Skip to main content
Log in

Intentional Gaps In Mathematical Proofs

  • Published:
Synthese Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

REFERENCES

  • Albers, Donald J., Gerald L. Alexanderson, and Constance Reid: 1990, More Mathematical People, Harcourt Brace Jovanovich, Boston.

    Google Scholar 

  • Anglin, W. S.: 1991, ‘Mathematics and Value’, Philosophia Mathematica (2) 6(2), 145–173.

    Google Scholar 

  • Azzouni, Jody: 1994, Metaphysical Myths, Mathematical Practice, Cambridge University Press, New York.

    Google Scholar 

  • Babai, Laszlo, Lance Fortnow, Leonid A. Levin, and Mario Szegedy: 1991, ‘Checking Computations in Polylogarithmic Time’, Proceedings of the 23rd ACM Symposium on Theory of Computing, pp. 21–31.

  • Ball, W. W. R.: 1960, A Short Account of the History of Mathematics, Dover Publications, New York.

    Google Scholar 

  • Blum, Manuel: 1987, ‘How to Prove a Theorem So No One Else Can Claim It’, Proceedings of the International Congress of Mathematicians 1986, American Mathematical Society, Providence, RI, pp. 1444–1451.

    Google Scholar 

  • Corcoran, John: 1973, ‘Gaps Between Logical Theory and Mathematical Practice’, in Mario Bunge (ed.), The Methodological Unity of Science, D. Reidel Publishing Co., Boston, pp. 23–50.

    Google Scholar 

  • Dauben, Joseph W.: 1994, ‘Topology: Invariance of Dimension’, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, I. Grattan-Guinness, Routledge, pp. 939–946.

    Google Scholar 

  • Davis, Philip J.: 1972, ‘Fidelity in Mathematical Discourse: Is One and One Really Two?’, American Mathematical Monthly 79(3), 252–263.

    Google Scholar 

  • Dawson, John W.: 1985, ‘The Reception of Godel's Incompleteness Theorems’, PSA 1984, 2, 253–271.

    Google Scholar 

  • Descartes, René: 1952, The Geometry of René Descartes, trans. David E. Smith and Marcia L. Latham, Open Court Publishing Company, La Salle, IL.

    Google Scholar 

  • Descartes, René: 1927, Selections, trans. Ralph M. Eaton, Charles Scribner's Sons, New York.

    Google Scholar 

  • Dieudonné, Jean: 1992, ‘The Concept of “Rigorous Proof”’, Mathematics-The Music of Reason, Springer-Verlag, Berlin, pp. 235–238.

    Google Scholar 

  • Enderton, Herbert B.: 1972, A Mathematical Introduction to Logic, Academic Press, San Diego.

    Google Scholar 

  • Fallis, Don: 1997, ‘The Epistemic Status of Probabilistic Proof’, Journal of Philosophy 94(4), 165–186.

    Google Scholar 

  • Faltings, Gerd: 1995, ‘The Proof of Fermat's Last Theorem by R. Taylor and A. Wiles’, Notices of the American Mathematical Society 42(7), 743–746.

    Google Scholar 

  • Frege, Gottlob: 1980, The Foundations of Arithmetic, 2nd edn., trans. J. L. Austin, Northwestern University Press, Evanston, IL.

    Google Scholar 

  • Gödel, Kurt: 1992, On Formally Undecidable Propositions of Principia Mathematica and Related Systems, trans. B. Meltzer, Dover Publications, New York.

    Google Scholar 

  • Hadamard, Jacques: 1945, The Psychology of Invention in the Mathematical Field, Princeton University Press, Prentice.

    Google Scholar 

  • Hardwig, John: 1985, ‘Epistemic Dependence’, Journal of Philosophy 82(7), 335–349.

    Google Scholar 

  • Harel, David: 1989, The Science of Computing, Addison-Wesley, Reading, MA.

    Google Scholar 

  • Hersh, Reuben: 1993, ‘Proving Is Convincing and Explaining’, Educational Studies in Mathematics 24(4), 389–399.

