So what are we supposed to learn from the attacks on the Theory of Forms in the first half of the Parmenides and the litany of arguments in the second half?
According to Samuel Rickless, in his intensive study of the dialogue, we are to learn that four of the assumptions of Plato’s Theory of Forms are untenable. The arguments of the second half have shown that they lead to contradictory results and so must be abandoned. Dialogues written after the Parmenides show that Plato does indeed modify his Theory of Forms to avoid the problematic assumptions. He does not indeed forsake the Theory of Forms altogether, but he does accept a modified theory in which the Forms are less transcendent than they are presented as being in the middle-period dialogues.[26]
According to Rickless, the rethinking of the theory goes with the introduction of a new method. In the Phaedo, Plato had recommended the Method of Hypothesis, according to which the investigator should posit the existence of a Form of F to account for the many F things. One would then deduce the consequences of the Form; if it should generate contradictions, then one would reject that Form and posit another, which would not lead to contradictions. One could then posit a higher-level Form from which one could deduce the original Form, until there were no higher-level Forms to be identified.
In light of the criticisms of the Parmenides, Plato recommends the Method of Division and Collection. According to this method, one should posit a Form F for F things. Then one should divide this into subordinate kinds, as one might, for instance divide the Form mammal into different genera, until one reached the level of species. One could then define any given species as the differentia of a genus, or a series of genera. Man might be understood as rational, two-footed mammal. This new method is only rendered possible by the recognition that the Forms may have contrary properties, such as being one (Form) while consisting of many (subordinate Forms), a possibility that was precluded by the earlier Theory of Forms.[27]
This interpretation does offer a helpful roadmap from the problematic dialogue Parmenides to Plato’s later dialogues. Rickless’s account offers a rigorous analysis of the Theory of Forms in both its earlier and its later iterations. It may well be true. Plato’s purpose in composing it, however, remains difficult to discern. For even if Plato has charted a clear path for himself through the maze of his refutations, his purpose can hardly have been clear to a contemporary audience. The barrage of 94 arguments (by Rickless’s count) seems designed not to enlighten (as Plato’s dialectic usually does) but to overwhelm the reader. The overall impression that results must have seemed very much like that of Zeno’s book, which is featured in the introductory conversation, designed to induce aporia or bewilderment rather than illumination. If we call the study of being that Plato undertakes in the second half of the Parmenides ontology, the experience would tend to convince the reader that ontology was aporos, a dead end, an impossibility.
In this way, this dialogue written at the end of Plato’s middle period seems to echo the so-called aporetic dialogues of the early period, which seek a definition but fail to find one. Plato must, figuratively speaking, go back to the drawing board and begin again to tell us how things are, now that the Theory of Forms is under attack, from inside the Academy.
[26] Rickless 2007: 240-250.
[27] Rickless 2007: 246-248.