The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics

Mathematical Reasoning: Analogies, Metaphors, and Images

Volumn , Issue , 2013, Pages 21-90

  Lakoff, George ^a   Núñez, Rafael E ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

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EID: 85061659351     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (66)

1. Gentner, D., & Gentner, D. R. (1982). Flowing waters or teeming crowds: Mental models of electricity. In D. Gentner & A. L. Stevens (Eds.), Mental models (pp. 99-129). Hillsdale, NJ: Lawrence Erlbaum Associates
2. Gibbs, R. (1994). The poetics of mind: Figurative thought, language, and understanding. Cambridge, England: Cambridge University Press
3. Johnson, M. (1987). The body in the mind: The bodily basis of meaning, reason and imagination. Chicago: University of Chicago Press
4. Johnson, M, (Ed.). (1981). Philosophical perspectives on metaphor. Minneapolis: University of Minnesota Press
5. Lakoff, G. (1993). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor and thought (2nd ed., pp. 202-251). Cambridge, England: Cambridge University Press
6. Lakoff, G., Johnson, M. (1980). Metaphors we live try. Chicago and London: University of Chicago Press
7. Lakoff, G., & Turner, M. (1989). More than cool reason: A field guide to poetic metaphor. Chicago and London: University of Chicago Press
8. Reddy, M. (1979). The conduit metaphor. In A. Ortony (Ed.), Metaphor and thought (pp. 284-324). Cambridge, England: Cambridge University Press
9. Sweetser, E. (1990). From etymology to fmigmatics: Metaphorical and cultural aspects of semantic structure. Cambridge, England: Cambridge University Press
10. Talmy, L. (1988). Force dynamics in language and cognition. Cognitive Science, 12, 49-100
11. Turner, M. (1991). Reading minds: The study of English in the age of cognitive science. Princeton, NJ: Princeton University Press
12. Turner, M. (1996). The literary mind. Oxford: Oxford University Press
13. Turner, M., & Fauconnier, G. (1995). Conceptual integration and formal expression. Journal of Metaphor and Symbolic Activity, 10(3), 183-204
14. Winter, S. (1989). Transcendental nonsense, metaphoric reasoning and the cognitive stakes for law. University of Pennsylvania Law Review, 137
15. Lakoff (1987) is a survey of categorization research up to the mid-1980s. The papers by Rosch are the classics in prototype theory
16. Barsalou, L. W. (1983). Ad-hoc categories. Memory and Cognition, 11, 211-227
17. Barsalou, L. W. (1984). Determination of graded structures in categories. Psychology Department, Emory University, Atlanta, GA
18. Brugman, C. (1981). Story of 'over. "Master's thesis, Unversity of California, Berkeley. Published by the Indiana University Linguistics Club
19. Kay, P. (1983). Linguistic competence and folk theories of language: Two English hedges. Proceedings of the Ninth Annual Meeting of the Berkeley Linguistics Society (pp. 128-137). Berkeley: Berkeley Linguistics Society
20. Kay, P., & McDaniel, C. (1978). The linguistic significance of the meanings of basic color terms. Language, 54, 610-646
21. Lakoff, G. (1972). Hedges: A study in meaning criteria and the logic of fuzzy concepts. Papers from the Eighth Regional Meeting, Chicago Linguistic Society (pp. 183-228). Chicago: Chicago Linguistic Society. Reprinted in Journal of Philosofjhical Logic, 2 (1973) pp. 458-508
22. Lakoff, G. (1987). Women, fire, and dangerous things: What categories reveal about the mind. Chicago and London: University of Chicago Press
23. McNeill, D., & Freiberger, P. (1993). Fuzzy logic. New York: Simon & Schuster
24. Rosch, E. (E. Heider). (1973). Natural categories. Cognitive Psychology, 4, 328-350
25. Rosch, E. (1975a). Cognitive reference points. Cognitive Psychology, 7, 532-547
26. Rosch, E. (1975b). Cognitive representations of semantic categories. Journal of Experimental Psychology: General, 104, 192-233
27. Rosch, E. (1977). Human categorization. In N. Warren (Ed.), Studies in cross-cultural psychology. London: Academic Press
28. Rosch, E. (1978). Principles of categorization. In E. Rosch & B. B. Lloyd (Eds.), Cognition and categorization (pp. 27-48). Hillsdale, NJ: Lawrence Erlbaum Associates
