Philosophical Uses of Categoricity Arguments (Elements in the Philosophy of Mathematics) - Softcover

Maddy, Penelope

Softcover

ISBN 10: 1009432923 ISBN 13: 9781009432924

Publisher: Cambridge University Press, 2023

Synopsis

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2023
• Language: English
• ISBN 10: 1009432923
• ISBN 13: 9781009432924
• Binding: Paperback
• Number of pages: 64