Surfaces and Essences

by Douglas Hofstadter

  Page 443an elegant and marvelous trick found in the miracle of Analysis… Leibniz (1702), p. 357.

  Page 454I saw that mathematics was split up… Einstein, cited by Banesh Hoffmann (1972), p. 8.

  Page 461That he may sometimes have missed the target… Planck, quoted in Stehle (1994), p. 152.

  Page 467That a principle of such broad generality… Einstein (1920), p. 17.

  Page 473With his instinctive sense of cosmic unity he now tosses off… Hoffmann (1972), p. 81.

  Page 477In his paper of 1905 Einstein said that all energy… Hoffmann (1972), p. 81.

  Page 495[The new principle] had artistic unity… Hoffmann (1972), p. 113.

  Page 498I first had the decisive idea of the analogy… Einstein, quoted in Stachel (2001), p. 255.

  Page 500What made my reputation as a mathematician is… Villani (2012), p. 146–147.

  Page 501Yet when we see how shaky were the ostensible foundations… Hoffmann (1972), pp. 127–128.

  Page 501Mr. Einstein is one of the most original minds I have known… Hoffmann (1972), p. 99.

  Page 501A contemporary of Johann Sebastian Bach once said… David and Mendel (1966), p. 222.

  Page 502Good mathematicians see analogies between theorems or theories… Ulam (1976), p. 203.

  Epidialogue

  Page 506categories allow us to treat new things as if… Spalding and Murphy (1996), p. 525

  Page 506analogy is what allows us… Gick and Holyoak (1983), p. 1.

  Page 507Analogy pervades all our thinking… Polya (1957), p. 37.

  Page 507When faced with something new, we cannot help… Oppenheimer (1956), p. 129.

  Page 507Analogies and metaphors are pervasive… Gentner and Clement (1988), p. 307.

  Page 507Analogy is ubiquitous in human thinking… Thagard, Holyoak, Nelson and Gochfeld (1990), p. 259.

  Page 509The trips we take in the world of mathematics… Alain Connes, in the short film Mathématiques, un dépaysement soudain, produced in November of 2011 by Raymond Depardon and Claudine Nougaret at the Fondation Cartier in Paris.

  Page 509a mobile army of metaphors… Nietzsche (1873), p. 46.

  Page 509Whoever first compared a woman to a rose was a poet… Georges Courteline.

  Page 509Henri Poincaré described mathematics as… Poincaré (1908), p. 29.

  Page 523the ability to separate things according to their natural divisions… Plato (1950), 265d–265e.

  BIBLIOGRAPHY

  We have divided our bibliography into eleven sections, one for each of the ten main parts of our book, with one extra section at the beginning providing a list of references that have global relevance to the ideas that we are exploring in our book. Since some of the works cited below are relevant to more than just one chapter of our book, certain entries appear in more than one section of the bibliography. We have preceded each section with a few very general comments about the books and articles listed in it.

  General

  We open our list of references with a set of books that are relevant to every aspect of our own work. In particular, the book by Fauconnier and Turner, like ours, places conceptual mapping at the center of cognition and also uses a rich and highly variegated array of examples to flesh out the key themes. The volume by Holyoak and Thagard and the anthology edited by Gentner, Holyoak, and Kokinov have become standard references for the field of analogy, seen from a cognitive-science perspective. Both Helman’s compilation and that by Vosniadou and Ortony tackle analogy from a number of angles, the former placing it in an interdisciplinary perspective and the latter focusing on links to similarity. Although these two works are not recent, many of their chapters are still highly relevant. Murphy’s book is an excellent resource on categorization, while Lakoff and Johnson’s study has greatly enhanced the recognition of the systematic role played by metaphor in human thought. Lastly, Sander’s book and that by Hofstadter and the Fluid Analogies Research Group paved the way for the present volume, although they are somewhat more traditionally academic in style.

  Fauconnier, Gilles and Mark Turner (2002). The Way We Think: Conceptual Blending and the Mind’s

  Hidden Complexities. New York: Basic Books.

