Ideas from 'Introduction to 'Hippias Minor'' by Robin Waterfield [1987], by Theme Structure

[found in 'Early Socratic Dialogues' by Plato (ed/tr Saunders,Trevor J) [Penguin 1987,0-14-044447-5]].

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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
A mathematical object exists if there is no contradiction in its definition
                        Full Idea: A mathematical object exists provided there is no contradiction implied in its definition.
                        From: Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4
                        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.