Single Idea 23456

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

Frege's idea is that the logical notion of predication is enough to generate appropriate objects. Every predicate defines a class, which is in turn an object to which predicates apply; and the notion of a class can be used to generate arithmetic.

Gist of Idea

Frege said logical predication implies classes, which are arithmetical objects

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H

Book Reference

Morris,Michael: 'Guidebook to Wittgenstein's Tractatus' [Routledge 2008], p.109


A Reaction

At last, a lovely clear account of what Frege was doing - and why Russell's paradox was Frege's disaster. Logicism must take the ingredients of logic, and generate arithmetical 'objects' from them alone. But do we need 'objects'?