more from Gottlob Frege

Single Idea 9883

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes]

Full Idea

Frege decided that all logical objects, or at least all those needed for mathematics, could be defined by logical abstraction, except the classes needed for such definitions. ..This definition by equivalence classes has been adopted as a standard device.

Gist of Idea

Frege introduced the standard device, of defining logical objects with equivalence classes


report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 64-68) by Michael Dummett - Frege philosophy of mathematics

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.233

A Reaction

This means if we are to understand modern abstraction (instead of the psychological method of ignoring selected properties of objects), we must understand the presuppositions needed for a definition by equivalence.