{"path":"research/what-a-rule-rests-on/cognitive-science-sources-as-read-2026-10-08.md","content":"> **Kept as it came back.** This is the report of a read-only helper (a language model) made on 2026-10-08 for [what-a-rule-rests-on.md](../what-a-rule-rests-on.md). It read sources in psychology and machine learning on rules, cases and likeness. Claude did not open these sources itself. Its findings are its own reading, with the depth of reading stated per item. Nothing was changed.\n\n# Do rules come from compared cases, and does likeness come first? Cognitive science and machine learning\n\nScope: cognitive science and machine learning only. Every statement below comes from a page I fetched in this run or, where flagged under \"Read\", from a search-tool excerpt of that page. Quotes are exact (PDF dash and hyphen artifacts aside). \"Read\" gives depth.\n\n## Part A. Items\n\n### 1. Hofstadter (2001); Hofstadter and Sander (2013)\n\n**Epilogue, \"Analogy as the Core of Cognition\" (2001).** He rejects the label of analogy as a special variety of reasoning and makes it nearly all of cognition: \"analogy is everything, or very nearly so, in my view.\" Concepts are tightly packaged bundles of analogies; thought is a chain of leaps between bundles, also made by analogy. His notion of analogy is wider than mapping two situations. Any activation of a stored category by input counts, because no instance equals an earlier one, so inexact matching always occurs: \"The triggering of prior mental categories by some kind of input ... is, I insist, an act of analogy-making.\" Perception, word choice, remindings and translation all count. The chapter does not treat induction: I found no occurrence of induction, generalization or law, and \"rules\" appear only as game rules. The step \"induction rests on analogy\" is therefore not argued here; the nearest claim is that categories, which do the work of general rules, are analogy bundles.\n- URL: https://worrydream.com/refs/Hofstadter_2001_-_Analogy_as_the_Core_of_Cognition.pdf\n- Read: full PDF fetched (about 88k characters); read thesis, perception/category section and \"central cognitive loop\"; searched the rest by keyword.\n\n**Surfaces and Essences (2013).** The publisher states the premise as \"Analogy is the core of all thinking\" and names one invariant core: an unconscious quest for analogical links to past experiences. A reader's page-cited quote (p. 3): \"Without concepts there can be no thought, and without analogies there can be no concepts.\" Page 19, as quoted, calls a sharp split between analogy-making and categorization misleading. I found no primary page with the authors' formal definition of analogy; a video-summary site's \"perception of a common essence between two things\" is unverified.\n- URLs: https://intertwingled.org/categories-are-connections/ ; https://www.hachettebookgroup.com/titles/douglas-r-hofstadter/surfaces-and-essences/9780465018475/ ; https://www.google.com/books/edition/Surfaces_and_Essences/XkQT5eTnurYC\n- Read: blog page fetched in full; publisher and Google Books blurbs through search excerpts only. The book is not read (Internet Archive copy is lending-only).\n\n### 2. Gentner and colleagues: structure mapping, similarity as process\n\n**Gentner 1983.** Analogy maps relations, not attributes: \"Relations between objects, rather than attributes of objects, are mapped from base to target\", selected by systematicity (higher-order relations tying lower ones together). It puts general laws on a scale with analogy: \"A different sort of continuum applies between analogies and general laws\"; as base objects become more abstract and variable-like, the comparison is read as an abstraction. A conjecture from one observed learner: early comparisons are literal similarity, then analogies, then a general law (Bernoulli's principle for flow through a constriction). Gentner and Markman (1997), abstract: \"similarity is like analogy\", i.e. both are structural alignment.\n- URLs: https://groups.psych.northwestern.edu/gentner/papers/Gentner83.2b.pdf (OCR scan); https://onlinelibrary.wiley.com/doi/10.1207/s15516709cog0702_3 (abstract); https://groups.psych.northwestern.edu/gentner/papers/GentnerMarkman97.pdf\n- Read: 1983 abstract plus the abstraction, general-law and analogical-shift passages; 1997 abstract only.\n\n**Gentner 2003, \"Why we're so smart.\"** Thesis: \"what makes humans smart is (1) our exceptional ability to learn by analogy, (2) the possession of symbol systems such as language and mathematics\", boosting each other. Comparison is \"a learning mechanism powerful enough to acquire structured rulelike knowledge.\" She treats Marcus et al.'s 7-month-old ABA/ABB results as consistent with structural alignment of repeated examples; her SEQL model reproduces them from just the 48 sentences the infants heard. Humans resemble other species in association and statistical learning; the difference is structure mapping plus relational language.\n- URL: https://groups.psych.northwestern.edu/gentner/papers/Gentner03b.pdf\n- Read: chapter text (about 92k characters), keyword-searched and read around hits.