Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology

Rav, Yehuda

Séminaire de Philosophie et Mathématiques, Philosophical problems of mathematics in the light of evolutionary epistemology, no. 6 (1988), pp. 1-30

Apostel, Leo, Evolutionary epistemology, genetic epistemology, history and neurology, in: W. Callebaut & R. Pinxten, (eds.), 1987, pp. 311-326.

Apostle, Hippocrates G., Aristotle's Philosophy of Mathematics, Univ. of Chicago Press, 1952. | Zbl | MR

Beth, Evert J. & Piaget, Jean, Epistémologie mathématique et psychologie, Press, Univ. France, Paris, 1961 = Mathematical epistemology and psychology, D. Reidel, Dordrecht, 1966. | MR

Bonner, John Tyler, The Evolution of Culture in Animals, Princeton Univ. Press, Princeton, 1980.

Borel, Armand, Mathematics, Art and Science, The Mathematical Intelligencer 5, (1983), no. 4, 9-17. | MR

Bradie, Michael, Assessing evolutionary epistemology, Biology and Philosophy 1 (1986), 401-459.

Callebaut, Werner & Pinxten, Rik (eds.), Evolutionary Epistemology. A Multiparadigm Program, D. Reidel, Dordrecht, 1987.

Campbell, Donald T., Methodological suggestions from a comparative psychology of knowledge processes, Inquiry 2 (1959), 152-182.

Campbell, Donald T., Evolutionary epistemology, in: P. A. Schlipp (ed.), The Philosophy of K. Popper, Open Court, La Salle, 1974, part I, pp. 413-463.

Campbell, Donald T., Heyes, Cecilia M. & Callebaut, Werner G., Evolutionary epistemology bibliography, in: W. Callebaut & R. Pinxten (eds.), 1987, pp. 402-431.

Carruccio, Ettore, Appunti di Storia delle matematiche, della logica, della metamatematica, Pitagora Editrice, Bologna, 1977. | MR

Church, Alonzo, Mathematics and Logic, in E. Nagel et. al, (eds.), Logic, Methodology and Philosophy of Science. (Proc. 1960 Intern. Congress, Stanford), Stanford Univ. Press, 1962, pp. 181-186. | Zbl

Corcoran, John, Gaps between logical theory and mathematical practice, in: M. Bunge (ed.), The Methodological Unity of Science, D. Reidel, Dordrecht, 1973, pp. 23-50.

D'Espagnat, Bernard, A la recherche du réel. Le regard d'un physicien. Gauthier-Villard, Paris, 1979.

D'Espagnat, Bernard & Paty, Michel, La physique et le réel. Bull. Soc. franc. Philo. 84 (1980), 1-42.

Dalla Chiara, Maria L. & Toraldo Di Francia, Giuliano, Consideraciones ontológicas sobre los objectos de la física moderna. Análisis Filosófico II (1982), 35-46.

Dalla Chiara, Maria Luisa, Some foundational problems in mathematical suggested by physics, Synthese 62 (1985), 303-315. | MR

Dobzhansky, Theodosius, Evolution, Genetics, and Man. John Wiley & Co., New York, 1955.

Edwards, Harold M., Dedekind's invention of ideals, Bull. London Math. Soc. 15 (1983)8-17. | Zbl | MR

Feferman, Solomon, Working foundations, Synthese 62 (1985), 229-254. | MR

Garciadiego, Alejandro R., On rewriting the history of the foundations of mathematics, Historia Math. 13 (1986), 38-41. | Zbl | MR

Gardner, Howard, The Mind's New Science: A History of the Cognitive Revolution, Basic Books, New York, 1985.

Goodstein, Reuben L., Empiricism in mathematics, Dialectica 23, (1970), 50-57. | Zbl

Granit, Ragnar, The Purposive Brain, MIT Press, Cambridge, Mass., 1977.

Hadamard, Jacques S., The Psychology of Invention in the Mathematical Field, Princeton Univ. Press, Princeton, 1945. | Zbl | MR

Hardy, Godfrey H., A Mathematicians's Apology, Cambridge Univ. Press, Cambridge, 1940 and 1969. | Zbl | MR

Hersh, Reuben, Some proposals for reviving the philosophy of mathematics, Advances in Math. 31 (1979), 31-50. | Zbl | MR

Hilbert, David, Über das Unendliche, Math. Annal. 95 (1926) 161-190 - On the infinite, in J. Van Heijenoort (ed.), From Frege to Gödel, Harvard Univ. Press, Cambridge, Mass., 1967, pp. 369-392. | MR | JFM

Kaspar, Robert, Die biologischen Grundlagen der evolutionären Erkenntnistheorie, in: K. Lorenz et al. (eds.), pp. 125-145.

