Single Idea 9854

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

Full Idea

We can introduce a new type of object from the obtaining of some equivalence relation between objects of some already known kind, by identifying the new objects as equivalence classes of the old ones under that equivalence relation.

Gist of Idea

We can introduce new objects, as equivalence classes of objects already known

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.14

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.167


A Reaction

Some accounts of abstraction merely describe the concept, but this is a rival to the traditional pyschological abstractionism that Frege attacked so vigorously. Should we take a platonist or constructivist view of the new objects?