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Gödel, Wittgenstein and the Nature of Mathematical Knowledge

Published online by Cambridge University Press:  28 February 2022

Thoma Tymoczko
Thoma Tymoczko*
Affiliation:
Smith College
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Extract

“And so, if I understand you correctly, you act and you know why act, but you don't know why you know that you know what you do?”

The problem that I want to discuss can be stated simply. For the sake of argument, I assume that knowledge is a relation between people and propositions, and that mathematical knowledge is a subspecies of this. Ordinarily, we are inclined to assume that we can account for one mathematician's knowledge without reference to any other mathematician. So in epistemology we assume that there is but a single ideal mathematician or that, at least as far as knowledge goes, an individual mathematician can be considered in isolation from all others. In so far as a community of mathematicians enters epistemology at all, it is after the already established fact of individual knowledge. The community typically serves as a device for the efficient distribution of knowledge.

Type
Part XI. New Directions in the Philosophy of Mathematics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1984 , Issue 2: Volume Two: Symposia and Invited Papers 1984 , 1984 , pp. 449 - 468
Copyright
Copyright © 1985 by the Philosophy of Science Association

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Footnotes

1

Several points of clarification were added to the paper after discussions with the commentator, Paul Benacerraf. It has benefited also from discussions with the Five-College Task Force of Propositional Attitudes including Murray Kiteley, John Connolly, Bill de Vries, Jay Garfield, Tom Magnell, Meredith Michaels and Tom Wartenburg. The opening quotation is from (Eco 1980, p. 244).

References

Addelson, Kathryn (1983). “The Man of Professional Wisdom.” In Discovering Reality; Feminist Perspeotives On Epistemology. Hetaphvaios. Methodology, and the Philosophy of Science. Edited by Harding, S and Hintikka, M Boston: D. Reidel. Pages 165-186.Google Scholar
Benacerraf, Paul (1965). “What Numbers Could Not Be.” The Philosophical Review 74: 17-73.CrossRefGoogle Scholar
Boolos, G and Jeffrey, R (1974). Computabilitv and Logic. Cambridge: Cambridge University Press.Google Scholar
Chaitin, Gregory (1982). “Gödel's Theorem and Information.” International Journal of Theoretical Physics 21: 941-954.CrossRefGoogle Scholar
Davis, Phili and Hersh, Reuben (1981). The Mathematical Experience. Boston: Birkhauser.Google Scholar
Dummett, Michael (1959). “Wittgenstein's Philosophy of Mathematics.” The Philosophical Review 68: 324-348.CrossRefGoogle Scholar
Eco, Umberto (1980). II nome della rosa. Milano: Bompiani. (As reprinted as The Name of the Rose, (trans.) William Weaver. New York: Warner Books, 1984.Google Scholar
Graham, R.; Rothschild, B.; and Spencer, J (1980). Ramsey Theory. New York: Wiley and Sons.Google Scholar
Kitoher, Philip (1983). The Nature of Mathematical Knowledge. Oxford: Oxford University Press.Google Scholar
Kripke, Saul (1982). Wittgenstein on Rules and Private Language. Cambridge: Harvard University Press.Google Scholar
Levi, Isaac (1983). The Enterprise of Knowledge. Cambridge: MIT Press.Google Scholar
Maddy, Penelope (1985). “New Directions in the Philosophy of Mathematics.” In PSA 1984. Volume 2. Edited by Asquith, P.D and Kitcher, P East Lansing: Philosophy of Science Association. Pages 427-148.Google Scholar
Tymoczko, Thomas (1979). “The Four-Color Problem and Its Philosophical Significance.” Journal of Philosophy 76: 57-83.CrossRefGoogle Scholar
Tymoczko, Thomas (1985). New Directions in the Philosophy of Mathematics. Boston: Birkhauser.Google Scholar
Tymoczko, Thomas (1986). “Making Room for Mathematicians in the Philosophy of Mathematics.” Mathematical Intelligencer (forthcoming.CrossRefGoogle Scholar
Wang, Hao (1974). From Mathematics to Philosophy. New York: Humanities Press.Google Scholar
Wittgenstein, Ludwig (1953). Philosophical Investigations, (trans.) Anscombe, G.E.M. New York: MacMillan.Google Scholar
Wittgenstein, Ludwi (1956). The Blue and Brown Books. Oxford: Basil Blackwell.Google Scholar