Keyser, Cassius J., Concerning the axiom of infinity and mathematical induction, Bull. Amer. Math. Soc. 9 (1902-03), 424-434. | MR | JFM

Kitcher, Philip, Mathematical rigor - who needs it? Noûs 15 (1981), 469-493. | MR

Kitcher, Philip, The Nature of Mathematics, Oxford Univ. Press, Oxford, 1984. | Zbl

Körner, Stephan, The Philosophy of Mathematics, Hutchins, London, 1960. | Zbl

Körner, Stephan, An empiricist justification of mathematics, in: Y. Bar-Hillel (ed.), Logic, Methodology and Philos. Science, (Proc. 1964 Intern. Congress, Jerusalem), North Holland, 1965, pp. 222-227. | Zbl | MR

Kreisel, Georg, Perspectives in the philosophy of mathematics, in: P. Suppes et al. (eds.), Logic, Methodology and Philosophy of Science IV, North-Holland, Amsterdam, 1973, pp. 255-277. | MR

Lakatos, Imre, Infinite regress and the foundations of mathematics, Aristotelian Society Proc, Suppl., 36 (1962), 155-184.

Lolli, Gabriele, La dimostrazione in matematica: analisi di un dibattido, Boll. Un. Mat. Ital. A (61) 1 (1982), 197-216. | Zbl

Lorenz, Konrad, Kants Lehre vom Apriorischen in Lichte gegenwärtiger Bilologie (1941)

Lorenz, Konrad reprinted in: Lorenz et al., (eds.), 1983, pp. 95-124 = Kant's doctrine of the a priori in the light of contemporary biology, in: Plotkin (ed.) 1982, pp. 121-143.

Lorenz, Konrad et al. (eds.), Die Evolution des Denkens, R. Pieper, München, 1983. English transl.: Concepts and Approaches in Evolutionary Epistemology (F.M. Wuketits, ed.), D. Reidel, Dordrecht, 1984.

Machover, Moshé, Towards a new philosophy of mathematics, British J. Philos. Sci. 34 (1983), 1-11. | Zbl | MR

Marshack, Alexander, The Roots of Civilization, Weiderfeld & Nicolson, London, 1972.

Maturana, Humberto R. & Varela, Francisco J., Autopoiesis and Cognition, D. Reidel, Dordrecht, 1980.

Michaels, Axel, Beweisverfahren in der vedischen Sakralgeometrie, Franz Steiner, Wiesbaden, 1978. | Zbl | MR

Mow, Shaw Kwei, What do we do if we do not have the concept of prime numbers? A note of the history of mathematics in China. (Chinese). J. Math. Res. Expositions 2 (1982), 183-187. English summary in Math Reviews 84i:01024. | Zbl | MR

Müller, Horst M., Evolution, Kognition und Sprache, Paul Parey, Berlin, 1987.

Oeser, Erhard, Psychoziokum. Evolution und Mechanismus der menschlichen Erkenntnisfähigkeit, Paul Parey, Berlin-Hamburg, 1987.

Oeser, Erhard & Seitelberger, Franz, Gehirn, Bewusstsein und Erkenntnis, Paul Parey, Berlin-Hamburg, 1987.

Piaget, Jean, Biologie et Connaissance, Gallimard, Paris, 1967 = Biology and Knowledge: An Essay on the Relations between Organic Regulations and Cognitive Processes, Univ. Chicago Press, Chicago, 1971. | MR

Piaget, Jean, Genetic Epistemology, Columbia Univ. Press, New York 1970.

Plotkin, H.C. (ed.), Learning, Development and Culture: Essays in Evolutionary Epistemology, John Wiley, New York, 1982.

Popper, Karl R., Objective Knowledge: An Evolutionary Approach, Oxford, 1972.

Quine, Williard V.O., On what there is, Review of Metaphysics (1948).

Quine, Williard V.O., On what there is Reprinted in: From a Logical Point of View, Harvard Univ. Press, Cambrdige Mass., 1980, pp. 1-19. | Zbl

Quine, W.V.O., Whither physical objects? in: R.S. Cohen et al. (eds.), Essays in Memory of Imre Lakatos, D. Reidel, Dordrecht, 1976, pp. 497-504.