    Google Scholar 

  • Hume, David: 1967, in L. A. Selby-Bigge (ed.), A Treatise of Human Nature, Clarendon Press, Oxford.

    Google Scholar 

  • Jackson, Allyn: 1994, ‘Update on Proof of Fermat's Last Theorem’, Notices of the American Mathematical Society 41(3), 185–186.

    Google Scholar 

  • Kershner, R. B.: 1968, ‘On Paving the Plane’, American Mathematical Monthly 75(8), 839–844.

    Google Scholar 

  • Kitcher, Philip: 1984, The Nature of Mathematical Knowledge, Oxford University Press, New York.

    Google Scholar 

  • Kitcher, Philip and William Aspray: 1988, ‘An Opinionated Introduction’, in Philip Kitcher and William Aspray (eds.), History and Philosophy of Modern Mathematics, University of Minnesota Press, Minneapolis, pp. 3–57.

    Google Scholar 

  • Lakatos, Imre: 1976, Proofs and Refutations: The Logic of Mathematical Discovery, Cambridge University Press, New York.

    Google Scholar 

  • Lehman, Hugh: 1980, ‘An Examination of Imre Lakatos, Philosophy of Mathematics’, The Philosophical Forum 12(1), 33–48.

    Google Scholar 

  • Mac Lane, Saunders: 1996, ‘Structure in Mathematics’, Philosophia Mathematica (3) 4(2), 174–183.

    Google Scholar 

  • Maddy, Penelope: 1988, ‘Believing the Axioms’, Journal of Symbolic Logic 53, 481–511, 736-764.

    Google Scholar 

  • Plato: 1948, Euthyphro, Apology, Crito, trans. F. J. Church and Robert D. Cumming, Liberal Arts Press, New York.

    Google Scholar 

  • Poincaré, Henri: 1952, Science and Method, trans. Francis Maitland, Dover Publications, New York.

    Google Scholar 

  • Pólya, George: 1957, How To Solve It, 2nd edn., Princeton University Press, Princeton.

    Google Scholar 

  • Pólya, George: 1954, Mathematics and Plausible Reasoning, Vol. 1, Princeton University Press, Princeton.

    Google Scholar 

  • Rabin, M. O.: 1980, ‘Probabilistic Algorithm for Testing Primality’, Journal of Number Theory 12, 128–138.

    Google Scholar 

  • Reid, Constance: 1986, Hilbert-Courant, Springer-Verlag, New York.

    Google Scholar 

  • Ribet, Kenneth A.: 1993, ‘Wiles Proves Taniyama's Conjecture; Fermat's Last Theorem Follows’, Notices of the American Mathematical Society 40(6), 575–576.

    Google Scholar 

  • Schattschneider, Doris: 1981, ‘In Praise of Amateurs’, in Klarner and David A. Belmont (eds.), The Mathematical Gardner, Wadsworth International, Belmont, CA, pp. 140–166.

    Google Scholar 

  • Shakespeare, William: 1963, The Tragedy of Julius Caesar, Signet Classic. New York.

    Google Scholar 

  • Shoenfield, Joseph R.: 1967, Mathematical Logic, Addison-Wesley, Reading, MA.

    Google Scholar 

  • Smale, Steve: 1981, ‘The Fundamental Theorem of Algebra and Complexity Theory’, Bulletin of the American Mathematical Society 4, 1–36.

    Google Scholar 

  • Steiner, Mark: 1975, Mathematical Knowledge, Cornell University Press, Ithaca, NY.

    Google Scholar 

  • Stewart, Ian: 1996, From Here to Infinity, Oxford University Press, New York.

    Google Scholar 

  • Struik, D. J.: 1969, A Source Book in Mathematics, 1200-1800, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Tarski, Alfred: 1956, ‘The Concept of Truth in Formalized Languages’, Logic, Semantics, Metamathematics: Papers From 1923 to 1938, trans. J. H. Woodger, Clarendon Press, Oxford.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fallis, D. Intentional Gaps In Mathematical Proofs. Synthese 134, 45–69 (2003). https://doi.org/10.1023/A:1022131513275

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022131513275

Keywords

Navigation