Anaximander of Miletus (Coast of Turkey), mid 6th Century.

First principle ("Arche") is the infinite, boundless ("apeiron").

NB: For an interesting use of the word "apeiron" applied to mathematics, see Euclid's Definition 23, "Parallel Straight Lines." What do you make of that definition? Is there any way to relate Euclid's language to that of Anaximander? How would you compare their projects?

Note that in his commentary on Anaximines (Curd, 14) Simplicius refers to Anaximander's idea of "underlying nature" as "indeterminate." What does this mean? How does it contrast with Anaximines?

Look at the end of Passage 6 (Curd, 12). Anaximander seems to want to account for the phenomenon of change -- of how new things come out of the destruction of old things. A principle of necessity is introduced here, and the dominant metaphor attached to that principle is legal: "they pay the penalty" is a phrase out of Greek law courts. What do you make of the introduction of this trial language into a discourse on change?

Anaximander is interested in the way the physical cosmos came into being, as well as the shape of the planets and their alignment and orientation. What do his descriptions in passages like 8, 9, 10 (Curd, 12) remind you of? Does he seem to be able to connect his speculations with his first principles?

There seems also to be the beginnings of an idea of evolution in Anaximander's writing.

Anaximines of Miletus, late 6th Century.

aer / air / mist as "Arche" or "First Principle."

Simplicius tells us that for Anaximines, the underlying nature is "one and boundless," but also "definite." What does this mean? How does it move away from, or improve on, Anaximander?

A beautiful passage from Hippolytus on Anaximines (Curd, 15): "The form of air if the following: when it is most even, it is invisible, but it is revealed by the cold and the hot and the wet, and movement. It is always moving, for all the things that undergo change would not change unless it was moving." These words, and the explanation that follows them, seem to contain the idea of a system at work behind the physical world. What ideas are at work here in the language? Can you see language in other passages that reinforces this picture of the what "stuff" is composed of?

Note the analogy in Passage 17 (Curd, 14) -- SOUL : "US" :: AER : COSMOS. Is this analogical argument plausible?

Pythagoras / Pythagoreans (of Southern Italy), 6th Century.

Numbers / mathematical ratios / quantitative laws of nature as "First Principle."

The Pythagoreans were primarily formalists in their approach to philosophy. Mathematical relationships, which are to be heard and seen in the physics of music, and confirmed in the practice of geometry, are at the heart of the ordering of the cosmos.

Q. For you math buffs, answer me this. If you are going to claim the above, how will you be able to explain the phenomenon of "incommensurability"? (This term applies to the existence of things like irrational numbers.)

What do you make of the way Pythagoras gets talked about? How can we account for his existence as a mythical -- even holy -- figure?

NB: You will see tons of traces of Pythagorean philosophy in THE PHAEDO.

Xenophanes of Colophon (Turkey, but spends much of his life in Southern Italy), end of 6th Century.

Xenophanes is a critic of traditional orthodoxies based on the texts of Homer and Hesiod. He recognizes the existence of one God. But how much can we know about this God?

NB: Xenophanes' attack on the gods of the great epic poets is critical to Plato's own critique of the poets in THE REPUBLIC.

In statements like those in passages 5 and 6 (Curd, 26), what form of argumentation does X. use to get his point across? How could this apply to the poets he criticizes? 

Xenophanes seems to have a good understanding of the nature of divinity in passages 6-11 (Curd, 26). How can he know this much about God? Where, according to him, are our limits in knowing about divinity, and how does this relate to our limitations in knowing the physical universe?