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Single Idea 10010

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique ]

Full Idea

Frege's views on arithmetic centred on two central theses, that mathematics is really logic, and that it is about distinctively mathematical sorts of objects, such as cardinal numbers. These theses seem uncomfortable passengers in a single boat.

Gist of Idea

Frege's belief in logicism and in numerical objects seem uncomfortable together

Source

comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic

Book Ref

-: 'Journal of Philosophy' [-], p.123


A Reaction

This question pinpoints precisely my unease about Frege. I take logic to be the rules for successful reasoning, so I don't see how they can have ontological implications. It is very extreme platonism to say that right reasoning requires logical objects.

Related Idea

Idea 13864 Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C on Frege]