practice\"},{\"title\":\"Citation (Version of Record):\",\"url\":\"https://research-information.bris.ac.uk/ws/files/250846813/Rigour_and_Proof.pdf\"},{\"title\":\"Notre Dame Journal of Formal Logic Volume 50, Number 1, 2009 Book Review\",\"url\":\"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-1/Book-Review--Jody-Azzouni-Tracking-Reason---Proof/10.1215/00294527-2008-030.pdf\"},{\"title\":\"[PDF] Interpreting Naproche - An algorithmic approach to the derivation-indicator view\",\"url\":\"https://www.semanticscholar.org/paper/3928df8b11a0e42a0bcef34a7431d6ed7b4e4bef\"},{\"title\":\"arXiv:1411.4857v1 [math.LO] 17 Nov 2014 Why Do We Believe Theorems?\",\"url\":\"https://arxiv.org/pdf/1411.4857\"},{\"title\":\"Heuristics and Mathematical Practice\",\"url\":\"https://link.springer.com/10.1007/978-3-030-19071-2_42-1\"},{\"title\":\"Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof\",\"url\":\"https://arxiv.org/pdf/2602.12463\"},{\"title\":\"The Algorithmic-Device View of Informal Rigorous Mathematical Proof\",\"url\":\"https://www.researchgate.net/publication/374754164_The_Algorithmic-Device_View_of_Informal_Rigorous_Mathematical_Proof\"}]\n\nBased on the search results, I've found comprehensive information about Don Fallis's work on intentional gaps in mathematical proofs and its relation to Azzouni's derivation-indicator view. Here's what the research shows:\n\n## Fallis's Classification of Gaps in Mathematical Proofs\n\nFallis distinguishes between three types of gaps in ordinary proofs: inferential gaps, untraversed gaps, and enthymematic gaps.\n\n**Inferential Gaps:** A mathematician has left an inferential gap whenever the particular sequence of propositions that the mathematician has in mind (as being a proof) is not a proof.\n\n**Enthymematic Gaps:** Enthymematic gaps arise when the mathematician has worked through the proof in detail, but chosen to omit some steps from the presentation, presuming that the missing steps will be unnecessary for the intended audience.\n\n**Untraversed Gaps:** Untraversed gaps occur when a mathematician does not attempt to verify every step of the proof. In exceptional cases, even \"universally untraversed gaps\", unverified by any mathematician have been admitted in proofs.\n\n## Importance in Mathematical Practice\n\nFallis argues for the philosophical thesis that gaps in proofs are not necessarily a bad thing. Fallis claims that such gaps are not unusual and that at least some of the time proofs containing them are accepted by mathematicians in a justificatory context.\n\n## Connection to Azzouni's Derivation-Indicator View\n\nAzzouni defends the \"derivation-indicator view of ordinary mathematical proof,\" which is the view that the role of proof in practice is to convince other mathematicians of the existence of a certain kind of \"derivation\", or formal proof—and not, necessarily, to directly encode that proof. Jody Azzouni has argued that underlying the practice of creating mathematical proofs there is a very specific norm: to each proof there should be a corresponding algorithmic derivation, a derivation in an algorithmic system.\n\n## 60. Page: https://plato.stanford.edu/entries/frege-logic/\n\n**Asked:** Answer in under 110 words, paraphrasing, naming the section. Does the entry say that one of Frege's aims in the Begriffsschrift (1879) was to make proofs gapless, so that every premise or presupposition a proof relies on is explicitly stated and nothing intuitive can slip in unnoticed? What does it say he was trying to find out by doing this (e.g. whether arithmetic rests on logic alone or on intuition)? If the entry does not say this, say so plainly.\n\nThe entry does not discuss Frege's aims regarding gapless proofs or his investigation into whether arithmetic depends on logic alone versus intuition. The provided content focuses on the technical features of Frege's logical systems in *Begriffsschrift* and *Grundgesetze*—such as operators, axioms, and rules of inference—rather than his foundational motivations or philosophical goals regarding proof rigor and the nature of arithmetic.\n\n## 61. Page: https://en.wikipedia.org/wiki/Toulmin_method\n\n**Asked:** In under 120 words: list the six parts of Toulmin's layout of arguments (claim, ground or data, warrant, backing, rebuttal, qualifier) with a one-line gloss each, and say what the article states about warrants being field-dependent or about the difference between a warrant and its backing. If the page is about something else, say so.\n\n# Toulmin's Six Components of Argument\n\n1. **Claim**: The conclusion requiring support\n2. **Ground**: Supporting facts or evidence\n3. **Warrant**: Statement authorizing movement from ground to claim\n4. **Backing**: Credentials certifying the warrant's credibility\n5. **Rebuttal**: Recognized restrictions on the claim's validity\n6. **Qualifier**: Words expressing degree of certainty\n\n## Key Points on Warrants\n\nThe article states that \"some aspects of arguments vary from field to field\" (field-dependent), while others remain constant across all fields (field-invariant). However, the document doesn't explicitly state whether warrants themselves are field-dependent.