Readings in Analogy-Making

Posted on December 20, 2007 by Peter Turney

Here are some links to interesting books, papers, people, and websites related to analogy-making and metaphor. If I’m missing a link that you would recommend, please leave a comment. Look here for a list of quotations about analogy-making and metaphor. There is no particular order to these lists.


Books

Papers

People

Websites

Filed under: Philosophy of Mind, Semantics | Tagged: , ,

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12 Responses to “Readings in Analogy-Making”

  1. Stergos D. Afantenos, on December 20th, 2007 at 7:26 pm Said:

    Great list Peter! I personally find it very interesting. Although I am familiar with more or less the research of the aforementioned people (or at least struggling to get familiar), some of the papers you mention were unknown to me. I guess that Mitchell’s and French’s books would be relevant to the list of books (Analogy Making as Perception and The Subtlety of Sameness respectively).

    Thanks again :)

  2. lemire, on December 20th, 2007 at 8:26 pm Said:

    There are two French-speaking researchers (at least) in your list. I wonder whether one’s natural languages might bring a different view point on analogies. I mean to say that if I know both French and English, whereas you know English and Spanish, will we think of the same analogies. Are analogies language-independent?

  3. Peter Turney, on December 20th, 2007 at 9:24 pm Said:

    Are analogies language-independent?

    I suppose that some analogies are and some aren’t. For example, the word analogy “savoir:nom::connaître:personne” does not translate well from French to English, so it seems to be language-dependent, whereas “dog:bark::cat:meow” translates as “chien:aboyer::chat:miauler”. It’s easy to make a language-dependent analogy that depends on spelling, such as “smile:smiling::rate:rating”. But this answer is rather shallow. I would guess that deeper analogies (analogies that are not based on superficial aspects of words; analogies that are based on concepts), such as the scientific analogy between electricity and hydrodynamics, are independent of language (that is, they require some language, but not one particular language). This leads us to the Sapir-Whorf hypothesis. Gentner is interested in both analogy-making and the Sapir-Whorf hypothesis, but I don’t remember whether she discussed their relation to each other.

  4. Peter Turney, on December 20th, 2007 at 9:39 pm Said:

    I guess that Mitchell’s and French’s books would be relevant to the list of books.

    Added.

    Thanks again.

    You’re welcome!

  5. James Bowery, on December 23rd, 2007 at 12:15 am Said:

    Has anyone investigated finitary relational similarity in cognition? Taking an example from Wikipedia’s article on relations a triadic analogy given the relation “X thinks that Y likes Z” might be stated as something like “Alice is to Bob and Denise as Charles is to Alice and Bob.”

    Generalizing to finitary relations could provide the link to Tom Etter’s correction of Russell’s Relation Arithmetic I mentioned quite some time ago ago here. In fact, the above example is a good match for Etter’s proof that Russel’s definition of relation number is inadequate since their composition becomes problematic under Russell’s definition where their domains overlap.

  6. Peter Turney, on December 23rd, 2007 at 10:22 am Said:

    Has anyone investigated finitary relational similarity in cognition?

    The proportional analogy A:B::C:D, “A is to B as C is to D”, can be interpreted as saying that the set of relations between A and B, {R1(A,B), R2(A,B), R3(A,B), … }, is similar (or identical) to the set of relations between C and D. This could be generalized to triadic relations by interpreting A:B:C::D:E:F as saying that the set of triadic relations for A, B, and C, {R1(A,B,C), R2(A,B,C), R3(A,B,C), … }, is similar to the set of triadic relations for D, E, and F.

    In traditional logic (predicate calculus), triadic relations can be reduced to dyadic relations, but Peirce believed that some triadic relations cannot be reduced. This is an issue I’ve been thinking about a lot recently, but I haven’t reached any conclusions.

    http://plato.stanford.edu/entries/peirce/#triad
    http://plato.stanford.edu/entries/peirce/#red
    http://www.helsinki.fi/science/commens/terms/thirdness.html

  7. James Bowery, on December 23rd, 2007 at 4:07 pm Said:

    Perhaps also relevant to Pierce’s obsession with triads might be gleaned from Etter’s unpublished paper “Three Place Identity“, the abstract for which reads:

    In this paper it will be shown that all of mathematics can be expressed in terms of relative identity when this concept is formalized as a three-place predicate. My focus here will be on the proof of this theorem, though I’ll also take a brief look at how three-place identity might help to expand the horizons of science, which is the main topic of a longer paper, Membership and Identity.

