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.