\n\n**Gentner and Medina 1998, \"Similarity and the development of rules\" (Cognition 65).** The closest paper to the question. Claim: comparison bridges similarity and rules. Comparing two cases aligns relations; repeated comparison makes the common system abstract \"until it can be represented as a schema containing variables rather than objects\"; such a schema can then be applied as a rule. They adopt Smith et al.'s (1992) definition of a rule: an explicit abstract schema with variables. Points:\n- A continuum: fully concrete mapping, then analogy, then a base with variables, where the mapping amounts to unification or rule application. Even with a rule in hand, alignment is needed to extend it to new cases.\n- Not all likeness works. Mere-appearance matches have virtually no predictive utility. Memory retrieval follows surface similarity (their proverb study), so spontaneous comparison can mislead. They rely on a \"kind world\" in which looks and relational structure correlate, plus language and culture to steer which cases are compared.\n- Induction: young children's property induction is comparison-based, adults mix comparison and categories (Carey 1985; Lopez et al. 1992, where only second-graders showed premise-diversity effects). Lassaline (1996): argument strength followed a causally connected inference, not overall similarity. Itzaj-Maya adults leaned on ecological knowledge rather than diversity. They accept much of Sloman's two-system proposal but refuse to place comparison in the associative system; comparison, they say, belongs in the same symbolic system as rules.\n- Limits they state: comparison is not the only force in development or the only kind of learning. On Wittgenstein and Goodman they conclude: \"similarities without rules are empty, rules without similarities are blind.\" Their last line makes comparison fundamental to the development and use of rules.\n- URL: https://groups.psych.northwestern.edu/gentner/papers/GentnerMedina98.pdf\n- Read: full text fetched (about 114k characters), all sections except experiment details in 4.1 to 4.5 and references.\n\n**Gentner, Rattermann and Forbus 1993 (Cognitive Psychology 25).** Retrieval and judged soundness run on different similarity. Experiment 1 (stories): soundness (1 to 5) was 4.40 for analogies, 2.80 for surface matches, 2.74 for first-order-relation-only matches; proportion recalled was .78 for surface, .44 for analogies, .25 for first-order-only. \"The accessibility of matches from memory was strongly influenced by surface commonalities and weakly influenced by structural commonalities.\" Model: MAC/FAC, a two-stage similarity retrieval process.\n- URL: https://groups.psych.northwestern.edu/gentner/papers/GentnerRattForbus93.pdf\n- Read: abstract, Experiment 1 results, General Discussion opening.\n\n**Medin, Goldstone and Gentner 1993, \"Respects for similarity.\"** Answers the charge that similarity is empty until \"respects\" are fixed: \"an important source of constraints derives from the similarity comparison process itself\" (alignment; features constrain each other). The paper quotes Murphy and Medin's view that similarity is \"at least as much a consequence as a cause of conceptual coherence\" and treats it as a serious challenge.\n- URLs: https://pages.ucsd.edu/~scoulson/203/medin.pdf ; https://psycnet.apa.org/record/1993-28260-001\n- Read: abstract, introduction, framework summary (not the experiments).\n\n### 3. Rules formed by comparing cases\n\n**Gick and Holyoak 1980, 1983.** 1980: after reading a story about splitting an army along several roads, about 75% of those given the hint solved Duncker's radiation problem against under 10% of controls; with no hint only about 30% did, so most did not notice the analogy (figures as restated in the 1983 paper). 1983: one story gave little schema; two stories did. \"Forty-five percent of subjects in the two-analog conditions generated the convergence solution prior to the hint, as opposed to only 21%\" with one analog (totals 80% vs 53%). Describing the likeness of two stories yielded a schema as an incidental product; only 21% wrote a good schema, 59% a poor one, yet 91% of good-schema writers solved without a hint. Definition: \"the process of schema induction involves deleting the differences between the analogs while preserving their commonalities.\"\n- URLs: https://gwern.net/doc/psychology/1983-gick.pdf ; https://eric.ed.gov/?id=EJ233237 (1980 abstract)\n- Read: 1983 abstract, theory, Part II results; 1980 abstract plus the 1983 summary only.\n\n**Gentner, Loewenstein and Thompson 2003, analogical encoding.** Novices learning negotiation strategies: those who compared two cases \"were over twice as likely (48% of participants) to transfer the principle to the test case as participants in the separate-cases condition (19%)\" (N = 128). An earlier face-to-face study found nearly three times the strategy use.\n- URL: https://groups.psych.northwestern.edu/gentner/papers/GentnerLoewensteinThompson03.pdf\n- Read: abstract, introduction, Experiment 2 results.