  Gentner, Dedre, Keith J. Holyoak, and Boicho N. Kokinov, editors (2001). The Analogical Mind: Perspectives from Cognitive Science. Cambridge, Mass.: MIT Press (Bradford Books).

  Helman, David H., editor (1988). Analogical Reasoning: Perspectives of Artificial Intelligence, Cognitive Science, and Philosophy. Boston: Kluwer Academic Publishers.

  Hofstadter, Douglas and the Fluid Analogies Research Group (1995). Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought. New York: Basic Books.

  Holyoak, Keith J. and Paul Thagard (1995). Mental Leaps. Cambridge, Mass.: MIT Press (Bradford Books).

  Lakoff, George and Mark Johnson (1980). Metaphors We Live by. Chicago: University of Chicago Press.

  Murphy, Gregory L. (2002). The Big Book of Concepts. Cambridge, Mass.: MIT Press.

  Sander, Emmanuel (2000). L’Analogie, du naïf au créatif: Analogie et catégorisation. Paris: L’Harmattan.

  Vosniadou, Stella and Andrew Ortony, editors (1989). Similarity and Analogical Reasoning. New York: Cambridge University Press.

  Prologue

  The selections by Alberic of Monte Cassino, Bachelard, Bartha, Bouveresse, Hobbes, Lloyd, Nietzsche and Plato deal with the question of analogy’s reliability as a mode of thinking. The far-ranging studies of chairs by Danto and Lévy, by Fiell and Fiell, and by Samaras, as well as the large collections of typefaces by Weinberger and by Jaspert, Berry, and Johnson, are aimed at revealing the astonishing variety of the categories in question. The article by Anderson stresses the psychological value of categorization, while that by Tversky and those by Medin, Goldstone, Gentner and colleagues explore the psychological process of observing similarity.

  Alberic of Monte Cassino (1973). “The Flowers of Rhetoric”. In Joseph M. Miller, Michael H. Prosser, and Thomas W. Benson (eds.), Readings in Medieval Rhetoric. Bloomington: Indiana University Press.

  Anderson, John R. (1991). “The adaptive nature of human categorization”. Psychological Review, 98, pp. 409–429.

  Bachelard, Gaston (1934). The Formation of the Scientific Mind: A Contribution to a Psychoanalysis of Objective Knowledge, translated by Mary McAllester Jones. Manchester: Clinamen Press.

  Bartha, Paul (2010). By Parallel Reasoning: The Construction and Evaluation of Analogical Arguments. New York: Oxford University Press.

  Bouveresse, Jacques (1999). Prodiges et vertiges de l’analogie. Paris: Raisons d’agir.

  Danto, Arthur C. and Jennifer Lévy (1988). 397 Chairs. New York: Harry N. Abrams.

  Fiell, Charlotte and Peter Fiell (1997). 1000 Chairs. Cologne: Benedikt Taschen Verlag.

  Goldstone, Robert L. (1994). “Similarity, interactive activation, and mapping”. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20, pp. 3–28.

  Goldstone, Robert L. and Son, Ji Yun (2005). “Similarity”. In Keith J. Holyoak and Robert G. Morrison (eds.), Cambridge Handbook of Thinking and Reasoning. New York: Cambridge University Press, pp. 13–36.

  Hobbes, Thomas (1651). Leviathan. Reissued by Cambridge University Press (New York), 1996.

  Hofstadter, Douglas (1985). “Analogies and roles in human and machine thinking”. In Douglas Hofstadter, Metamagical Themas: Questing for the Essence of Mind and Pattern. New York: Basic Books, pp. 547–603.

  Jaspert, W. Pincus, W. Turner Berry, and A. F. Johnson (1983). The Encyclopædia of Type Faces. Poole, Dorset: Blandford Press.

  Lloyd, G. E. R. (1966). Polarity and Analogy: Two Types of Argumentation in Early Greek Thought. New York: Cambridge University Press.

  Medin, Douglas L., Robert L. Goldstone, and Dedre Gentner (1993). “Respects for similarity”. Psychological Review, 100, pp. 254–278.

