The Logic of Mathematical Discovery versus The Logical Structure of Mathematics
Solomon Feferman
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Source: Crossref
Published: Nov 19, 1998
DOI: 10.1093/oso/9780195080308.003.0003
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Abstract 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 nontrivial 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.
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