\n\n**Christie and Gentner 2010, \"Where hypotheses come from.\"** Preschoolers extended a label for a novel spatial pattern. Relational choices: M = 0.60 after comparing two standards, 0.14 after one (F(1, 54) = 22.86), 0.13 when two were shown apart with fillers; over 90% of 3-year-olds with one standard chose the object match. \"The clearest reading of the results is that the children did not entertain the relational hypothesis in any real sense until they engaged in comparison.\"\n- URL: https://groups.psych.northwestern.edu/gentner/papers/christie&Gentner_2010.pdf\n- Read: results and discussion (about 47k characters).\n\n**SEQL and SAGE (Forbus and colleagues).** SEQL: categories are \"formed by a process of progressive abstraction, through successive comparison with incoming exemplars\": a new case is aligned with a stored generalization or exemplar and, if close enough, their structural overlap replaces them. SAGE (successor) clusters cases by analogical retrieval and gives each expression a probability, \"separating characteristic (high probability) structure from incidental (low-probability) structure.\" A 2010 paper: \"Progressive alignment alone may suffice to generate rule-like concepts\"; it adds near-miss negatives and uses alignment as \"the analogical equivalent of rule application.\"\n- URLs: https://qrg.northwestern.edu/papers/Files/SEQL_CogSci2000.pdf ; https://www.qrg.northwestern.edu/papers/Files/QRG_Dist_Files/QRG_2010/SketchedConcepts-CogSci10.pdf ; https://qrg.northwestern.edu/papers/Files/QRG_Dist_Files/QRG_2015/McLure-Friedman-Forbus-AAAI15.pdf\n- Read: SEQL text fetched (about 31k characters); 2010 and 2015 papers through long search excerpts only.\n\n### 4. Categorization theories as rival answers\n\n**Exemplar.** Medin and Schaffer 1978: \"judgments are assumed to derive exclusively from stored exemplar information\"; a probe retrieves similar stored items. They call it \"a device for reasoning by analogy inasmuch as classification of new stimuli is based on stored information concerning old exemplars.\" Across four experiments it beat additive prototype-type models. Nosofsky 1986 extends it: \"Classification decisions are based on the similarity of stimuli to the stored exemplars\", with selective attention reshaping similarity by task.\n- URLs: https://groups.psych.northwestern.edu/medin/documents/MedinSchaffer1978PsychRev.pdf ; https://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/nosofsky-JEP-Gen-1986.pdf\n- Read: Medin and Schaffer abstract, theory section, quoted passages; Nosofsky abstract only.\n\n**Prototype.** Rosch and Mervis 1975: \"prototypicality is a function of the total cue validity of the attributes of items\" (shared within a category, not with contrasting ones); in artificial categories it tracked learning ease, identification speed and rated typicality. URL: http://matt.colorado.edu/teaching/categories/rm75.pdf. Read: abstract. Rosch's other papers not read.\n\n**Rules.** Smith, Langston and Nisbett 1992 give eight criteria and report \"substantial evidence\" for modus ponens, contractual, causal and law-of-large-numbers rules, granting \"people can reason both ways: by applying abstract rules and by analogizing to stored instances.\" Their strictest test, performance unaffected by similarity to earlier items, is left out because they found no study where it bolstered the case for rules. Sloman 1996: an associative system tracking similarity and contiguity and a rule system over symbols with variables; the two \"can simultaneously generate different solutions to a reasoning problem\" (his \"Criterion S\": two contradictory beliefs at once).\n- URLs: https://oipub.com/papers/77426762 ; https://exa.ai/library/publication/sj18k4n8kd6 ; http://matt.colorado.edu/teaching/highcog/readings/s96.pdf\n- Read: Smith et al. abstract and search excerpts (journal PDF blocked); Sloman abstract and Criterion S section.\n\n**Is the split real? Hybrids.** Hahn and Chater 1998: the difference is how a new item is matched: a rule antecedent is matched strictly (all or none) and abstracts away from the instance; similarity matches partially against equally specific stored cases. Each can mimic the other (a rule R defines a dissimilarity D(x,y)=0 iff R(x)=R(y)). Moral: \"pure rule- and similarity-based mechanisms appear not to be computationally viable for solving real-world problems\", so study hybrids. Pothos 2005 reduces one to the other: \"A rules process is considered to be a similarity one where only a single or a small subset of an object's properties are involved.\" The 25 commentaries split: Marcus says \"rules and similarity are not in genuine conflict\"; Ashby and Casale cite dissociations against a single process; Hahn says evidence was turned into definition; Smith frames rule use and similarity use as prototypes on a continuum; Sloman keeps dichotomous traits (drive for consistency).