  Nietzsche, Friedrich (1873). “On Truth and Lies in a Nonmoral Sense”. In The Porta
ble Nietzsche, translated by Walter Kaufmann, 1976 edition. New York: Viking Press.

  Plato (1977). The Sophist. In Jacob Klein (ed.), Plato’s Trilogy. Chicago: University of Chicago Press.

  ————— (2008). The Republic, translated by R. E. Allen. New Haven: Yale University Press. Poincaré, Henri (1908). Science et méthode. Paris: Flammarion.

  Samaras, Lucas (1970). Chair Transformation. New York: Pace.

  Selvinsky, Il’ya L. (1920). “К вопросу о русской речи”. In Il’ya L. Selvinsky, Selected Works. Leningrad: Sovetskii Pisatel’ (Biblioteka Poeta, Bol’šaya seriya), 1972.

  Sternberg, Robert J. (2005). Barron’s Miller Analogies Test. Hauppauge, New York: Barron’s Educational Series.

  Tversky, Amos (1977). “Features of similarity”. Psychological Review, 84, pp. 327–352.

  Weinberger, Norman (1971). Encyclopedia of Comparative Letterforms for Artists & Designers. New York: Art Directions.

  Chapter 1

  The selections by Carey, Gelman, Gentner, Goldin-Meadows, Keil, Malt, Mandler, Oakes, Pinker, Prinz, Rakison, and Wolff are important works on conceptual development and language, and are relevant throughout the chapter. The pieces by Bruner, Collins, Hull, and Smoke explain the classical approach to categorization, while those by Barsalou, Glucksberg, Goldstone, Hampton, Lamberts, McCloskey, Medin, Nosofsky, Osherson, Pothos, Richard, and Smith, as well as their colleagues, represent a more contemporary approach, which was launched largely by the article by Wittgenstein. The works by Boroditsky, Gibbs, Johnson, and Lakoff and Turner are relevant to this chapter’s sections on the metaphorical usage of words. Duvignau’s article concerns semantic approximations by children, and that by Atran and Medin concerns the influence of culture on categorization. The article by Ma is about syntactic analogies, while that by Huth and colleagues investigates the neural substrate of semantic spaces. Finally, Kaluża’s monograph is an in-depth study of the categories denoted by the definite and indefinite articles in English.

  Aitchison, Jean (1994). Words in the Mind: An Introduction to the Mental Lexicon (second edition). Oxford: Blackwell Publishers.

  Atran, Scott and Douglas L. Medin (2008). The Native Mind and the Cultural Construction of Nature. Cambridge, Mass.: MIT Press.

  Barsalou, Lawrence W. (1985). “Ideals, central tendency, and frequency of instantiation as determinants of graded structures in categories”. Journal of Experimental Psychology: Learning, Memory and Cognition, 11, pp. 629–654. Barsalou, Lawrence W. and Douglas L. Medin (1986). “Concepts: Static definitions or context-dependent representations?” Cahiers de psychologie cognitive, 6, pp. 187–202.

  Boroditsky, Lera (2000). “Metaphoric structuring: Understanding time through spatial metaphors”. Cognition, 75 (1), pp. 1–28.

  Bruner, Jerome, Goodnow, Jacqueline J. and Austin, George A. (1956). A Study of Thinking. New York: John Wiley and Sons.

  Carey, Susan (2009). The Origin of Concepts. New York: Oxford University Press.

  Collins, Allen M. and M. Ross Quillian (1969). “Retrieval time from semantic memory”. Journal of Verbal Learning and Verbal Behavior, 8, pp. 240–247.

  Duvignau, Karine (2003). “Métaphore verbale et approximation”. Revue d’intelligence artificielle, special issue 5–6, pp. 869–881.

  Duvignau, Karine, Marion Fossard, Bruno Gaume, Marie-Alice Pimenta, and Élie Juliette (2007). “Semantic approximations and flexibility in the dynamic construction and ‘deconstruction’ of meaning”. Linguagem em Discurso, 7 (3), pp. 371–389.

