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.

Alfred North Whitehead, Process and Reality (Free Press, 1969) p. 53.

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BILL MURRAY: “What did you study?”

SCARLETT JOHANSSON: “Philosophy.”

BILL MURRAY: “Yeah, there’s a good buck in that racket.”

SCARLETT JOHANSSON: “Well, so far it’s pro bono.”

Lost in Translation (2003)

Far from seeing Neo-Platonism as a far-fetched corruption of Plato’s thought, these thinkers emphasize the continuity between Plato and his traditional interpreters (e.g. Plotinus).

The term “unwritten doctrine” or “unwritten dogma” comes from Aristotle’s Physics

“It is true, indeed, that the account he gives there of the participant is different from what he [Plato] says in his so-called unwritten teaching (agrapha dogmata).” – 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).

What are the so-called “unwritten doctrines”? Aristotle explains it as amounting to the teaching of the “One and the Dyad.” To this is often added the “third hypostasis” of Plotinus, which is “nous” or “intellect.”

Those that favor this interpretation of Plato often see Platonism as reconcilable to Christianity.

Pertinent dialogues to this debate are: Republic, Timaeus, Parmenides, Philebus, Phaedrus, Phaedo and Epistle 7.

“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.

1.    Thales (624-546 B.C.) – The “Father of Greek philosophy”. All things are water

2.    Anaximander (610-546 B.C.) – The first principle is an undefined, unlimited substance without qualities, out of which the primary opposites, (e.g. hot and cold, moist and dry) are differentiated.

3.    Anaximenes (585-525 B.C.) – All things are air – as air “thickens” it becomes fire, cloud, water, earth.

By the way, the first known philosophic critique: Anaximander critiques Thales regarding water.

Pythagorean School – Harmony and Numbers

4.    Pythagoras of Samos (582-496 B.C.). All is number and harmony. He had a cult following.

Ephesian School – Fire and Flux

5.    Heraclitus of Ephesus (535-475 B.C.) – He said that all is fire. Fire is always in flux and so all things are always changing in an unending process.

Eleatic School – The Doctrine of the One

6.    Parmenides of Elea (510-440 B.C.) – All is one and change is only apparent.

7.    Zeno of Elea (490-430 B.C.) – A disciple of Parmenides (not the same Zeno who was the founder of the Stoics). Zeno listed a number of celebrated paradoxes (e.g. Achilles and the Tortoise).

Atomist School – All is Small, Little Things

8.    Leucippus (5th century B.C.) and Democritus of Abdera (460-370 B.C.). All is atoms. Moving along an infinite void, atoms “swerve” and “crash”, thereby generating things.

The Sophists – Wise Guys

9.    Protagoras (490-420 BC) – He is regarded as the “First Sophist”. Diogenes Laertius wrote that Protagoras—a sophist—invented the “Socratic” method. Protagoras said things appear differently to different persons. He creates a system of relativism. Things are and are not.

10.    Gorgias (487-376 BC) – emphasizes the persuasive power of logos or language. He wrote an Encomium of Helen. He defends Helen. She had not power to resist the words convincing her to go to Troy. Language is all powerful for those who are skillful.

11.    Hippias of Elis (485-499 BC) – He was a younger contemporary of Protagoras and Socrates who claimed to make his own clothing. He also claimed to be an authority on all subjects, and lectured on economics, politics, poetry, grammar, history, archaeology, mathematics and astronomy.

12.    Prodicus (465-390 BC) – He carefully distinguishes the meanings of words. Aristotle actually outdoes him because Aristotle classifies the different meanings of a single word.

Remember the Sophists tend to be focused on langauge and rhetoric. They seem to be disillisioned with the cosmologies of earlier thinkers.

Many believe that the hand gestures of Plato and Aristotle (in the center of the painting) denote two ways of doing metaphysics. Plato points to the heavens–Aristotle to the earth. If look closely, Plato is holding a book: Timaeus, one of his most celestial and abstract dialogues. Aristotle is holding his Nichomachean Ethics, a rather terrestrial treatise.

Here are the philosophers featured by Raphael in the Scuola di Atene by number:

1: Zeno of Citium 2: Epicurus 3: Federico II of Mantua? 4: Boethius or Anaximander or Empedocles?

5: Averroes 6: Pythagoras 7: Alcibiades or Alexander the Great? 8: Antisthenes or Xenophon? 9: Hypatia 10: Aeschines or Xenophon?

11: Parmenides? 12: Socrates 13: Heraclitus (as Michelangelo) 14: Plato (as Leonardo da Vinci) 15: Aristotle

16: Diogenes of Sinope? 17: Plotinus? 18: Euclid or Archimedes with students 19: Strabo or Zoroaster? 20: Ptolemy? R: Apelles (as Raphael) 21: Protogenes

For the all the ladies, the only woman to make it into the painting was Hypatia who is located at #9.

Defining Justice
I.1. 327a—328b. Down to the Piraeus
I.2—I.5. 328b—331d. Cephalus. Justice of the Good Ol’ Boy
I.6—1.9. 331e—336a. Polemarchus. Justice of the Heir
I.10—1.24. 336b—354c. Thrasymachus. Justice of the Sophist

The Ring of Gyges
II.1—II.10. 357a—369b. Is Justice Better than Injustice?

Genesis and Order of the Polis
II.11—II.16. 369b—376e. Origin of the Polis
II.1—III.18. 376e—412b. Education of the Guardians
III.19—IV.5. 412b—427c. Constitution of the Polis
IV.6—IV.I9. 427c—445e. Justice in the Polis

Embodiment of the Idea
V.1—V.16. 449a—471c. Somatic Unit of Polis and Hellenes
V.17—VI.14. 471c—502c. Philosopher Kings
VI.19—VII.5. 502c—521c. The Allegory of the Cave
VII.6—VII.18. 521c—541b. Education of the Philosophers

Defective Forms of Polity
VIII.1—VIII.5. 543a—550c. Timocracy
VIII.6—VIII.9. 550c—555b. Oligarchy
VIII.10—VIII.13. 555b—562a. Democracy
VIII.I4—IX-3. 562a—576b. Tyranny

Conclusion
IX.4—IX.13. 576b—592b Answer: Justice is Better than Injustice

Epilogue
X.1—X.8. 595a—608b. Rejection of Mimetic Art
X.9—X.11. 608c—612a. Immortality of the Soul
X.12. 612a—613e. Rewards of Justice in Life
X.13—X.16. 613e—631d. The Myth of Er and the Judgment of the Dead

1. Books I-V: The definition of “justice” and the Utopian Republic
2. Books VI-VII: The definition of “philosopher” and Philosopher Kings as the ideal rulers
3. Books VIII-X: Discussion of the various forms of government (their pros and cons)

- Bertrand Russell, History of Western Philosophy, Book I, part 2, ch. 14