Full Idea
A mathematical object exists provided there is no contradiction implied in its definition.
Gist of Idea
A mathematical object exists if there is no contradiction in its definition
Source
Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4
Book Reference
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.17
A Reaction
A rather bizarre criterion for existence. Not one, for example, that you would consider applying to the existence of physical objects! But then Poincaré is the father of 'conventionalism', rather than being a platonist.