\n- URLs: https://www.dectech.co.uk/publications/LinksNick/CategorizationPerceptionAndMemory/similarity%20and%20rules%20distinct%20exhaustive%20empirically%20disting.pdf ; https://research.gold.ac.uk/5108/1/S0140525X05000014a.pdf\n- Read: Hahn and Chater abstract, explication, conclusion; Pothos abstract, start of the article and every commentary abstract (not the rest of the target article).\n\n**Named rule and hybrid models.** RULEX (Nosofsky, Palmeri and McKinley 1994): people classify by \"forming simple logical rules and remembering occasional exceptions\", which also accounts for prototype and exemplar effects. ATRIUM (Erickson and Kruschke 1998): two experiments show \"evidence of both rule induction and exemplar encoding\"; exemplar representation handles both rules and exceptions, and one experiment examined how people extrapolate beyond the training range. URLs: https://pubmed.ncbi.nlm.nih.gov/8121960/ ; https://pubmed.ncbi.nlm.nih.gov/9622910/. Read: abstracts only.\n\n### 5. Category-based induction\n\n- **Rips 1975.** Told all members of one species have a new disease, adults judged how many of another would (Heit 2000); a search summary says species typicality shaped answers. Paper not fetched.\n- **Osherson et al. 1990.** Similarity-coverage model: strength depends on premise-conclusion similarity and on \"average maximum similarity of premises to a more general category\" containing both; it yields typicality and diversity effects (hippo+hamster support \"mammal\" better than hippo+rhino, as cited in Gentner and Medina). Described via Hayes and Heit (2018); the paper itself not fetched.\n- **Heit 2000** (review). Touchstones include \"Similarity between premise and conclusion categories promotes induction\", and \"The assessment of similarity between categories in an argument depends on the property being projected.\"\n- **Gelman and Markman 1986.** Preschoolers and adults carried a hidden property from a target to a category match (gray squirrel) rather than a look-alike (brown rabbit), above chance. Per Godwin and Fisher (2015), this is read either as a naive theory that kinds share hidden properties or, in Sloutsky and Fisher's model, as labels adding featural overlap; their own test of 3- to 5-year-olds was \"not fully consistent with either theoretical account.\" Original not fetched.\n- **Murphy and Medin 1985.** Concepts cohere to the extent they fit background theories; \"similarity may be a by-product of conceptual coherence rather than its determinant.\" They hedge: the similarity approach is insufficient, not wrong, and a theory is \"supplying the constraints missing from the similarity explanation.\"\n- **Medin, Coley, Storms and Hayes 2003.** Relevance theory: \"people assume that premises are informative with respect to conclusions\", so causal scenarios and property reinforcement matter; tested in three countries.\n- **Hayes and Heit 2018.** Reviews the Bayesian turn: premises are evidence revising beliefs over prior hypotheses; relevance theory explains context effects.\n- URLs: http://faculty.ucmerced.edu/eheit/heit2000.pdf ; https://course-resources.minerva.edu/uploaded_files/mke/00231149-5644/hayes-and-heit--2018.pdf ; https://www.ebi.ac.uk/europepmc/webservices/rest/PMC4493371/fullTextXML ; http://matt.colorado.edu/teaching/highcog/spr10/readings/mm85.pdf ; https://pubmed.ncbi.nlm.nih.gov/14620347/\n- Read: Heit Table 1 and Rips section; Hayes and Heit abstract and two sections; Murphy and Medin full PDF (quotes verified); Medin et al. abstract only; Godwin and Fisher full text.\n\n### 6. The reversal: likeness derived from generalization\n\n**Shepard 1987.** A psychological space is built from generalization data: distances are set so the probability a learned response generalizes is \"an invariant monotonic function of the distance between them\", decaying exponentially. The rationale: meeting a new object poses \"the problem of inferring the consequential region to which that object belongs.\" URL: http://matt.colorado.edu/teaching/categories/s87.pdf. Read: abstract, introduction, keyword hits.\n\n**Tenenbaum and Griffiths 2001.** Recasts Shepard as Bayesian inference over a hypothesis space; the \"size principle\" favors smaller hypotheses exponentially more as examples accumulate. The framework also covers a version of Tversky's set-theoretic similarity model. Limit: \"the assignment of prior probabilities lies outside the scope of a basic Bayesian analysis\", yet priors can overrule likelihood, which they call essential to every successful inductive generalization. URL: https://faculty.cc.gatech.edu/~isbell/reading/papers/TenenbaumGriffiths_2001.pdf. Read: abstract, method, conclusions.\n\n**Kemp and Tenenbaum 2009.** Property induction as Bayesian inference over structured priors. Their tree and space models are similarity-based reasoning with similarity defined as proximity in the underlying structure; the threshold and causal models \"capture inferences that cannot be explained by similarity alone and that often run counter to similarity.\" Of theory-based and similarity-based traditions: \"each of these traditions needs the other.