  Duvignau, Karine and Bruno Gaume (2005). “Linguistic, psycholinguistic and computational approaches to the lexicon: For early verb-learning”. Cognitive Systems, 6 (1), pp. 255–269.

  Garrod, Simon and Anthony Sanford (1977). “Interpreting anaphoric relations: The integration of semantic information while reading”. Journal of Verbal Learning and Verbal Behavior, 16, pp. 77–79.

  Gelman, Susan A. (2005). The Essential Child: Origins of Essentialism in Everyday Thought. Oxford: Oxford University Press.

  Gentner, Dedre (2003). “Why we’re so smart”. In Dedre Gentner and Susan Goldin-Meadow (eds.), Language in Mind: Advances in the Study of Language and Thought. Cambridge, Mass.: MIT Press, pp. 195–235.

  Gentner, Dedre and Susan Goldin-Meadow, editors (2003). Language in Mind: Advances in the Study of Language and Thought. Cambridge, Mass.: MIT Press.

  Gibbs, Raymond W. (1994). The Poetics of Mind. New York: Cambridge University Press. Hampton, James A. (1979). “Polymorphous concepts in semantic memory”. Journal of Verbal Learning and Verbal Behavior, 18, pp. 441–461.

  Hobbes, Thomas (1651). Leviathan, revised student edition. Reissued in 1996 by Cambridge University Press (New York).

  Hofstadter, Douglas R. (2001). “Analogy as the Core of Cognition”. In Dedre Gentner, Keith J. Holyoak, and Boicho N. Kokinov (eds.), The Analogical Mind: Perspectives from Cognitive Science. Cambridge, Mass.: MIT Press (Bradford Books).

  Hull, Clark L. (1920). “Quantitative aspects of the evolution of concepts”. Psychological Monographs, XXVIII (1.123), pp. 1–86.

  Huth, Alexander G., Shinji Nishimoto, An T. Vu, and Jack L. Gallant (2012). “A continuous semantic space describes the representation of thousands of object and action categories across the human brain”. Neuron, 76 (6), pp. 1210–1224.

  Kałuża, Henryk (1976). The Articles in English. Warsaw: Panstwowe Wydawnictwo Naukowe.

  Keil, Frank C. (1979). Semantic and Conceptual Development: An Ontological Perspective. Cambridge. Mass.: Harvard University Press.

  ————— (1989). Concepts, Kinds, and Cognitive Development. Cambridge, Mass.: Harvard University Press.

  Lakoff, George (1987). Women, Fire, and Dangerous Things: What Categories Reveal about the Mind. Chicago: University of Chicago Press.

  Lamberts, Koen and David Shanks (1997). Knowledge, Concepts, and Categories. Cambridge, Mass.: MIT Press.

  Ma, Yulei (2011). Analogy and Its Use in Grammatical Constructions: A Cognitive–Functional Linguistic Perspective. Saarbrücken: Verlag Dr. Müller.

  Manea, Norman (1992). Felix Culpa. New York: Grove Press.

  Malt, Barbara and Phillip Wolff (2010). Words and the Mind: How Words Capture Human Experience. Oxford: Oxford University Press.

  Mandler, Jean M. (2004). The Foundations of Mind: Origins of Conceptual Thought. Oxford: Oxford University Press.

  Markman, Ellen M. (1991). Categorization and Naming in Children: Problems of Induction. Cambridge, Mass.: MIT Press (Bradford Books).

  McCloskey, Michael E. and Sam Glucksberg (1978). “Natural categories: Well defined or fuzzy sets?” Memory and Cognition, 6, pp. 462–472.

  Medin, Douglas L. and M. M. Schaffer (1978). “A context theory of classification learning”. Psychological Review, 85, pp. 207–238.

  Mervis, Carolyn B., Jack Catlin, and Eleanor Rosch (1976). “Relationships among goodness of example, category norms, and word frequency”. Bull. of the Psychonomic Soc., 7, pp. 283–294.