29. Rosch, E. (1981). Prototype classification and logical classification: The two systems. In E. Scholnick (Ed.), New trends in cognitive representation: Challenges to Piaget's theory (pp. 73-86). Hillsdale, NJ: Lawrence Erlbaum Associates
30. Rosch, E., & Lloyd, B. B. (1978). Cognition and categorization. Hillsdale, NJ: Lawrence Erlbaum Associates
31. Smith, E. E., & Medin, D. L. (1981). Categories and concepts. Cambridge, MA: Harvard University Press
32. Taylor, J. (1989). Linguistic categorization: Prototypes in lingustic theory. Oxford: Clarendon Press
33. Wittgenstein, L. (1953). Philosophical investigations. New York: Macmillan
34. Zadeh, L. (1965). Fuzzy sets. Information and Control, 8, 338-353
35. Lakoff (1987) contains a survey of evidence for the fundamental embodiment of mind up to 1985. Johnson (1987) discuss the embodiment of mind extensively from a philosophical perspective
36. Damasio, A. (1994). Descartes' error: Emotion, reason and the human mind. New York: Putnam
37. Edelman, G. (1992). Bright air, brilliant fire: On the matter of the mind. New York: Basic Books
38. Nunez, R. E. (1995). What brain for God's-eye? Biological naturalism, Ontological objectivism, and Searle. Journal of Consciousness Studies, 2(2), 149-166
39. Nunez, R. E. (1997). Eating soup with chopsticks: Dogmas, difficulties, and alternatives in the study of conscious experience. Journal of Consciousness Studies, 4(2), 143-166
40. Regier, T. (1996). The human semantic potential. Cambridge, MA: MIT Press
41. Thelen, E. (1995). Time-scale dynamics and the development of an embodied cognition. In R. F. Port & T. van Gelder (Eds.), Mind as motion: Explorations in the dynamics of cognition (pp. 69-100). Cambridge, MA: MIT Press
42. Varela, F., Thompson, E., & Rosch, E. (1991). The embodied mind. Cambridge, MA: MIT Press
43. Aspray, W., & Kitcher, P. (Eds.). (1988). History and philosophy of modem mathematics. Minneapolis: University of Minnesota Press
44. Barwise, & Moss, L. (1991). Hypersets. The Mathematical Intelligencer, 13(4), 31-41
45. Chiu, M. (1996). Building mathematical understanding during collaboration. Unpublished dissertation, University of California, Berkeley
46. Davis, P. J., & Hersh, R. (1981). The mathematical experience. Boston: Birkhauser
47. Hersh, R. (1986). Some proposals for reviving the philosophy of mathematics. In T. Tymoczco (Ed.), New directions in the philosophy of mathematics (pp. 9-28). Boston: Birkhauser
48. Kline, M. (1980). Mathematics: The loss of certainty. Oxford: Oxford University Press
49. Kramer, E. (1981). The nature and growth of modem mathematics. Princeton, NJ: Princeton University Press
50. Lavine, S. (1994). Understanding the infinite. Cambridge, MA: Harvard University Press
51. MacLane, S. (1981). Mathematical models: A sketch for the philosophy of mathematics. American Mathematical Monthly, Aug.-Sept., pp. 462-472
52. Maor, E. (1987). The infinity and beyond: The cultural history of the infinite. Boston: Birkhauser
53. Moore, A. W. (1990). The infinite. London: Routledge
54. Nagel, E., & Newman, J. (1958). Gödel's proof. New York: New York University Press
55. Nunez, R. E. (1993). En dcQtï du transfini: Aspects psychocognitifs sousyjacents au concept d'infini en mathématiques. Fribourg: Editions Universitaires
56. Pierpont, J. (1899). On the arithmetization of mathematics. Bulletin of the American Mathematical Society, 394-406
57. Rucker, R. (1982). Infinity and the mind. Boston; Birkhåuser
58. Simmons, G. F. (1985). Calculus with analytic geometry. New York: McGraw-Hill
59. Stein, S. K. (1982). Calculus and analytic geometry. New York; McGraw Hill
60. Stewart, I. (1995). Concefjts of modem mathematics. New York; Dover
61. Swokowski, E. W. (1988). Calculus with analytic geometry. Boston: PWS-Kent
62. Tymoczco, T. (Ed.). (1986). New directions in the philosophy of mathematics. Boston: Birkhåuser
63. Vilenkin, N. Y. (1995). In search of infinity. Boston; Birkhåuser
64. Weyl, H. (1994). The continuum: A critical examination of the foundation of analysis. New York: Dover
65. Wilder, R. (1952). Introduction to foundations of mathematics. New York; Wiley
66. Wilder, R. (1986). The cultural basis of mathematics. In T. Tymoczco (Ed.), New directions in the philosophy of mathematics (pp. 185-199). Boston; Birkhåuser