Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T18:52:03.011Z Has data issue: false hasContentIssue false
  • English
  • Français

How Foundational Work in Mathematics Can be Relevant to Philosophy of Science

Published online by Cambridge University Press:  19 June 2023

John P. Burgess
John P. Burgess*
Affiliation:
Princeton University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A common metaphor compares mathematics to a building: The axioms are its foundation, the lemmas and theorems and corollaries are its stones and bricks, logical deduction is the mortar or cement that holds them together. Once it is agreed, as it came to be in the nineteenth century, that mathematics is to be organized as a deductive science, with new results logically deduced from old, and ultimately from axioms, certain questions, not themselves straightforwardly mathematical, about the choice and status of the axioms to be adopted then arise. These are metaphorically called “foundational” questions by philosophers.

Type
Part XIII. Is Foundational Work in Mathematics Relevant to the Philosophy of Science?
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1992 , Issue 2: Volume Two: Symposia and Invited Papers 1992 , 1993 , pp. 432 - 441
Copyright
Copyright © 1993 by the Philosophy of Science Association

References

Dummett, M. (1987), “The Intelligibility of Eucharistic Doctrine”, The Rationality of Religious Belief, W.J. Abraham and W.W. Holtzer (eds.). Oxford : Clarendon Press, pp. 231-261.Google Scholar
Kline, M. (1972), Mathematical Thoughtfrom Ancient to Modern Times. New York: Oxford University Press.Google Scholar
Latour, B. (1987), Science in Action. Cambridge: Harvard University Press.Google Scholar
Tymoczko, T. (ed.) (1985), New Directions in the Philosophy of Mathematics. Boston: Birkhauser.Google Scholar