Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs

1. Asprey, W., and P. Kitcher (eds.). History and philosophy of modern mathematics, Minneapolis: University of Minnesota Press, 1988.Search in Google Scholar

2. Brown, J. R. Philosophy of Mathematics. A Contemporary Introduction to the World of Proofs and Pictures, New York and London: Routledge, 1999, 2008².Search in Google Scholar

3. Byers, W. How Mathematicians Think; Using Ambiguity, Contradiction, and Paradox to Create Mathematics, Princeton: Princeton University Press, 2007.Search in Google Scholar

4. Cellucci, C. Why Proof? What is a Proof? In G. Corsi and R. Lupacchini (eds.), Deduction, Computation, Experiment. Exploring the Effectiveness of Proof, Berlin: Springer-Verlag, 2008, pp. 1-27.10.1007/978-88-470-0784-0_1Search in Google Scholar

5. Cellucci, Carlo. Rethinking logic: Logic in relation to mathematics, evolution, and method, Dordrecht: Springer 2013.10.1007/978-94-007-6091-2Search in Google Scholar

6. Cellucci, C. Rethinking knowledge: The heuristic view, Dordrecht: Springer, 2017.10.1007/978-3-319-53237-0Search in Google Scholar

7. Davis, P. J., and R. Hersh. The Mathematical Experience, Boston, Basel, Berlin: Birkhäuser, 1981, 1995².Search in Google Scholar

8. Dehaene, S. The Number Sense: How the Mind Creates Mathematics, Oxford: Oxford University Press, 1997.Search in Google Scholar

9. Enayat, A, and A. Visser. New constructions of satisfaction classes. Unifying the philosophy of truth, pp. 321-335, Logic, Epistemology, and the Unity of Science 36, Dordrecht: Springer, 2015.10.1007/978-94-017-9673-6_16Search in Google Scholar

10. Epstein, R. L. Five Ways of Saying “Therefore” Arguments, Proofs, Conditionals, Cause and Effect, Explanations, Belmont, CA: Wadsworth/Thomson Learning, 2002.Search in Google Scholar

11. Ernest, P. Social Constructivism as a Philosophy of Mathematics, Albany, NY: SUNY Press, 1998.Search in Google Scholar

12. Friend, M. Pluralism in Mathematics: A New Position in Philosophy of Mathematics, Dodrecht: Springer, 2014.10.1007/978-94-007-7058-4Search in Google Scholar

13. Giaquinto, M. Visualising in Mathematics, In P. Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford: Oxford University Press, 2008, pp. 22-42.Search in Google Scholar

14. Hardy, G. H. Mathematical Proof, Mind 38 (1928), pp. 1-25.10.1093/mind/XXXVIII.149.1Search in Google Scholar

15. Hersh, R. Some proposals for reviving the philosophy of mathematics, Advances in Mathematics 31, 31-50, reprinted in T. Tymoczko (ed.), New Directions in the Philosophy of Mathematics, An Antology, Basel: Birkhäuser, 1986.10.1016/0001-8708(79)90018-5Search in Google Scholar

16. Hersh, R. Math Has a Front and a Back, Eureka 1988, and Synthese 88 (2), 1991.10.1007/BF00567741Search in Google Scholar

17. Hersh, R. Proving is convincing and explaining, Educational Studies in Mathematics 24, 1993, pp. 389-399.10.1007/BF01273372Search in Google Scholar

18. Hersh, R. What Is Mathematics, Really? Oxford: Oxford University Press, 1997.10.1515/dmvm-1998-0205Search in Google Scholar

19. Hersh, R. (ed.). 18 Unconventional Essays on the Nature of Mathematics, New York: Springer, 2006.10.1007/0-387-29831-2Search in Google Scholar

20. Hersh, R. Experiencing mathematics: What do we do, when we do mathematics? Providence: American Mathematical Society, 2014.Search in Google Scholar

21. Kitcher, P. The Nature of Mathematical Knowledge, Oxford: Oxford University Press, 1985.10.1093/0195035410.001.0001Search in Google Scholar

22. Kotlarski, H., S. Krajewski, and A. H. Lachlan. Construction of satisfaction classes for nonstandard models, Canadian Math. Bulletin 24, 1981, pp. 283-293.10.4153/CMB-1981-045-3Search in Google Scholar

