Single Idea 10033

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

Full Idea

If a distinguishing features of logic is its complete generality, focusing on truth in general, why should the existence of logic entail the existence of infinitely many objects? ..How can it be completely general if it has ontological commitments?

Gist of Idea

Why should the existence of pure logic entail the existence of objects?

Source

comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.39


A Reaction

This strikes me as simple and devastating. It depends how you conceive logic, but I only conceive it as the formalised rules of successful reasoning. I can't comprehend the claim that without certain objects, reasoning would be impossible.