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Poincaré on Mathematics, Intuition and the Foundations of Science

Published online by Cambridge University Press:  28 February 2022

Janet Folina
Janet Folina*
Affiliation:
Macalester College
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Extract

In his first philosophy book, Science and Hypothesis, Poincaré gives us a picture which relates the different sciences to different kinds of hypotheses. In fact, as Michael Friedman has pointed out (Friedman 1995), Poincaré arranges this book—chapter by chapter—in terms of a hierarchy of sciences. Arithmetic is the most general of all the sciences because it is presupposed by all the others. Next comes mathematical magnitude, or the analysis of the continuum, which presupposes arithmetic; then geometry which presupposes magnitude; the principles of mechanics which presuppose geometry; and finally experimental physics which presupposes mechanics. Poincaré's basic view was that experiment in science depends on fixing other concepts first. In particular he believed at the time that our concept of space had to be fixed before we could discover truths about the objects in space.

Type
Part VII. Foundational Projects in Mathematics at the Beginning of the 20th Century in Their Systematic and Historical Contexts
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1994 , Issue 2: Volume Two: Symposia and Invited Papers 1994 , 1994 , pp. 217 - 226
Copyright
Copyright © 1995 by the Philosophy of Science Association

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Footnotes

1

I would like to thank David Stump and especially Peter Clark for helpful discussion, Henry West for editing suggestions, and Alan Richardson for all his work.

References

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