23. Krajewski, S. Remarks on Mathematical Explanation, In B. Brozek, M. Heller and M. Hohol (eds.), The Concept of Explanation, Kraków: Copernicus Center Press, 2015, pp. 89-104.Search in Google Scholar

24. Krajewski, S. On Suprasubjective Existence in Mathematics, Studia semiotyczne XXXII (No 2), 2018, pp. 75-86.Search in Google Scholar

25. Lakatos, I. Proofs and refutations; The logic of mathematical discovery, edited by J. Worral and E. Zahar, Cambridge: Cambridge University Press 1976, 2015². (Original papers in British Journal for the Philosophy of Science 1963-64.)Search in Google Scholar

26. Lakatos, I. A renaissance of empiricism in the recent philosophy of mathematics? In I. Lakatos, Philosophical Papers, vol. 2, edited by J. Worrall and G. Curie, Cambridge: Cambridge University Press, 1978, pp. 24-42.Search in Google Scholar

27. Lakoff, G., and R. E. Núñez. Where Mathematics Comes From. How the Embodied Mind Brings Mathematics into Being, New York: Basic Books, 2000.Search in Google Scholar

28. Mancosu, P (ed.). The Philosophy of Mathematical Practice, Oxford: Oxford University Press, 2008.10.1093/acprof:oso/9780199296453.001.0001Search in Google Scholar

29. Polya, G. Mathematics and Plausible Reasoning, vol I, Princeton: Princeton University Press, 1973.Search in Google Scholar

30. Putnam, H. What is Mathematical Truth? In Philosophical Papers, vol. 1, Mathematics, Matter and Method, Cambridge: Cambridge University Press, 1975, pp. 60-78.Search in Google Scholar

31. Rav, Y. Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology, Philosophica 43, No. 1, 1989, pp. 49-78; also Chapter 5 in Hersh, R (ed.). 18 Unconventional Essays on the Nature of Mathematics, New York: Springer, 2006.Search in Google Scholar

32. Rav, Y. Why Do We Prove Theorems? Philosophia Mathematica (3) 7, 1999, pp. 5-41.10.1093/philmat/7.1.5Search in Google Scholar

33. Rav, Y. The Axiomatic Method in Theory and in Practice, Logique & Analyse 202, 2008, pp. 125-147.Search in Google Scholar

34. Rotman, B. Toward a Semiotics of Mathematics, Semiotica 72, 1988, pp. 1-35.10.1515/semi.1988.72.1-2.37Search in Google Scholar

35. Rotman, B. Ad Infinitum … the Ghost ln Turing’s Machine: Taking God Out Of Mathematics And Putting the Body Back In, Stanford, CA: Stanford University Press, 1993.10.1515/9781503622135Search in Google Scholar

36. Rotman, B. Mathematics as Sign: Writing, Imagining, Counting, Stanford, CA: Stanford University Press, 2000.Search in Google Scholar

37. Sriraman, B. (ed.). Humanizing Mathematics and its Philosophy. Essays Celebrating the 90th Birthday of Reuben Hersh, Basel: Birkhäuser 2017.10.1007/978-3-319-61231-7Search in Google Scholar

38. Schmerl, J. Kernels, Truth and Satisfaction, to be published.Search in Google Scholar

39. Tymoczko, T. The four-color problem and its philosophical significance, The Journal of Philosophy 76, 1979, pp. 57-83.10.2307/2025976Search in Google Scholar

40. Tymoczko, T. (ed.), New Directions in the Philosophy of Mathematics, An Antology, Basel: Birkhäuser, 1986.Search in Google Scholar

41. Wagner, R. Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice, Princeton: Princeton University Press, 2017.10.23943/princeton/9780691171715.003.0002Search in Google Scholar

42. White, L. The Locus of Mathematical Reality: An Anthropological Footnote, Philosophy of Science 14, 1947, pp. 289-303, reprinted in Hersh, R (ed.). 18 Unconventional Essays on the Nature of Mathematics, New York: Springer, 2006, pp. 304-319.10.1007/0-387-29831-2_17Search in Google Scholar

43. Wilder, R. L. The Cultural Basis of Mathematics, in Proceedings of the International Congress of Mathematicians, AMS 1952, pp. 258-271.Search in Google Scholar

44. Wilder, R. L. Mathematics as a cultural system, Oxford: Pergamon Press, 1981.Search in Google Scholar