Rényi, Alfréd, Dialogues on Mathematics, Holden-Day, San Francisco, 1967. | Zbl

Resnik, Michael, Mathematical knowledge and pattern cognition, Canad. J. Pilos., 5 (1975), 25-39.

Resnik, Michael, Mathematics as a science of patterns: ontology and references, Noûs 15, (1981), 529-550. | Zbl | MR

Resnik, Michael, Mathematics as a science of patterns: epistemology, Noûs 16 (1982), 95-107. | Zbl | MR

Resnik, Michael & Kushner, David, Explanation, independence and realism in mathematics, British J. Phil. Sci. 38 (1987), 141-158. | Zbl | MR

Riedl, Rupert, Biologie der Erkenntnis: Die stammgeschichtlichen Grundlagen der Vernunft, Paul Parey, Berlin, 1979, DTV, 1988 = Biology of Knowledge: The Evolutionary Basis of Reason, John Wiley, Chichester, 1984.

Riedl, Rupert et al. (eds.), Die Evolutionäre Erkenntnistheorie, Paul Parey, Berlin, 1987.

Ruzavin, G.I., Die Natur der mathematischen Erkenntnis, Akademie Verlag, Berlin, 1977 (Transl, from Russian, original, 1968). | MR

Seidenberg, Abraham, The ritual origin of counting, Arch. Hist. Exact Sci. 2 (1962), 1-40. | Zbl | MR

Seidenberg, Abraham, The origin of mathematics, Arch. Hist. Exact Sci. 18 (1977/78), 301-342. | Zbl | MR

Seidenberg, Abraham, The ritual origin of the circle and square, Arch. Hist. Exact Sci. 25 (1981), 269-327. | Zbl | MR

Shapiro, Stewart, Mathematics and reality, Philos. Sci. 50 (1983), 523-548. | Zbl | MR

Shepard, Roger N. & Cooper, Lynn A., Mental Images and their Transformations, MIT Press, 1981.

Simpson, George, G., Biology and the nature of science, Science 139 (1963), 81-88.

Steiner, Mark, Mathematics, explanation, and scientific knowledge, Noûs 12 (1978) 17-28. | MR

Steiner, Mark, Mathematical explanation, Philos. Studies 34 (1978) 135-151. | MR

Steiner, Mark, Mathematical realism, Noûs 17 (1983), 363-385. | MR

Toraldo Di Francia, Giuliano, What is a physical object? Scientia 113 (1978), 57-65.

Toth, Imre, Mathematische Philosophie und hegelsche Dialektik, in: M.J. Petry, (ed.), Hegel und die Naturwissenschaften, Frommann-Holzboog, Stuttgart, 1986, pp. 89-182. | Zbl | MR

Ursúa, Nicanor, Conocimento y realidad: aproximación a una hipótesis, Theoria (San Sebastián) II (1986/87), n° 5-6, 461-502.

Van Bendegem, Jean Paul, Fermat's last theorem seen as an exercise in evolutionary epistemology, in: W. Callebaut &. R. Pinxten, (eds.), 1987, pp. 337-363.

Vollmer, Gerhard, Evolutionäre Erkenntnistheroie, S. Hirzel, Stuttgart, 1975; 4th ed. 1987.

Vollmer, Gerhard, Mesokosmos und objektive Erkenntnis, in: Lorenz et al. (eds.) 1983, pp. 29-91; English version: Mesocosm and objective knowledge, in: F.M. Wuketits (ed.), Concepts and Approaches in Evolutionary Epistemology, pp. 69-121, D. Reidel, Dordrecht, 1984.

Vollmer, Gerhard, Was können wir wissen? Band 1: Die Natur der Erkenntnis, S. Hirzel, Stuttgart 1985/86.

Vollmer, Gerhard, Was können wir wissen? Band 2: Die Erkenntnis der Natur, S. Hirzel, Stuttgart, 1985/86.

Vollmer, Gerhard, Was evolutionäre Erkenntnistheorie nicht ist, in: Riedl, et al. (eds.) 1987, pp. 140-155; English version: What evolutionary epistemology is not, in: W. Callebaut & R. Pinxten (eds.), 1987, pp. 203-221.

White, Leslie A., The locus of mathematical reality: An anthropological footnote, in: J.R. Newman (ed.), The World of Mathematics, Simon & Schuster, New York, 1956, vol. 4, pp. 2348-2364. | Zbl

Wigner, Eugene P., The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure Appl. Math. 13 (1960), 1-14. | Zbl | MR

Wilder, Raymond L., Mathematics as a Cultural System, Pergamon Press, Oxford, 1981. | Zbl | MR