Single Idea 16896

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory]

Full Idea

Frege thought that if one could derive the existence of numbers from logical concepts, one would not need set theory to explain number theory, or for any other good purpose.

Gist of Idea

If numbers can be derived from logic, then set theory is superfluous

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority (with ps) 2

Book Reference

Burge,Tyler: 'Truth, Thought, Reason (on Frege)' [OUP 2001], p.371


A Reaction

Note that we have two possible routes to 'explain' numbers. I'm inclined to see set theory as modelling numbers rather than explaining them. Frege did better at explanation, but I suspect he is wrong too.