Mathematical reasoning: induction, deduction and beyond

Studies in History and Philosophy of Science Part A

Volumn 37, Issue 3, 2006, Pages 489-504

  Sherry, David ^a  

^a NORTHERN ARIZONA UNIVERSITY   (United States)

Author keywords

Informal proof; Mathematical reasoning; Thought experiment

Indexed keywords

EID: 33747816446     PISSN: 00393681     EISSN: 18792510     Source Type: Journal    
DOI: 10.1016/j.shpsa.2005.06.012     Document Type: Article

References (37)

1. Aristotle (1941). Basic works (R. McKeon, Ed.). New York: Random House.
2. Biggs N., Lloyd E., and Wilson R. Graph theory 1736-1936 (1976), Clarendon Press, Oxford
3. Bloor D. Polyhedra and the abominations of Leviticus. In: Douglas M. (Ed). Essays in the sociology of perception (1982), Routledge and Kegan Paul, London 191-218
4. Cauchy A. Oeuvres complètes d'Augustin Cauchy, Ser. 2, Vol. 1 (1905), Gauthiers-Villars, Paris
5. Coxeter H. Regular polytopes. 2nd ed. (1963), Macmillan, New York
6. Cromwell P. Polyhedra (1997), Cambridge University, Cambridge
7. Davis P. Fidelity in mathematical discourse: Is one and one really two?. American Mathematical Monthly 79 (1972) 252-263
8. Eilenberg S., and Steenrod N. Foundations of algebraic topology (1952), Princeton University, Princeton
9. Euler L. Opera omnia, Ser. 1 (1925), Teubner, Leipzig and Berlin
10. Federico P. Descartes on polyhedra (1982), Spring Verlag, New York
11. Heath T. The thirteen books of Euclid's Elements (1956), Dover, New York
12. Hempel C. Philosophy of natural science (1966), Prentice Hall, Englewood Cliffs, NJ
13. Hume, D. (1951). Enquiries concerning the human understanding and concerning the principles of morals (L. A. Selby-Bigge, Ed.). Oxford: Clarendon Press.
14. Hume, D. (1973). A treatise of human nature (L. A. Selby-Bigge, Ed.). Oxford: Clarendon Press.
15. Jaffe A., and Quinn F. Response to comments on Theoretical mathematics. Bulletin of the American Mathematical Society 30 (1994) 208-211
16. Kline M. Mathematical thought from ancient to modern times (1972), Oxford University, Oxford
17. Lakatos I. Proofs and refutations (1976), Cambridge University Press, Cambridge
18. Lakatos I. Mathematics, science and epistemology: Philosophical papers Vol. 2 (1978), Cambridge University Press, Cambridge
19. Legendre A. Éléments de géométrie (1794), Didot, Paris
20. L'Huilier S. Mémoire sur la polyedrométrie. Annales de Mathématiques, Pures et Appliquées 3 (1812-1813) 169-189 (Partially translated in Biggs, Lloyd, & Wilson, 1976, p. 84 and passim)
21. Mueller I. Euclid's Elements and the axiomatic method. British Journal for Philosophy of Science 20 (1969) 289-309
22. Mueller I. Greek mathematics and Greek logic. In: Corcoran J. (Ed). Ancient logic and its modern interpretation (1974), D. Reidel, Dordrecht 35-70
23. Nagel, E. (1979). The formation of modern conceptions of formal logic in the development of geometry. In idem, Teleology revisited (pp. 195-259). New York: Columbia University Press.
24. Pasch M. Vorlesungen uber neuere Geometrie (1882), Teubner, Leipzig
25. Peirce, C. S. (1956). The philosophy of Peirce: Selected writings (J. Buchler, Ed.). London: Routledge and Kegan Paul.
26. Plato. (1961). The collected dialogues of Plato (E. Hamilton & H. Cairns, Eds.). Princeton: Princeton University.
27. Polya G. Mathematics and plausible reasoning 2 vols. (1954), Princeton University, Princeton
28. Putnam, H. (1975). What is mathematical truth? In idem, Mathematics, matter and method (pp. 60-78). Cambridge: Cambridge University Press.
29. Seidenberg A. The ritual origins of geometry. Archive for History of Exact Sciences 1 (1962) 488-527
30. Seidenberg A. The origin of mathematics. Archive for History of Exact Sciences 18 (1977) 301-342
31. Sherry D. On mathematical error. Studies in History and Philosophy of Science 28 (1997) 393-416
32. Sherry D. Thales's sure path. Studies in History and Philosophy of Science 31 (1999) 621-650
33. Szabó A. The transformation of mathematics into deductive science and the beginning of its foundation on definitions and axioms. Scripta Mathematica 27 (1964) 27-48 113-139
34. Szabó A. The beginning of Greek mathematics (1978), D. Reidel, Dordrecht
35. von Staudt K. Geometrie der Lage (1847), F. Korn, Nürnberg
36. Wallis W. A beginner's guide to graph theory (2000), Birkhauser, Boston
37. Wittgenstein L. Remarks on the foundations of mathematics (1983), MIT Press, Cambridge, MA