Participation

Participation (methexis) is the relation Plato uses to connect the world of becoming to the Forms: a beautiful thing is beautiful by participating in Beauty itself, a just act just by sharing in Justice. The Form is the one present, somehow, in the many things named after it; it is what they have in common and what makes them what they are.

The puzzles

But how the many can share in the one is deeply problematic, and Plato presses the difficulties himself in the Parmenides. Is the whole Form present in each participant, or only a part of it — and if the latter, the Form is divided and no longer one? If we explain why many things are large by positing Largeness, does that not require yet another Form to cover the large things together with Largeness, and so on without end (the 'third man' regress)? Plato leaves these objections unanswered, as a standing challenge.

The tradition's answer

The later Platonists worked hard at the problem. Proclus distinguished three terms: the unparticipated Form, which remains transcendent and undivided; the participated character it gives off; and the participating thing that receives it. In this way the higher reality can be shared by the lower without being divided or diminished — the tradition's most careful response to Plato's own doubts, and a model for later accounts of how the universal relates to the particular.