Linked bibliography for the SEP article "Non-Deductive Methods in Mathematics" by Alan Baker

This is an automatically generated and experimental page

If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

This experiment has been authorized by the editors of the Stanford Encyclopedia of Philosophy. The original article and bibliography can be found here.

Adleman, L., 1994, “Molecular Computation of Solutions to Combinatorial Problems”, Science, CCLXVI: 1021–1024. (Scholar)
Andersen, L., 2018, “Acceptable Gaps in Mathematical Proofs”, Synthese, URL = <https://doi.org/10.1007/s11229-018-1778-8>. (Scholar)
Avigad, J., 2006, “Mathematical Method and Proof”, Synthese, 153: 105–159. (Scholar)
–––, 2007, “5 Questions”, in Philosophy of Mathematics: 5 Questions, V. Hendricks & H. Leitgeb (ed.), Copenhagen: Automatic Press, p 1–10. (Scholar)
Azzouni, J., 2013, “The Relationship of Derivations in Artificial Languages to Ordinary Rigorous Mathematical Proof”, Philosophia Mathematica, 21: 247–254. (Scholar)
–––, 2013, “That We See that Some Diagrammatic Proofs are Perfectly Rigorous”, Philosophia Mathematica, 21: 323–338. (Scholar)
Baker, A., 2007, “Is There a Problem of Induction for Mathematics?”, in Mathematical Knowledge, M. Leng, A. Paseau, & M. Potter (eds.), Oxford: Oxford University Press, pp. 59–73 (Scholar)
–––, 2008, “Experimental Mathematics”, Erkenntnis, 68: 331–344. (Scholar)
Berry, D., 2016, “Proof and the Virtues of Shared Enquiry”, Philosophia Mathematica, 26: 112–130. (Scholar)
–––, 2019, “Should Mathematicians Play Dice?”, Logique et Analyse, 246: 135–160. (Scholar)
Borwein, J., & D. Bailey, 2003, Mathematics by Experiment: Plausible Reasoning for the 21^st Century, Natick, MA: A K Peters. (Scholar)
–––, 2004, Experimentation in Mathematics: Computational Paths to Discovery, Natick, MA: AK Peters. (Scholar)
–––, 2015, “Experimental Mathematics as an Ontological Game Changer: the Impact of Modern Mathematical Computation Tools on the Ontology of Mathematics”, in Mathematics, Substance and Surmise, E. Davis & P. Davis (eds.), Springer, pp. 25–68. (Scholar)
Brown, J., 2008, Philosophy of Mathematics: a Contemporary Introduction to the World of Proofs and Pictures, 2^nd Edition, New York: Routledge. (Scholar)
Burgess, J., 1992, “Proofs about Proofs: a Defense of Classical Logic. Part 1: the Aims of Classical Logic”, in Proof, Logic and Formalization, M. Detlefsen (ed.), London and New York: Routledge, pp. 8–23. (Scholar)
Carroll, L. [C. L. Dodgson], 1895, “What the Tortoise Said to Achilles,”, Mind, 4: 278–280. (Scholar)
Corfield, D., 2003, Towards a Philosophy of Real Mathematics, Cambridge: Cambridge University Press. (Scholar)
Courant, R., & H. Robbins, 1941, What Is Mathematics?, Oxford: Oxford University Press. (Scholar)
Crandall, R., & C. Pomerance, 2001, Prime Numbers: a Computational Perspective, New York: Springer-Verlag. (Scholar)
De Toffoli, S., & V. Giardino, 2014, “Forms and Roles of Diagrams in Knot Theory”, Erkenntnis, 79(4): 829–842. (Scholar)
De Toffoli, S., 2017, “‘Chasing’ the Diagram: the Use of Visualizations in Algebraic Reasoning”, Review of Symbolic Logic, 10: 158–186. (Scholar)
