Here are Aristotle’s “predicables” explained:

1. Definition or Species: a statement of the things essence (to ti en einai or “that which makes it what it is”). Aristotle called this “horos” or “definition.” Porphyry referred to this as “eidos” or “form.” Boethius introduced into the Latin tradition as  “species.” It denotes the specific essence of a thing.
2. Genus: Genus is that part of the essence which is also predicable of other things different from them in kind. The key to understand “genus” is that it is “general.” For example the “genus” of a triangle would be that it is a “shape.”
3. Differentia: that which distinguishes one species from another within a genus. The square species and triangle species are differentiated from one another within the shape genus by the number of their sides. Triangles have three. Squares have four.
4. Propria: A “property” is an attribute which is common to all the members of a class, but is not part of its essence or definition. The fact that the interior angles of all triangles are equal to two right angles is not part of the definition, but is universally true.
5. Accidentia: An accident is an attribute which may or may not belong to a subject. With a “green triangle” the color green is “accidental” – it is not something essential to “triangle-ness.”

Leave a comment if you need more help.

“It is true, indeed, that the account he gives there of the participant is different from what he says in his so-called unwritten teaching.”

- Aristotle, Physics 209b

This secret teaching conforms to something said by Plato in his Seventh Letter:

“Every serious man in dealing with really serious subjects carefully avoids writing” (344c).

So what is this secret “unwritten doctrine” of Plato? I can’t write it down. Come to class and find out…

Here’s how it goes:

1. Bill Clinton, George W. Bush and Barack Obama are each “human”.
2. We infer that there must be a Form called “Human-ness” by which these “humans” participate.
3. Now these three men are alike because they are human. Moreover, these humans are like the Form of “Human-ness.” Consequently, we now have new set of things that are human: Human-ness, Bill Clinton, George W. Bush and Barack Obama.
4. We now need a new Form of Human-ness to account for all these human things, including the original Form of “Human-ness”. Let’s call this new overarching Form “Super-Human-ness.”
5. But now we have an entirely new set of things all alike by way of being human: Super-Human-ness, Human-ness, Bill Clinton, George W. Bush and Barack Obama. It doesn’t stop with this third “Super-Form.” We would have to keep on supplying “Super-Duper Form of Human-ness” and “Even-More-Super-Duper Form of Human-ness: it goes on and on forever. We have an infinite regress, which shows that the theory is absurd.

What does this all mean? The theory of forms assumes that predication is explained by participation and that arguments should not be circular. The Third Man Argument indicates a problem.

Here are some helpful articles on the Third Man Argument:

Cohen, S. M., “The Logic of the Third Man,” Philosophical Review 80 (1971) 448-475.

Geach, P. T., “The Third Man Again,” Philosophical Review 65 (1956) 72-82.

Owen, G.E.L., “The Place of the Timaeus in Plato’s Dialogues,” Classical Quarterly n.s. 3 (1953) 79-95; also in Studies in Plato’s Metaphysics, ed. by R. E. Allen (London: Routledge & Kegan Paul, 1965) 313-338.

Sellars, W., “Vlastos and the Third Man,” Philosophical Review 64 (1955) 405-437.

Strang, C., “Plato and the Third Man,” Proceedings of the Aristotelian Society, Suppl. vol. 37 (1963) 147-164; also in Plato: A Collection of Critical Essays, vol. 1, ed. by G. Vlastos (New York: Anchor, 1971) 184-200, and on reserve in OUGL.

Vlastos, G., “The Third Man Argument in the Parmenides,” Philosophical Review 63 (1954) 319-349; also in Studies in Plato’s Metaphysics, ed. by R. E. Allen (London: Routledge & Kegan Paul, 1965) 231-263.