  Nosofsky, Robert M. (1986). “Attention, similarity, and the identification–categorization relationship”. Journal of Experimental Psychology: General, 115, pp. 39–57.

  Osherson, Daniel and Edward E. Smith (1981). “On the adequacy of prototype theory as a theory of concepts”. Cognition, 9, pp. 35–58.

  Pinker, Steven (1997). How the Mind Works. New York: Norton.

  ————— (1999). Words and Rules: The Ingredients of Language. New York: Basic Books.

  ————— (2007). The Stuff of Thought. New York: Viking.

  Poitrenaud, Sébastien, Jean-François Richard, and Tijus, Charles A. (2005). “Properties, categories, and categorisation”. Thinking and Reasoning, 11, pp. 151–208.

  Pothos, Emmanuel M. and Andy J. Wills (2011). Formal Approaches in Categorisation. New York: Cambridge University Press.

  Prinz, Jesse J. (2002). Furnishing the Mind: Concepts and their Perceptual Basis, Cambridge, Mass.: MIT Press.

  Rakison, David H. and
Lisa M. Oakes (2008). Early Category and Concept Development. New York: Oxford University Press.

  Rosch, Eleanor (1975). “Cognitive representations of semantic categories”. Journal of Experimental Psychology: General, 104, pp. 192–233.

  ————— (1976). “Classifications d’objets du monde réel: Origines et représentations dans la cognition”. Bulletin de psychologie, special issue edited by Stéphane Ehrlich and Endel Tulving, pp. 242–250.

  ————— (1978). “Principles of categorization”. In Eleanor Rosch and Barbara Lloyd (eds.), Cognition and Categorization. Hillsdale, New Jersey: Lawrence Erlbaum Associates, pp. 27–48.

  Rosch, Eleanor and Carolyn B. Mervis (1975). “Family resemblances: Studies in the internal structure of categories”. Cognitive Psychology, 7, pp. 573–605.

  Rosch, Eleanor, Carolyn B. Mervis, Wayne D. Gray, David M. Johnson, and Penny Boyes Braem (1976). “Basic objects in natural categories”. Cognitive Psychology, 8, pp. 382–439.

  Ross, James F. (1981). Portraying Analogy. New York: Cambridge University Press.

  Smith, Edward E. and Douglas L. Medin (1981). Categories and Concepts. Cambridge Mass.: Harvard University Press.

  Smoke, Kenneth Ludwig (1932). “An objective study of concept formation”. Psychological Monographs, XLII (191), pp. 1–46.

  Stevens, Wallace (1923). Harmonium. New York: Alfred E. Knopf.

  Turner, Mark (1987). Death is the Mother of Beauty: Mind, Metaphor, Criticism. Chicago: University of Chicago Press.

  Wittgenstein, Ludwig (1953). Philosophical Investigations. Oxford: Basil Blackwell.

  Woo-Kyoung, Ahn, Robert L. Goldstone, Bradley C. Love, Arthur B. Markman and Phillip Wolff (2005). Categorization Inside and Outside the Laboratory: Essays in Honor of Douglas L. Medin. Washington, D.C.: American Psychological Association.

  Chapter 2

  The books by Aitchison, Braitenberg, Itkonen, Malt and Wolff, and Pinker, as well as the article by Gentner and that by Hofstadter, are relevant to the chapter as a whole. The humorous volumes by Chiflet and Whistle (actually just one person), as well as the books by Glucksberg and by Langlotz, deal with idiomatic expressions; Brézin-Rossignol, Schank, and Visetti consider the categories of proverbs and fables, while Benserade, La Fontaine, Morvan de Bellegarde and Phædrus are relevant to our section on Æsop’s fable “The Fox and the Grapes”. Festinger’s book is a classic on cognitive dissonance. The books by Carroll and by Sapir deal with the Sapir–Whorf hypothesis, and the volume by Atran and Medin covers the way that culture channels human language and thought. Finally, the books by Flynn and by Sternberg tackle the topic of intelligence.