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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

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