\" URL: https://sites.socsci.uci.edu/~lpearl/courses/readings/KempTenenbaum2009_InductiveReasoning.pdf. Read: abstract, introduction, keyword hits.\n\n**Kemp, Perfors and Tenenbaum 2007, overhypotheses.** \"Inductive learning is impossible without overhypotheses, or constraints on the hypotheses considered by the learner.\" Hierarchical Bayesian models learn them from earlier cases. In their marble-bag example, bags seen so far are each uniform in colour, so a single black marble from a new bag says something about the whole bag; they also model the shape bias in word learning, where \"a single labelled example is enough for children to learn the meanings of some words\" (their introduction). Reading: one case can suffice once an abstraction over earlier cases exists. URLs: https://www.mit.edu/~jbt/temp/KempPerforsTenenbaum.pdf (conference version) ; https://pubmed.ncbi.nlm.nih.gov/17444972/ (journal abstract). Read: conference version abstract and marble-bag section (about 33k characters); journal text not read.\n\n### 7. Penn, Holyoak and Povinelli 2008, \"Darwin's mistake\"\n\nThe human/animal gap is a symbolic-relational discontinuity: a difference in approximating the higher-order, systematic, relational powers of a symbol system. Perceptual similarity is shared and basic: \"The ability to evaluate the perceptual similarity between stimuli is clearly the sine qua non of biological cognition.\" Same-different and relational-match-to-sample successes in parrots, dolphins, baboons and pigeons do not show analogy, they argue. \"the only evidence that any nonhuman animal is capable of analogical reasoning sensu stricto comes from the unreplicated feats of a single chimpanzee\" (Sarah, 1981). On this view analogy sets humans apart and perceptual-similarity induction does not. Gentner and Christie's rival commentary (relational language) is in the same issue; not read.\n- URL: https://reasoninglab.psych.ucla.edu/wp-content/uploads/sites/273/2021/04/Penn-Holyoak-Povinelli.2008.pdf\n- Read: abstract, introduction, sections 2.1 and 2.2, keyword hits (target plus commentaries about 520k characters; mostly unread).\n\n### 8. Is representation separable from mapping?\n\n**Chalmers, French and Hofstadter 1992.** Analogy models that start from hand-built representations (BACON, the Structure-Mapping Engine) are \"flawed precisely because they downplay the role of high-level perception\"; \"perceptual processes cannot be separated from other cognitive processes even in principle.\" Their model (Copycat) builds representations while mapping. URL: https://consc.net/papers/highlevel.pdf (1991 technical report text). Read: abstract and the passages on the \"representation module\".\n\n**Forbus, Gentner, Markman and Ferguson 1998.** They reply that most of the specific arguments about SME are wrong and that \"analogy is high-level perception\" is \"too vague to be useful as a technical proposal.\" Copycat's non-identical correspondences are hand-coded by its designers, which bars cross-domain use; SME's alignment is domain-general. They accept common ground that comparison can alter how things are conceived, and hold that \"re-representation allows relational identicality to arise out of an analogical alignment.\" URL: https://groups.psych.northwestern.edu/gentner/papers/ForbusGentner98.pdf (file for this paper). Read: abstract, discussion, conclusion (about 99k characters fetched).\n\n### 9. The case against similarity as the whole story\n\n**Marcus.** The Algebraic Mind (2001) argues the mind needs operations over variables; I saw only excerpts of its preface and chapter 1 through a search tool (preface: he opposes \"a particular subset of the possible connectionist models\", not connectionism). Primary support: Marcus 1998 shows popular networks \"cannot learn to extend universals outside the training space\" (the glork/frum example); Marcus et al. 1999: three experiments with 7-month-olds, designed so counting, transitional probabilities or simple networks could not succeed, \"suggest that infants can represent, extract, and generalize abstract algebraic rules.\" In the Pothos commentary he says rules and similarity \"are not in genuine conflict.\"\n- URLs: https://www.researchgate.net/publication/13395667_Rethinking_Eliminative_Connectionism (abstract) ; https://pubmed.ncbi.nlm.nih.gov/9872745/ ; https://research.gold.ac.uk/5108/1/S0140525X05000014a.pdf\n- Read: abstracts and excerpts only. I did not obtain the book text.\n\n**Lake and Baroni 2018.** On SCAN, RNNs generalize when test commands are near training commands (\"mix-and-match\") but when systematic composition is needed, as with a new verb \"dax\", \"RNNs fail spectacularly.\" URL: https://arxiv.org/abs/1711.00350. Read: abstract.\n**Lake and Baroni 2023 (Nature).** Humans matched the algebraic standard in 80.7% of cases and handled longer outputs in 72.5%. A standard transformer meta-trained on streams of compositional tasks (MLC) handled longer outputs at 77.8% and reproduced human-like error biases; \"only MLC achieves both the systematicity and flexibility needed for human-like generalization\", against rigid symbolic models and flexible unsystematic networks. Systematicity here arose from meta-training, not from built-in rules. URL: https://www.nature.com/articles/s41586-023-06668-3. Read: abstract and results passages.