The Timpson Lyceum · History of Philosophy (2024)

Anaxagoras: Mind and Matter – Lecture 9 (History of Philosophy)

Overview

Anaxagoras of Clazomenae (~500–428 BC) is the next pluralist, and the first philosopher to work in Athens — arriving (probably with the Persian military) and staying through the city's golden-age rebuilding. A friend of Pericles, he was eventually prosecuted for impiety (for teaching that the sun and moon are physical bodies, not gods) and driven out, ending his life honored in Lampsacus.

His philosophy has two great moves. First, a critique and radicalization of Empedocles: four elements are not enough. Where do a banana's taste, or flesh, or hair come from, if only earth/air/fire/water (hot/cold/wet/dry) are real? To avoid "what is not" coming into being, Anaxagoras argues there must be infinitely many kinds of "seeds," and "everything is in everything" — every portion of matter contains a bit of every kind of seed; a thing appears to be what predominates in it. Second, and what he is most famous for, he introduces Nous (Mind) as the one thing not mixed into everything — a pure, knowing, ordering force that sets the cosmos spinning. This is the first sharp distinction between mind and matter, and the first teleological (purpose-based) account of the world's origin.

Key Concepts

• Critique of Empedocles — Four elements can't explain the sheer variety of qualities (a banana's taste, flesh, hair). If those qualities weren't there and then are, that's still "what is not" becoming "what is" — the very thing Parmenides forbade.
• Infinite kinds of seeds (spermata) — For every quality and combination of qualities there must be a corresponding kind of seed. So the fundamental "stuffs" are not four but infinite in kind (Empedocles called them roots; the atomists will call them atoms; Anaxagoras calls them seeds).
• "Everything is in everything" — Every region of matter contains an infinite number of every kind of seed. Nothing is pure.
• Predominance — A thing looks and behaves like X because X-seeds predominate in it, not because it is made only of X. Burn a log → ash-seeds come to predominate as wood-seeds separate off; there is still an infinity of wood-seeds left in the ash.
• Infinite divisibility — "There is no smallest": any bit, however tiny, can always be divided further, so it contains infinitely many parts — which is how infinitely many seeds fit in a finite object.
• The flesh argument — Cut flesh in half and you get flesh, again and again; you never reach earth/air/fire/water. So flesh must itself be a fundamental stuff (a seed), not a mixture of four elements.
• Change as separation, not creation — All change is seeds separating off and shifting the ratios of seeds. Nothing new is created or destroyed — satisfying Parmenides — yet the world genuinely changes (as Empedocles wanted).
• Nous (Mind) — The great innovation: an infinite, self-ruling, unmixed, purest thing that alone knows all things and can originate motion without a prior physical cause. In the beginning Nous started the cosmic rotation that separated the seeds and formed the world.
• Mind vs. matter — Nous is the one thing not blended into everything; only some things (living, thinking ones) partake of it. This cleanly separates knowing/self-moving mind from inert matter for the first time.
• Teleology vs. mechanism — Explaining by purpose (why you drank: thirst) versus by cause (why the rock fell: gravity). By having Mind order the world for a purpose, Anaxagoras gives the first teleological cosmogony — though he's later criticized (by Plato/Aristotle) for using Nous only as a "god of the gaps" and otherwise explaining nature mechanically.
• Astronomy — The sun is a fiery mass larger than the Peloponnese; the moon is earthy and shines by reflected sunlight, with mountains and valleys; correct-ish accounts of eclipses and rainbows. These physical (non-divine) heavens got him charged with impiety.
• The scientific dead end — If each thing is just its own kind of seed and nothing reduces to anything else, you cannot relate or unify phenomena — the opposite of Thales' original goal. This impasse sets up the atomists.

Worked Example

Comparing infinities — why Anaxagoras' "one infinity is bigger than another" is subtler than it looks. Anaxagoras assumed an object could hold, say, "100 banana-seeds for every 1 rock-seed" while both counts are infinite — treating one infinity as a fixed multiple of another. This is bad math: for infinite sets, "how many" is measured by one-to-one correspondence (bijection), not by ratios. The classic demonstration (Cantor, ~1874, ~2,300 years later):

1. Claim: there are "twice as many" integers $\mathbb{Z} = \{\dots,-2,-1,0,1,2,\dots\}$ as natural numbers $\mathbb{N} = \{0,1,2,3,\dots\}$, since $\mathbb{Z}$ adds all the negatives.
2. Test it the right way — try to pair each natural number with exactly one integer, none left over on either side. Define $f(n) = \begin{cases} \dfrac{n}{2}, & n \text{ even} \\ -\dfrac{n+1}{2}, & n \text{ odd.} \end{cases}$
3. Check the pairing: $f(0)=0,\; f(1)=-1,\; f(2)=1,\; f(3)=-2,\; f(4)=2,\; f(5)=-3,\dots$
4. Every integer appears exactly once, and every natural number is used exactly once — a perfect bijection $\mathbb{N} \leftrightarrow \mathbb{Z}$.
5. Therefore $\mathbb{N}$ and $\mathbb{Z}$ have the same size (cardinality $\aleph_0$), even though $\mathbb{Z}$ "obviously" looks twice as big. Infinite quantities do not obey "twice as many."
6. So Anaxagoras was right that a finite object can contain infinitely many seeds of every kind (infinite divisibility guarantees it) — but wrong to say one such infinity is "100×" another. The mathematics needed to make ratios-of-infinities precise (and to see when they fail) simply didn't exist yet. $\blacksquare$

Summary

• Anaxagoras, the first Athenian philosopher and a pluralist, argued Empedocles' four elements can't explain the world's endless qualities — so there must be infinitely many kinds of seeds.
• "Everything is in everything": every bit of matter holds a portion of every seed; a thing is whatever seed predominates in it, and change is just seeds separating and shifting ratios — no true creation or destruction.
• His signature contribution is Nous (Mind): a pure, all-knowing, unmixed force that starts the cosmic rotation — the first clear mind/matter split and the first teleological cosmogony.
• He got the physics of the heavens strikingly right (sun as huge fiery mass, moon reflecting sunlight) — which got him prosecuted for impiety.
• His seed-theory is a scientific dead end (nothing relates to anything), which — together with his relied-on-but-underused Mind — pushes philosophy toward the atomists next.