The Peri ideôn (On Ideas) is the only work in which Aristotle systematically sets out and criticizes arguments for the existence of Platonic forms. Gail Fine presents the first full-length treatment in English of this important but neglected work. She asks how, and how well, Aristotle understands Plato's theory of forms, and why and with what justification he favors an alternative metaphysical scheme. She examines the significance of the Peri ideôn for some central questions about Plato's theory of forms--whether, for example, there are forms corresponding to every property or only to some, and if only to some, then to which ones; whether forms are universals, particulars or both; and whether they are meanings, properties or both. Fine also provides a general discussion of Plato's theory of forms, and of our evidence about the Peri ideon and its date, scope, and aims. While she pays careful attention to the details of the text, she also relates it to contemporary philosophical concerns. The book will be valuable for anyone interested in metaphysics ancient or modern. "
The idea which occurred to me this morning must surely have been thought of many times before, though a quick Google search didn't find anything. Briefly, what happens if you apply Cantor's diagonalization argument to Plato's Theory of Forms? As many people, starting with Aristotle, have pointed out, the theory has obvious weaknesses. (Are we really supposed to believe that there is an Ideal Bed in some other universe, and that all beds in our own world are imperfect instantiations of it?) But if we take the Theory of Forms seriously, does it not follow that the theory itself, as shown to us, is only an imperfect instantiation of the true theory, which is far more coherent and convincing?
Of course, this does beg the question of what the Ideal Theory of Forms might be. Presumably we can never actually know it. But it would at any rate follow that we could get closer to it than Plato did, and viewed in this way - as a kind of research program, rather than a theory per se - it seems to me that it's both plausible and widely accepted.
Meticulous and exhaustive analysis of the arguments from the Peri Ideōn fragment by one of the best Anglo-American readers of Plato, which the patient reader will find to offer significant support for the interpretation of Plato offered elsewhere by Fine, an interpretation which Fine's more accessible works, however, are better suited to present in itself.