\n\n### 10. Machine learning's own versions\n\n- **Case-based reasoning (Aamodt and Plaza 1994).** CBR relies on the specific knowledge of earlier concrete cases rather than only on general knowledge: \"A new problem is solved by finding a similar past case, and reusing it in the new problem situation.\" General knowledge may support the cycle from very weak (or none) to very strong, and similar cases may form generalized cases. URL: https://www.iiia.csic.es/~enric/papers/AICom.pdf. Read: abstract, background, cycle section.\n- **Instance-based learning (Aha, Kibler and Albert 1991).** \"Instance-based learning algorithms do not maintain a set of abstractions derived from specific instances\"; extends nearest neighbour, cuts storage with small loss, degrades with attribute noise unless a significance test is added. URL: https://mlanthology.org/mlj/1991/aha1991mlj-instancebased/. Read: abstract only.\n- **Transduction (Gammerman, Vovk and Vapnik 1998).** \"'Transduction' is inference from particular to particular\": classify a test point, not learn a general rule. They note it relates to instance-based learning such as nearest neighbour, but their method \"is not based on the similarities between examples\", using support vectors with confidence values. Vapnik's own books not read. URL: https://arxiv.org/pdf/1301.7375. Read: selected sections (introduction, the transduction-and-induction discussion, Remark 5) of about 32k characters.\n- **Mitchell 1980.** If consistency with training cases is the only criterion, \"a program can never make the inductive leap necessary to classify instances beyond those it has observed\"; unbiased learners \"cannot outperform programs that use rote learning.\" Bias is required. URL: https://www.cs.cmu.edu/~tom/pubs/NeedForBias_1980.pdf. Read: full text (about 15k characters).\n- **No free lunch (Wolpert).** Wolpert 1996 was blocked; I read his 2020 review: under a uniform distribution over induction problems \"all induction algorithms perform equally\"; performance depends on alignment between algorithm and the real world. URL: https://arxiv.org/abs/2007.10928. Read: abstract and parts of the text.\n\n### 11. Language models and analogy\n\n- **Webb, Holyoak and Lu 2023.** GPT-3 on matrix, letter-string, verbal and story analogies: \"a surprisingly strong capacity for abstract pattern induction, matching or even surpassing human capabilities in most settings.\" On Digit Matrices (40 undergraduates) GPT-3 beat the human average on all problem types (odds ratios 1.88, generation; 6.27, multiple choice). URL: https://arxiv.org/pdf/2212.09196. Read: abstract and results excerpts.\n- **Lewis and Mitchell 2024.** Counterfactual letter-string variants (permuted alphabets) were built to separate humanlike abstract reasoning from \"less general processes that rely on similarity to what has been seen in their training data.\" Humans stayed high; the GPT models' performance \"declines sharply\". URL: https://arxiv.org/abs/2402.08955. Read: abstract; accuracy tables unparsed.\n- **Webb, Holyoak and Lu 2025 (PNAS Nexus).** Reply: models \"are also capable of generalizing to these new counterfactual task variants\" (a search summary adds: with code execution; not verified). URL: https://arxiv.org/abs/2404.13070. Read: abstract.\n- **Mitchell 2021.** Following Hofstadter: \"analogy-making is not a rare and exalted form of reasoning, but rather a constant, ubiquitous, and lifelong mode of thinking\"; \"no current AI system is anywhere close to a capability of forming humanlike abstractions or analogies.\" URL: https://arxiv.org/abs/2102.10717. Read: abstract and passages.\n- **Chollet 2019.** The paper says little about analogy (\"analog\" appears five times, mostly historical). Its closing lists \"achieving extreme generalization through strong abstraction\" as a direction. It does say a lookup using \"a locality-sensitive hash function (e.g. nearest neighbor) to map new inputs to previously seen inputs\" gives only local generalization, the machine-learning stage, as against broad generalization. In talks (transcripts), he says intelligence \"is literally sensitivity to abstract analogies\"; value-analogy compares by distance and merges into prototypes (deep learning); program-analogy finds structural isomorphisms (reasoning). URLs: https://arxiv.org/pdf/1911.01547 ; https://joepalermo.github.io/2021/01/10/talk-review-francois-chollet-neurips-2020.html ; https://arcmira.com/watch?v=5QcCeSsNRks. Read: paper searched by keyword; talks via excerpts.\n- **Induction heads (Olsson et al. 2022).