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Series:   Elements in the Philosophy of Mathematics

Philosophical Uses of Categoricity Arguments

Published online by Cambridge University Press:  02 December 2023

Penelope Maddy  and
Jouko Väänänen
Penelope Maddy
Affiliation:
University of California, Irvine
Jouko Väänänen
Affiliation:
University of Hesinki

Summary

This Element addresses the viability of categoricity arguments in philosophy by focusing with some care on the specific conclusions that a sampling of prominent figures have attempted to draw – the same theorem might successfully support one such conclusion while failing to support another. It begins with Dedekind, Zermelo, and Kreisel, casting doubt on received readings of the latter two and highlighting the success of all three in achieving what are argued to be their actual goals. These earlier uses of categoricity arguments are then compared and contrasted with more recent work of Parsons and the co-authors Button and Walsh. Highlighting the roles of first- and second-order theorems, of external and internal theorems, the Element concludes that categoricity arguments have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.
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Keywords

categoricitysecond-order logicphilosophy of mathematicsset theoryhistory of logicA12B34C56D78E90
Type
Element
Information
Series: Elements in the Philosophy of Mathematics
Online ISBN: 9781009432894
Publisher: Cambridge University Press
Print publication: 21 December 2023

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