Speusippus rejected Plato's Theory of Forms; whereas Plato distinguished between ideal numbers (i.e. the Platonic Forms of numbers) and mathematical numbers, Speusippus rejected the ideal numbers, and consequently the ideas. He tried to determine the idea of substance more distinctly by separating its types, the difference between which he considered would result from the difference between the "principles" ("archai") on which they are based. Thus he distinguished substances of number, of size, of soul, while Plato had referred them, as separate entities, to the ideal numbers.