Delariviere, S.,& Van Kerkhove, B., 2017, “The Artificial Mathematician Objection: Exploring the (Im)possibility of Automating Mathematical Understanding”, in Humanizing Mathematics and its Philosophy, B. Sriraman (ed.), Springer International Publishing, pp. 173–198. (Scholar)
Descartes, R., 1627–28, Rules for the Direction of the Mind, in Descartes: Selections, R. Eaton (tr.), New York: Charles Scribner’s Sons, 1927, pp. 38–83. (Scholar)
Detlefsen, M. (ed.), 1992, Proof, Logic and Formalization, London and New York: Routledge. (Scholar)
Dummett, M., 1978, “Wang’s Paradox”, in Truth and Other Enigmas, London: Duckworth, pp. 248–268. (Scholar)
Easwaran, K., 2005, “The Role of Axioms in Mathematics”, Erkenntnis, 68: 381–391. (Scholar)
–––, 2009, “Probabilistic Proofs and Transferability”, Philosophia Mathematica, 17: 341–362. (Scholar)
Echeverria, J., 1996, “Empirical Methods in Mathematics. A Case-Study: Goldbach’s Conjecture”, in Spanish Studies in the Philosophy of Science, G. Munévar (ed.) , Dordrecht: Kluwer, pp. 19–55. (Scholar)
Fallis, D., 1997, “The Epistemic Status of Probabilistic Proof”, Journal of Philosophy, 94(4): 165–186. (Scholar)
–––, 2002, “What Do Mathematicians Want? Probabilistic Proofs and the Epistemic Goals of Mathematicians”, Logique et Analyse, 45: 373–388. (Scholar)
–––, 2003, “Intentional Gaps in Mathematical Proofs”, Synthese, 134: 45–69. (Scholar)
–––, 2011, “Probabilistic Proofs and the Collective Epistemic Goals of Mathematicians”, in Collective Epistemology, H.B. Schmid, D. Sirtes & M. Weber (eds.), Ontos Verlag, pp. 157–176. (Scholar)
Fontanella, L., 2019, “How to Choose New Axioms for Set Theory?”, in Reflections on the Foundations of Mathematics, D. Sarikaya, D. Kant & S. Centrone (eds.), Springer Verlag. (Scholar)
Franklin, J., 1987, “Non-Deductive Logic in Mathematics”, British Journal for the Philosophy of Science, 38: 1–18. (Scholar)
Frege, G., 1884, Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau: W. Koebner. Translated as The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number, by J.L. Austin, Oxford: Blackwell, second revised edition, 1974. Reprinted 1980. (Scholar)
Gallian, J., & M. Pearson, 2007, “An Interview with Doron Zeilberger”, FOCUS (the newsletter of the Mathematical Association of America), 27(5): 14–17. (Scholar)
Giaquinto, M., 2007, Visual Thinking in Mathematics: an Epistemological Study, Oxford: Oxford University Press. (Scholar)
Gonthier, G., et al., 2008, “Formal Proof – The Four-Color Theorem”, Notices of the American Mathematical Society, 55(11): 1382–1393. (Scholar)
Gonthier, G., 2013, “A Machine-Checked Proof of the Odd Order Theorem”, in Interactive Theorem Proving: 4th International Conference Proceedings, S. Blazy, C. Paulin-Mohring & D. Pichardie (eds.), Berlin / Heidelberg: Springer-Verlag, pp. 163–179. (Scholar)
Haack, S., 1976, “The Justification of Deduction”, Mind, 85: 112–119. (Scholar)
Jackson, J., 2009, “Randomized Arguments are Transferable”, Philosophia Mathematica, 17: 363–368. (Scholar)
Lakatos, I., 1976, Proofs and Refutations, Cambridge: Cambridge University Press. (Scholar)
