Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs
References
- 1. Asprey, W., and P. Kitcher (eds.).
History and philosophy of modern mathematics , Minneapolis: University of Minnesota Press, 1988. - 2. Brown, J. R.
Philosophy of Mathematics. A Contemporary Introduction to the World of Proofs and Pictures , New York and London: Routledge, 1999, 20082. - 3. Byers, W.
How Mathematicians Think; Using Ambiguity, Contradiction, and Paradox to Create Mathematics , Princeton: Princeton University Press, 2007. - 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. - 5. Cellucci, Carlo.
Rethinking logic: Logic in relation to mathematics, evolution, and method , Dordrecht: Springer 2013. - 6. Cellucci, C.
Rethinking knowledge: The heuristic view , Dordrecht: Springer, 2017. - 7. Davis, P. J., and R. Hersh.
The Mathematical Experience , Boston, Basel, Berlin: Birkhäuser, 1981, 19952. - 8. Dehaene, S.
The Number Sense: How the Mind Creates Mathematics , Oxford: Oxford University Press, 1997. - 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. Epstein, R. L.
Five Ways of Saying “Therefore” Arguments, Proofs, Conditionals, Cause and Effect, Explanations , Belmont, CA: Wadsworth/Thomson Learning, 2002. - 11. Ernest, P.
Social Constructivism as a Philosophy of Mathematics, Albany, NY: SUNY Press, 1998. - 12. Friend, M.
Pluralism in Mathematics: A New Position in Philosophy of Mathematics , Dodrecht: Springer, 2014. - 13. Giaquinto, M. Visualising in Mathematics, In P. Mancosu (ed.),
The Philosophy of Mathematical Practice , Oxford: Oxford University Press, 2008, pp. 22-42. - 14. Hardy, G. H. Mathematical Proof,
Mind 38 (1928), pp. 1-25. - 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. - 16. Hersh, R. Math Has a Front and a Back,
Eureka 1988, andSynthese 88 (2), 1991. - 17. Hersh, R. Proving is convincing and explaining,
Educational Studies in Mathematics 24, 1993, pp. 389-399. - 18. Hersh, R.
What Is Mathematics, Really? Oxford: Oxford University Press, 1997. - 19. Hersh, R. (ed.).
18 Unconventional Essays on the Nature of Mathematics , New York: Springer, 2006. - 20. Hersh, R.
Experiencing mathematics: What do we do, when we do mathematics? Providence: American Mathematical Society, 2014. - 21. Kitcher, P.
The Nature of Mathematical Knowledge , Oxford: Oxford University Press, 1985. - 22. Kotlarski, H., S. Krajewski, and A. H. Lachlan. Construction of satisfaction classes for nonstandard models,
Canadian Math. Bulletin 24, 1981, pp. 283-293. - 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. - 24. Krajewski, S. On Suprasubjective Existence in Mathematics,
Studia semiotyczne XXXII (No 2), 2018, pp. 75-86. - 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 inBritish Journal for the Philosophy of Science 1963-64.) - 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. - 27. Lakoff, G., and R. E. Núñez.
Where Mathematics Comes From. How the Embodied Mind Brings Mathematics into Being , New York: Basic Books, 2000. - 28. Mancosu, P (ed.).
The Philosophy of Mathematical Practice , Oxford: Oxford University Press, 2008. - 29. Polya, G.
Mathematics and Plausible Reasoning , vol I, Princeton: Princeton University Press, 1973. - 30. Putnam, H. What is Mathematical Truth? In
Philosophical Papers , vol. 1,Mathematics, Matter and Method , Cambridge: Cambridge University Press, 1975, pp. 60-78. - 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. - 32. Rav, Y. Why Do We Prove Theorems?
Philosophia Mathematica (3) 7, 1999, pp. 5-41. - 33. Rav, Y. The Axiomatic Method in Theory and in Practice,
Logique & Analyse 202, 2008, pp. 125-147. - 34. Rotman, B. Toward a Semiotics of Mathematics,
Semiotica 72, 1988, pp. 1-35. - 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. - 36. Rotman, B.
Mathematics as Sign: Writing, Imagining, Counting , Stanford, CA: Stanford University Press, 2000. - 37. Sriraman, B. (ed.).
Humanizing Mathematics and its Philosophy . Essays Celebrating the 90th Birthday of Reuben Hersh, Basel: Birkhäuser 2017. - 38. Schmerl, J. Kernels, Truth and Satisfaction,
to be published . - 39. Tymoczko, T. The four-color problem and its philosophical significance,
The Journal of Philosophy 76, 1979, pp. 57-83. - 40. Tymoczko, T. (ed.),
New Directions in the Philosophy of Mathematics, An Antology , Basel: Birkhäuser, 1986. - 41. Wagner, R.
Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice , Princeton: Princeton University Press, 2017. - 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. - 43. Wilder, R. L. The Cultural Basis of Mathematics, in
Proceedings of the International Congress of Mathematicians , AMS 1952, pp. 258-271. - 44. Wilder, R. L.
Mathematics as a cultural system , Oxford: Pergamon Press, 1981.
DOI: https://doi.org/10.2478/sh-2020-0034 | Journal eISSN: 2299-0518
Language: English
Page range: 154 - 164
Published on: Nov 11, 2020
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