** Heads complete [A][B] ... [A] -> [B]; the thesis is that larger models use circuits that \"perform a 'fuzzy' or 'nearest neighbor' version of pattern completion\" where A* is similar to A, accounting for most in-context learning. Causal evidence only for small attention-only models; correlational for larger. URL: https://arxiv.org/abs/2209.11895 and https://transformer-circuits.pub/2022/in-context-learning-and-induction-heads/index.html. Read: abstract and thesis passages.\n- **ICL as kernel regression.** Han et al. (TMLR 2025): Bayesian inference on prompts approaches kernel regression, a weighted sum over similar demonstrations; attention and hidden features match it. URL: https://arxiv.org/abs/2305.12766. Read: abstract. Dasgupta, Grant and Griffiths (ICML 2022): \"standard neural network models are feature-biased and exemplar-based.\" URL: https://arxiv.org/abs/2110.04328. Read: abstract.\n- **2024 to 2026.** Hofmann et al. (arXiv 2024): for variable English adjective nominalizations GPT-J is matched by an exemplar-analogy model and not a rule model (\"the analogical model provides a much better match\"); word frequency effects even on regular forms. URL: https://arxiv.org/abs/2411.07990. Yang et al. (ICML 2025): \"symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens\", then symbolic induction heads and retrieval heads: an emergent symbolic architecture. URL: https://proceedings.mlr.press/v267/yang25c.html. AAAI proceedings (online March 2026), \"The Curious Case of Analogies\": LLMs show \"emerging but limited capabilities in encoding and applying high-level relational concepts\"; success goes with structural alignment between situations. URL: https://ojs.aaai.org/index.php/AAAI/article/view/40414. arXiv 2602.01992: analogy emerges later than memorization and composition, depends on data and optimization, and decomposes into geometric alignment of relational structure plus a \"functor\" applied by attention. URL: https://arxiv.org/html/2602.01992v5. arXiv 2603.05143: \"entities with shared properties become aligned in representation space, enabling property transfer through feature resemblance\"; training order matters (similarity first works, attributes first fails to generalize). URL: https://arxiv.org/pdf/2603.05143. ARC-AGI-2 (Chollet et al., v2 Jan 2026) uses tasks with an unstated rule shown by 2 to 5 demonstration pairs and stresses compositional generalization. URL: https://arxiv.org/pdf/2505.11831. Read: abstracts or search excerpts for all of these (ARC-AGI-2: first pages).\n\n### 12. Relational shift and language (time permitting)\n\nGentner 1988: children's metaphor interpretations by attributes come early; relational responding rises with age while attribute responding does not (abstract). Loewenstein and Gentner 2005: hearing spatial-relation words improved preschoolers' mapping and the benefit lasted 2 days. Christie and Gentner 2014: children under 4 failed relational match-to-sample (AA matches BB), and \"children learn to become adept analogical thinkers, and that language fosters this learning in at least two distinct ways.\" URLs: https://groups.psych.northwestern.edu/gentner/papers/Gentner88b.pdf ; https://pubmed.ncbi.nlm.nih.gov/15893523/ ; https://pubmed.ncbi.nlm.nih.gov/24215433/. Read: abstracts.\n\n### 13. Neuroscience (only where a review concludes clearly)\n\nHobeika et al. 2016 (meta-analysis of 27 experiments): \"The left rostrolateral prefrontal cortex was one of the regions most consistently activated across the studies\"; domain-general and specialized for analogy tasks. Holyoak and Monti 2021 (review): posterior parietal cortex represents first-order relations; rostrolateral PFC is \"apparently central in integrating first-order relations so as to generate and/or evaluate higher-order relations.\" URLs: https://pubmed.ncbi.nlm.nih.gov/27012301/ ; https://pubmed.ncbi.nlm.nih.gov/32762521/. Read: abstracts.\n\n## Part B. Closing, strictly from the sources read\n\n### (a) Rules are built from compared cases, and likeness comes first\n- Experiments: two analogs yield a schema where one does not (Gick and Holyoak: 45% vs 21% pre-hint solutions); comparing two cases roughly doubles rule transfer (48% vs 19%, Gentner et al. 2003); preschoolers pick the relational match 0.60 after comparing two standards, 0.14 after one, 0.13 when apart (Christie and Gentner). Comparison, not mere exposure, is the active ingredient.\n- Models and theory: SEQL/SAGE form rule-like generalizations by alignment; SEQL reproduces the infant ABA/ABB result from 48 sentences; Gentner (1983) and Gentner and Medina place general laws at the abstract end of a continuum that starts with literal similarity. Novices and children begin with overall similarity, adults add category knowledge (Gentner and Medina; Gentner 1988).\n- Categorization and induction: exemplar models classify with no category-level information (Medin and Schaffer, who call it reasoning by analogy); premise-conclusion similarity promotes induction (Heit).\n- Machine learning: instance and case-based learning keep no abstractions; transduction predicts particular from particular; unbiased fitting is no better than rote (Mitchell). GPT-J's morphology generalization fits exemplar analogy; standard networks are exemplar-based; in-context learning is described as nearest-neighbour completion or kernel regression.