–––, 1980, “What Does a Mathematical Proof Prove?”, in Mathematics, Science and Epistemology (Imre Lakatos: Philosophical Papers, Volume 2), J. Worrall & G. Currie (eds.), Cambridge: Cambridge University Press, pp. 61–69. (Scholar)
Lingamneni, S., 2017, “Can we Resolve the Continuum Hypothesis?”, Synthese, URL = < https://doi.org/10.1007/s11229-017-1648-9>. (Scholar)
Maddy, P., 1988, “Believing the Axioms. I & II”, Journal of Symbolic Logic, 53(2): 481–511, 736–764. (Scholar)
–––, 1997, Naturalism in Mathematics, Oxford: Oxford University Press. (Scholar)
–––, 2001, “Some Naturalistic Remarks on Set Theoretic Method”, Topoi, 20: 17–27. (Scholar)
–––, 2011, Defending the Axioms: On the Philosophical Foundations of Set Theory, Oxford: Oxford University Press. (Scholar)
Mancosu, P., 2008, “Mathematical Explanation: Why it Matters”, in The Philosophy of Mathematical Practice, P. Mancosu (ed.), Oxford: Oxford University Press, pp. 134–149. (Scholar)
McEvoy, M., 2008, “The Epistemological Status of Computer Proofs”, Philosophia Mathematica, 16: 374–387. (Scholar)
–––, 2013, “Experimental Mathematics, Computers and the A Priori”, Synthese, 190: 397–412. (Scholar)
Mumma, J., 2010, “Proofs, Pictures, and Euclid”, Synthese, 175: 255–287. (Scholar)
Paseau, A., 2015, “Knowledge of Mathematics without Proof”, British Journal for the Philosophy of Science, 66: 775–799. (Scholar)
Pólya, G., 1945, How to Solve It, Princeton: Princeton University Press. (Scholar)
Schlimm, D., 2013, “Axioms in Mathematical Practice”, Philosophia Mathematica, 21: 37–92. (Scholar)
Shin, S., & O. Lemon, 2008, “Diagrams”, The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.), URL = <Diagrams/">https://plato.stanford.edu/archives/win2008/entries/Diagrams/>. (Scholar)
Sorensen, H.K., 2010, “Exploratory Experimentation in Experimental Mathematics: a Glimpse at the PSLQ Algorithm”, in Philosophy of Mathematics: Sociological Aspects and Mathematical Practice, B. Lowe & T. Muller (eds.), London: College Publications, pp. 341–360. (Scholar)
–––, 2016, “‘The End of Proof’? The Integration of Different Mathematical Cultures as Experimental Mathematics Comes of Age”, in Mathematical Cultures, B. Larvor (ed.), Cham: Birkhauser, pp. 139–160. (Scholar)
Steiner, M., 1993, “Review of Proof, Logic and Formalization”, Journal of Symbolic Logic, 58(4): 1459–1462. (Scholar)
Tennant, N., 2005, “Rule Circularity and the Justification of Deduction”, Philosophical Quarterly, 55: 625–648. (Scholar)
te Riele, H., 1987, “On the Sign of the Difference p(x)–Li(x)”, Mathematics of Computation, 48: 323–328. (Scholar)
Tymoczko, T., 1979, “The Four-Color Problem and Its Philosophical Significance”, Journal of Philosophy, 76(2): 57–83. (Scholar)
van Bendegem, J., 1998, “What, if Anything, is an Experiment in Mathematics?”, in Philosophy and the Many Faces of Science, D. Anapolitanos, et al. (eds.), London: Rowman & Littlefield, pp. 172–182. (Scholar)
van Kerkhove, B., & J. van Bendegem, 2008, “Pi on Earth”, Erkenntnis, 68: 421–435. (Scholar)

Generated Sun Apr 27 20:09:38 2025

Applied ethics	Epistemology	History of Western Philosophy	Meta-ethics	Metaphysics	Normative ethics
Philosophy of biology	Philosophy of language	Philosophy of mind	Philosophy of religion	Science Logic and Mathematics	More ...