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Philosophical Uses of Categoricity Arguments

Jouko Väänänen author Penelope Maddy author

Format:Paperback

Publisher:Cambridge University Press

Published:21st Dec '23

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Philosophical Uses of Categoricity Arguments cover

Recent internal categoricity arguments are viewed compared to historical cases to reveal what categoricity arguments can and cannot do.

This Element addresses the categoricity arguments that have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.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.

ISBN: 9781009432924

Dimensions: 230mm x 153mm x 5mm

Weight: 114g

64 pages