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Plato lived from 428-7 BCE to 348-7 BCE, but Platonism surpassed him for hundreds or thousands of years. Neoplatonism was the dominant philosophical school of late antiquity and exerted strong influence on Christianity until the rediscovery of the major works by Aristotle around at 1200 CE, though there were revivals in the Renaissance and even later.

One very famous counter-argument to Plato's theory of forms was the "Third Man": to avoid the infinite regress, the Form of Beauty must either partake of itself, or must not be beautiful.

How did later Platonists deal with this argument?

It's difficult to imagine that they ignored it. But did they agree on a canonical solution?

According to a modern interpretation, Plato himself suggested a solution by introducing different modes of predication (see here). But did Plato's successors find this solution independently?

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  • But in the SEP's entry linked above there is an half-page of references to literature: "There is a vast literature on the Third Man argumet..."
    – Mauro ALLEGRANZA
    Commented Jan 18, 2023 at 9:02
  • @MauroALLEGRANZA it seems to be about the argument itself, not how it was regarded throughout history
    – viuser
    Commented Jan 18, 2023 at 9:23
  • The first critic was obviously Aristotle; see Metaphysics 990b17–1079a13: "Further, of the more accurate arguments, some lead to Ideas of relations, of which we say there is no independent class, and others involve the difficulty of the ‘third man’."
    – Mauro ALLEGRANZA
    Commented Jan 18, 2023 at 10:34
  • Maybe useful Proclus and Self-Predication.
    – Mauro ALLEGRANZA
    Commented Jan 18, 2023 at 10:36

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My two sikkas ...

Suppose {A, B, C} and its form F1

Now Parmenides argues a new set can be constructed {A, B, C, F1} and this new set has a form F2 (the third man). Repeat this procedure and you have an infinite regress of forms F1, F2, F3, ...

However, since we're dealing with forms, we can replace A, B, C with F1. The set {A, B, C, F1} is nothing but {F1, F1} but intriguingly, as in sets, since F1 = F1, {F1, F1} becomes {F1}. We can't abstract a form from only 1 instance of a thing, here F1. Hence, there's no F2, and so no F3, no Fn, ... ad infinitum i.e. the third man doesn't/can't exist. There is no infinite regress! Beautiful is beautiful. 🙂

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    From my understanding, OP was asking for an historical account of the solutions envisaged to the third man problem rather than for a solution.
    – Johan
    Commented Jan 24, 2023 at 22:57

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