\n\nRegarding warrant versus backing distinction: The backing is introduced \"when the warrant itself is not convincing enough to the readers or the listeners,\" serving to strengthen a warrant that needs additional support.\n\n## 62. Search: Frege Begriffsschrift preface gapless chain of inference \"prevent anything intuitive from penetrating here unnoticed\" every presupposition\n\nWeb search results for query: \"Frege Begriffsschrift preface gapless chain of inference \"prevent anything intuitive from penetrating here unnoticed\" every presupposition\"\n\nLinks: [{\"title\":\"Frege's Contribution to Philosophy of Language Richard G. Heck and Robert May\",\"url\":\"https://philarchive.org/archive/HECFAS-2\"},{\"title\":\"The Very Idea of Dynamic Semantics\",\"url\":\"https://arxiv.org/pdf/cmp-lg/9406026\"},{\"title\":\"Proof Without Gaps: Gottlob Frege and the Audacious Wager\",\"url\":\"https://medium.com/@krigerbruce/proof-without-gaps-gottlob-frege-and-the-audacious-wager-e8f2ea46c78e\"},{\"title\":\"Begriffsschrift ^ a formula language, modeled upon that of ...\",\"url\":\"https://www.informationphilosopher.com/solutions/philosophers/frege/Frege_Begriffsschrift.pdf\"},{\"title\":\"Basic Laws of Arithmetic. Derived using concept-script by Dr G. Frege\",\"url\":\"https://www.finophd.eu/wp-content/uploads/2018/11/06-BasicLaws-1.pdf\"},{\"title\":\"Full article: Frege’s Begriffsschrift: On the Visual Basis of Logical Articulation and Understanding\",\"url\":\"https://www.tandfonline.com/doi/full/10.1080/01445340.2024.2405417\"},{\"title\":\"Penultimate version. Please, do not distribute or quote without permission.\",\"url\":\"https://www.cs.mcgill.ca/~dirk/schlimm2017-begriffsschrift-prefinal.pdf\"},{\"title\":\"(PDF) Frege’s Begriffsschrift: On the Visual Basis of Logical Articulation and Understanding\",\"url\":\"https://www.researchgate.net/publication/388670783_Frege's_Begriffsschrift_On_the_Visual_Basis_of_Logical_Articulation_and_Understanding\"},{\"title\":\"Taking Frege at his Word 0198865473, 9780198865476 - DOKUMEN.PUB\",\"url\":\"https://dokumen.pub/taking-frege-at-his-word-0198865473-9780198865476.html\"}]\n\nBased on the search results, I found the passage you're looking for. To prevent anything intuitive from penetrating here unnoticed, I had to bend every effort to keep the chain of inferences free of gaps. This famous quote appears in the Preface to Frege's *Begriffsschrift*.\n\nThe search results also reveal the broader context of this statement. One of those hidden presuppositions might be a truth that must be supported by facts of experience, which is why Frege sought to prevent anything intuitive from penetrating unnoticed and to keep the chain of inferences free of gaps.\n\nAdditionally, every required axiom has to be uncovered, and the gaplessness of the chains of inferences brings to light each axiom, each presupposition, hypothesis on which a proof rests. This reflects Frege's foundational project of ensuring that arithmetic could be derived purely from logic without relying on intuitive or unexamined assumptions.\n\n## 63. Page: https://plato.stanford.edu/entries/logic-india/\n\n**Asked:** Answer in under 190 words, paraphrasing, naming sections. (a) What is the classical Nyāya five-membered argument (thesis, reason, example, application, conclusion) and what does the 'example' member contribute: does it state a general connection together with a familiar instance (as with smoke, fire and a kitchen)? (b) What is Dignāga's triple condition (trairūpya) for a good reason: present in the subject, present in similar cases, absent from dissimilar cases? (c) What is pervasion (vyāpti), and how is a reason shown to be bad (deviation or counterexample)? (d) Is the standard example an inference from a sign (smoke on a mountain) to what it indicates (fire)?\n\n# Classical Indian Logic: Core Concepts\n\n**(a) Five-Membered Argument Structure**\n\nThe classical Nyāya syllogism comprises thesis, reason, example, application, and conclusion. The example member functions crucially: it presents a \"universal statement and a phrase naming something\" (Section 4.1). For instance, the example establishes that whatever possesses the reason (like being unproduced) also possesses the property to be established (like eternality), illustrated through a familiar case such as space. This demonstrates the general connection through concrete instantiation.\n\n**(b) Dignāga's Triple Condition (Trairūpya)**\n\nA sound reason must satisfy three forms: the reason's \"definite existence in the subject\"; its \"existence in subject-like things only\"; and its \"utter non-existence in subject-unlike things\" (Section 4.2). This ensures the reason reliably indicates the conclusion across relevant cases.\n\n**(c) Pervasion (Vyāpti)**\n\nPervasion represents the indispensability relation between reason and property to be established. A reason fails when it deviates—occurring in dissimilar cases or absent from similar ones—indicating the universal connection doesn't hold.\n\n**(d) Sign Inference**\n\nYes, the canonical example involves inferring fire from observed smoke, exemplifying how reasons function as reliable signs pointing to conclusions.\n"}