\n- Reduction claims: Pothos (a rule is similarity on few properties) and Hofstadter (a category is an analogy bundle).\n\n### (b) Likeness is not enough, or is derived from something else\n- Cheap likeness misleads: mere-appearance matches have virtually no predictive use; retrieval favors surface (recall .78 surface vs .44 analogy) while soundness follows structure (4.40 vs 2.80).\n- Theories and causal knowledge: similarity as by-product of coherence (Murphy and Medin); similarity depends on the property projected (Heit); causal models run counter to similarity (Kemp and Tenenbaum); the data in Gelman and Markman fit neither account cleanly (Godwin and Fisher); relevance theory (Medin et al.). Medin, Goldstone and Gentner argue the respects of similarity come from the comparison process itself and treat Murphy and Medin's challenge as serious.\n- Priors over hypotheses: Shepard and Tenenbaum and Griffiths derive similarity from generalization over hypotheses, with priors outside the analysis; overhypotheses make one case enough (Kemp et al.); Mitchell and Wolpert: no induction without bias.\n- Variables and systematicity: Marcus (infants, networks failing outside the training space), Lake and Baroni 2018, Sloman's Criterion S, Ashby and Casale's dissociations, Hahn and Chater (pure similarity and pure rules both inadequate), Penn et al. (relational analogy, not perceptual similarity, marks humans). Lewis and Mitchell: GPT analogy accuracy falls on counterfactual variants; Chollet: nearest-neighbour lookup gives only local generalization.\n- Representation: Chalmers et al.: what counts as alike is constructed during mapping, not given.\n\n### (c) Accounts on which the two grow together\n- Gentner and Medina: \"similarities without rules are empty, rules without similarities are blind\"; rules form by progressive alignment and are applied by alignment.\n- Hybrids: Hahn and Chater, Smith et al., RULEX and ATRIUM (rules plus exceptions or exemplars, with attention shifting between them), Brooks and Hannah (commentary: \"instantiated rules and abstract analogy\").\n- Bayesian accounts: Kemp and Tenenbaum (\"each of these traditions needs the other\"; similarity as one prior); Tenenbaum and Griffiths unify Shepard and Tversky; Kemp et al.: abstractions learned from cases then constrain new cases.\n- Learning of bias: Lake and Baroni 2023 (systematicity learned by meta-learning); Yang et al. (symbol-like mechanisms emerge inside language models); Chollet's two analogies (distance-based and structure-based).\n- Mutual influence of perception and mapping: Forbus et al. concede comparison can alter how things are conceived, which Chalmers et al. press.\n- Murphy and Medin: theory supplies \"the constraints missing from the similarity explanation\" rather than replacing it.\n\nNet reading: step 1 (a rule can come from compared cases) is backed by experiments and models, as one route and not the only one. Step 2 (comparison rests on taking cases as alike) is backed for novices, for exemplar and instance-based learning, and for much in-context learning in language models, but contested on what fixes the likeness (relational structure, theories, priors). No source I read shows that induction reduces to analogy without remainder; the strongest reductions (Pothos, Hofstadter) were challenged (Marcus, Ashby and Casale, Hahn).\n\n## Part C. What I could not verify\n\n- Surfaces and Essences: book not read; quotes second-hand through a blog; no primary definition of analogy found.\n- Hofstadter's Stanford lecture text (page forbidden); the \"common essence\" wording is unverified.\n- Gentner 1983: only a scanned OCR copy plus a clean abstract; Gentner 1988, Gick and Holyoak 1980 and Rosch's papers not read beyond abstracts or summaries.\n- Rips 1975, Osherson et al. 1990, Gelman and Markman 1986: not fetched; read through reviews and a 2015 paper.\n- Smith, Langston and Nisbett 1992: abstract and search excerpts only (journal PDF blocked).\n- Medin et al. 2003, Nosofsky 1986, RULEX and ATRIUM: abstracts only.\n- Kemp et al. 2007: conference version, not the journal text.\n- Marcus 2001: no publisher text; excerpts only, via a search tool. Vapnik's books not read; Wolpert 1996 blocked (2020 review used).\n- Chollet: the \"analogy-making is the engine of abstraction\" idea appears only in talk transcripts I saw as excerpts; neither the 2019 paper nor the ARC Prize 2024 report states it.\n- Lewis and Mitchell 2024: accuracy table columns not parsed; Webb 2025 code-execution detail from a search summary.\n- Hofmann et al.: venue and later versions not checked. Webb et al. 2023: arXiv version, not the Nature Human Behaviour text. 2026 items (AAAI proceedings paper, arXiv 2602.01992, 2603.05143, 2602.07794): abstracts or excerpts only.\n- Penn et al.: only the early sections read; ARC-AGI-2 paper: first pages; Hayes and Heit: partly read.\n- A 2026 PNAS letter on human-LLM reasoning alignment was blocked and is not used.\n"}