1. Anaximander and Xenophanes

2. Short Biography Anaximander
Pupil of Thales, a fellow Milesian
First to think of arche as a principle (Thales thought of it as a kind of stuff)
First Full-Service pre-socratic philosopher; i.e., he had a system, a cosmology, a physics, explanation of earth and animals, and an account of human knowledge
First thinker to write in prose (former writer wrote exclusively in poetic form)

3. Anaximander Bio cont’d
First to create a map of the world (in the West), and thus was the first geographer
First to replace the ancient view of the world as a ‘closed vault’ with the familiar modern view of the world as an ‘open universe’.

4. Anaximander’s Metaphysics: Two Key Ideas
The world is accounted for by appeal to an Ur-Stuff he called Apeiron (deh pehroan): Apeiron means “the infinite, indefinite, the internally undifferentiated, the unlimited” (Anaximander preferred the idea of the unlimited, or boundless)
Idea of a ‘Natural Law’

5. First Idea: Apeiron
How Anaximander reasons about what could be the arche of Nature:
Since the four elements are opposites (water vs. fire, air vs. earth), and opposites cannot generate each other (because they are opposites), the arche we are looking for must be something that is free from this limitation.
Something that is in its nature unlimited is something that can act as that undifferentiated material that is capable of taking on any properties whatever.
This is the scientific idea of Matter: a substratum capable of taking any form.

6. Why the Unlimited Solves the Problem that Afflicts idea that the Arche is one of the Four Elements
“If you seek to explain that which underlies a finite world, and which is not itself explained by something else, then you are plausibly looking for something without a limit. And the infinite is such a thing, and further, is naturally thought of as a principle rather than as an entity, and it is a principle that Anaximander thought he must find to stand as the arche of the world.”

7. Second Idea: Natural Law
Anaximander noticed that most kinds of change in nature involve changes in an object associated with movement between opposite properties.
Example: the ice cube warms up and goes from cold to lukewarm to hot.
Anaximander also notices this: nothing keeps getting colder, or hotter…there is a limit to how far an object can go toward the ends of the spectrum defined by pairs of opposites (hot/cold, dry/wet, light/heavy, short/tall, large/small, fast/slow, etc.)

8. Natural Law cont’d
Since no object just keeps getting hotter, or heavier, or larger, or faster, something must explain this fact.
Anaximander’s Big Idea: there is a principle in the world that acts to restrain an object in its properties as those properties move toward the extreme ends of the spectrum (e.g., hot-lukewarm-cold)

9. Natural Law cont’d
What is this principle? He thinks it is moral necessity. Just as moral principles limit how far you can stray from what is just in action, so he thought there is a principle in nature that limits how far an object can go toward extremes of a given type of property
If an object goes too far in the direction of one of the opposing ends of a spectrum (too hot/too cold), the opposite property begins to exercise a counterbalancing force on the object, pulling back towards the middle (paying the price for disobeying the balancing law of nature).

10. To violate Natural Law requires that an object pay Penance
If you get too hot, you are forced to pay penance but coming under the influence of the opposite property, cold, until you have returned to what is just (=a balance between opposites, which lies somewhere in the middle)
Change is explained by the natural oscillation between opposites.
The oscillation is unavoidable because opposites are always trying to overcome each other, but the Law of Nature intervenes to prevent either from winning that battle for supremacy.

11. Anaximander’s Idea that the Earth is at the Center of Space and Motionless
Another application of the idea of a balance of opposites imposed by the Law of Nature can be seen in Anaximander’s idea that the Earth is motionless since it is at the center of space.
Why it must be so: if the Earth is at the center of space (assumed), then something must keep it there. What could that be but something like a nondirectional force keeping it equidistant from all other masses.
This is something like gravity, though without the role for magnitude of a mass, as in Newtonian gravity.

12. Xenophanes Possibly Parmenides teacher
Was also a poet, a peripatetic (what’s this mean?), and founder of the Eleatic school of thought (Elea: a Greek colony located in Italy)
Key ideas:
Nonanthropocentric, all-knowing, all-powerful, all-good single God idea
Skepticism about the range and power of human capacities for knowledge
Distinction between true belief/statement and knowledge.
2&3 make Xenophanes the Father of Epistemology