Note k — Chapter VIII · CLASSIFICATION.
Reading edition
According to Plato, it is τὸ ἓν παρὰ τὰ πολλά. According to Aristotle, it is ἓν κατὰ πολλῶν—ἓν καὶ τὸ αὐτὸ ἐπὶ πλειόνων μὴ ὁμώνυμον ἓν ἐπὶ πολλῶν. Analyt. Poster. I. 11, p. 77, a. 6. Metaphys. I. 9, p. 990, b. 7—13.
Whoever reads the portions of Plato’s dialogues indicated in my last preceding foot note, will see how material this difference is between the two philosophers.
In the remarkable passage of the Analyt. Post. I. 24, p. 85, a. 30, b. 20, Aristotle notices the Platonic hypothesis that the Universal has real objective, separate, existence apart from its particulars (τὸ καθόλου ἐπὶ τι παρὰ τὰ καθ’ ἕκαστα) as an illusion, mischievous and misleading—frequent, but not unavoidable.
See the antithesis between Plato and Aristotle, on the subject of Universals, more copiously explained in the recent work of Professor Bain, Mental and Moral Science, Appendix, pp. 6—20.