    Etter describes the three place identity as equivalent to the natural langauge statement: “y and z are the same in the way that matters to x.”

  8. Kevembuangga, on December 24th, 2007 at 10:31 am Said:

    Like it’s the case with the modal logics, I think Peirce is trying to “stuff in” his personal metaphysics into the logic apparatus. Though it is perfectly OK to have whatever metaphysic inclinations you would like, the “logic engine” is probably the wrong place to introduce such idiosyncratic biases. The logic should be free of whatever “gimmick” of disputable interest and be aimed only (IMHO) at navigating any space of concepts, such as to allow to also scrutinize the metaphysical biases.

    As for the irreducibility of thirdness (much more clearly exemplified by Tom Etter than by Peirce), I don’t really believe it’s an irreducibility but rather more a matter of technical convenience for some calculations, otherwise that would go against the proven equivalence of curried versus non-curried functions. This is also true for any other arity, many computations look more understandable when given their “natural” number of arguments rather than chopped up into closures and thunks for technical reasons.

    Finally, though analogies are indeed a key problem, I am not sure they are the best starting point to “bootstrap” some significant progress in AI; they are awfully difficult to pin down even informally. I would see the concept formation / concept representation problem as a more seminal “entry point”.

  9. Peter Turney, on December 24th, 2007 at 11:45 am Said:

    Like it’s the case with the modal logics, I think Peirce is trying to “stuff in” his personal metaphysics into the logic apparatus.

    I think you’re wrong about Peirce. He used graph structures to represent his logics, and his interest in thirdness was strongly encouraged by (and perhaps originated from) the fact that graphs with at most two edges (links) per vertex (node) can only form lines, whereas graphs with at most three edges per vertex can approximate arbitrary graph structures:

    “It is highly proper that Secondness should be searched to its very bottom. Thus only can the indispensableness and irreducibility of thirdness be made out, although for him who has the mind to grasp it, it is sufficient to say that no branching of a line can result from putting one line on the end of another.” (A Letter to Lady Welby)

    Contrary to what you suggest, it seems that Peirce was trying to “stuff in” his logical apparatus into his metaphysics. In any case, thinking about thirdness is a good antidote to the obsession with secondness that is built into our culture.

    As for the irreducibility of thirdness (much more clearly exemplified by Tom Etter than by Peirce), I don’t really believe it’s an irreducibility but rather more a matter of technical convenience for some calculations …

    Peirce’s Reduction Thesis is the thesis that all relations may be constructed from triadic relations alone, whereas monadic and dyadic relations alone are not sufficient. Increasingly stronger formal proofs of the Reduction Thesis have been given by Herzberger (1981), Burch (1991), and Correia and Pöschel (2006).

  10. Peter Turney, on December 24th, 2007 at 12:31 pm Said:

    Finally, though analogies are indeed a key problem, I am not sure they are the best starting point to “bootstrap” some significant progress in AI; they are awfully difficult to pin down even informally.

    This is why I like the SAT multiple-choice analogy questions: they help to “pin down” those slippery analogies. More generally, I am attracted to Psychometric AI, the idea of using psychometrics as a guide to AI research.

    An interesting aside: Albert Tucker and Richard Harshman both developed tensor decompositions for psychometrics. Tucker was Marvin Minsky’s PhD supervisor and Harshman is one of the inventors of Latent Semantic Analysis.

  11. James Bowery, on December 30th, 2007 at 2:29 pm Said:

    More generally, I am attracted to Psychometric AI, the idea of using psychometrics as a guide to AI research.

    You may be interested in the effort, published this month, by Legg and Hutter to formalize their survey of definitions of natural intelligence:

    http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3329v1.pdf

  12. Stergos D. Afantenos, on July 5th, 2008 at 11:51 am Said:

    I am currently reading Emmanuel Sander’s very nicely written book L’analogie, du naïf au créatif : analogie et catégorisation (yes, it is in French) and I think that it would merit being at your list with books on Analogies.

    Rather interestingly, D. R. Hofstadter seems to be working with Emmanuel Sander on a book.

    Stergos D. Afantenos

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