Sokrates, thus embarrassed, starts the hypothesis that perhaps each of these Forms may be a cogitation, and nothing more, existing only within the mind. How? rejoins Parmenides. Can there be a cogitation of nothing at all? Must not each cogitation have a real cogitatum correlating with it, — in this case, the one Form that is identical throughout many particulars? If you say that particulars partake in the Form, and that each Form is nothing but a cogitation, does not this imply that each particular is itself cogitant?
Again Sokrates urges that the Forms are constant, unalterable, stationary in nature; that particulars resemble them, and participate in them only so far as to resemble them. But (rejoins Parmenides), if particulars resemble the Form, the Form must resemble them; accordingly, you must admit another and higher Form, as the point of resemblance between the Form and its particulars; and so on, upwards.
And farther (continues Parmenides), even when admitting these Universal Forms as self-existent, how can we know anything about them? Forms can correlate only with Forms, Particulars only with Particulars. Thus, if I, an individual man, am master, I correlate with another individual man, who is my servant, and he on his side with me. But the Form of mastership, the Universal self-existent Master, must correlate with the Form of servantship, the Universal Servant. The correlation does not subsist between members of the two different worlds, but between different members of the same world respectively. Thus the Form of Cognition correlates with the Form of Truth; and the Form of each variety of Cognition, with the Form of the corresponding variety of Truth. But we, as individual subjects, do not possess in ourselves the Form of Cognition; our cognition is our own, correlating with such truth as belongs to it and to ourselves. Our cognition cannot reach to the Form of Truth, nor therefore to any other Form; we can know nothing of the Self-good, Self-beautiful, Self-just, &c., even supposing such Forms to exist.
These acute and subtle arguments are nowhere answered by Plato. They remain as unsolved difficulties, embarrassing the Realistic theory; they are reinforced by farther difficulties no less grave, included in the dialectical antinomies of Parmenides at the close of the dialogue, and by an unknown number of others indicated as producible, though not actually produced. Yet still Plato, with full consciousness of these difficulties, asserts unequivocally that, unless the Realistic theory can be sustained, philosophical research is fruitless, and truth cannot be reached. We see thus that the author of the theory has also left on record some of the most forcible arguments against it. It appears from Aristotle (though we do not learn the fact from the Platonic dialogues), that Plato, in his later years, symbolized the Ideas or Forms under the denomination of Ideal Numbers, generated by implication of The One with what he called The Great and Little, or the Indeterminate Dyad. This last, however, is not the programme wherein the Realistic theory stands opposed to Nominalism.
But the dialogue Parmenides, though full of acuteness on the negative side, not only furnishes no counter-theory, but asserts continued allegiance to the Realistic theory, which passes as Plato’s doctrine to his successors. To impugn, forcibly and even unanswerably, a theory at once so sweeping and so little fortified by positive reasons, was what many dialecticians of the age could do. But to do this, and at the same time to construct a counter-theory, was a task requiring higher powers of mind. One, however, of Plato’s disciples and successors was found adequate to the task — Aristotle.
The Realistic Ontology of Plato is founded (as Aristotle himself remarks) upon mistrust and contempt of perception of sense, as bearing entirely on the flux of particulars, which never stand still so as to become objects of knowledge. All reality, and all cognoscibility, were supposed to reside in the separate world of Cogitable Universals (extra rem or ante rem), of which, in some confused manner, particulars were supposed to partake. The Universal, apart from its particulars, was clearly and fully knowable, furnishing propositions constantly and infallibly true: the Universal as manifested in its particulars was never fully knowable, nor could ever become the subject of propositions, except such as were sometimes true and sometimes false.
Against this separation of the Universal from its Particulars, Aristotle entered a strong protest; as well as against the subsidiary hypothesis of a participation of the latter in the former; which participation, when the two had been declared separate, appeared to him not only untenable and uncertified, but unintelligible. His arguments are interesting, as being among the earliest objections known to us against Realism.
1. Realism is a useless multiplication of existences, serving no purpose. Wherever a number of particulars — be they substances, eternal or perishable, or be they qualities, or relations — bear the same name, and thus have a Universal in re predicable of them in common, in every such case Plato assumes a Universal extra rem, or a separate self-existent Form; which explains nothing, and merely doubles the total to be summed up.[14]
[14] Aristot. Metaph. A. ix. p. 990, a. 34; M. iv. p. 1079, a. 2. Here we have the first appearance of the argument that William of Ockham, the Nominalist, put in the foreground of his case against Realism: “Entia non sunt multiplicanda præter necessitatem.�
2. Plato's arguments in support of Realism are either inconclusive, or prove too much. Wherever there is cognition (he argues), there must exist an eternal and unchangeable object of cognition, apart from particulars, which are changeable and perishable. No, replies Aristotle: cognition does not require the Universale extra rem; for the Universale in re, the constant predicate of all the particulars, is sufficient as an object of cognition. Moreover, if the argument were admitted, it would prove that there existed separate Forms or Universals of mere negations; for many of the constant predicates are altogether negative. Again, if Self-existent Universals are to be assumed corresponding to all our cogitations, we must assume Universals of extinct particulars, and even of fictitious particulars, such as hippocentaurs or chimeras; for of these, too, we have phantasms or concepts in our minds.[15]