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The Logic of Mathematical Discovery Vs. the Logical Structure of Mathematics

Published online by Cambridge University Press:  31 January 2023

Solomon Feferman
Solomon Feferman*
Affiliation:
Stanford University
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Extract

Mathematics offers us a puzzling contrast. On the one hand it is supposed to be the paradigm of certain and final knowledge: not fixed to be sure, but a steadily accumulating coherent body of truths obtained by successive deduction from the most evident truths. By the intricate combination and recombination of elementary steps one is led incontrovertibly from what is trivial and unremarkable to what can be non-trivial and surprising.

On the other hand, the actual development of mathematics reveals a history full of controversy, confusion and even error, marked by periodic reassessments and occasional upheavals. The mathematician at work relies on surprisingly vague intuitions and proceeds by fumbling fits and starts with all too frequent reversals. In this picture the actual historical and individual processes of mathematical discovery appear haphazard and illogical.

The first view is of course the currently conventional one which descends from the classic work of Euclid.

Type
Part VIII. Lakatos’ Philosophy of Mathematics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 2: Volume Two: Symposia and Invited Papers 1978 , 1978 , pp. 309 - 327
Copyright
Copyright © 1981 Philosophy of Science Association

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References

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