14. Anaxagoras on Matter, Continuity, and Mind

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Lecture Notes

Main Topics #

Anaxagoras’s Theory of Matter and Change #

• Foundational principle: Nothing comes from nothing (a common Greek axiom)
• Empirical observation: Everything in the natural world eventually comes to be from everything else
• The inductive chain: Grass → Cow → Man → Lion → Worms → Birds → Cat → Daisies, showing that all things eventually emerge from all other things
• The logical conclusion: Everything must contain infinitesimal parts of everything else
• The infinity problem: To fit an infinity of pieces of different things inside finite objects, these pieces must be infinitely small
• Change as rearrangement: The only real change is change of place (mixing and separating); nothing truly comes into being or ceases to exist

The Continuous and Divisibility #

• Definition: The continuous is that which is divisible forever without reaching a smallest part
• Aristotle’s sixth book of Physics: Contains detailed treatment of continuity
• The point problem: A point (as a limit or boundary) has no parts and cannot compose a line
• Proof by elimination: Two points can only touch by coinciding; coinciding points produce no more length than one point; therefore infinite coinciding points produce no length
• Necessary conclusion: A line must be divisible forever (you cannot cut it into nothing, nor can you reach points)
• Anaxagoras’s insight: “Nor is there a smallest of the small, but there is always a smaller. For what is cannot cease to be by being cut”
• Number and division: Number arises from the division of the continuous; since the continuous is divisible forever, numbers can increase forever

The Problem of Potency (Ability) #

• Anaxagoras’s struggle: He attempts to express the idea of potency but cannot quite articulate it clearly
• The confusion: There is a tendency to imagine what is in something only in ability to be actually in there
• False imagination: When we imagine something, we make it actual in our imagination (Weizsäcker’s observation)
• Historical pattern: This difficulty with understanding potency recurs throughout the history of philosophy

The Greater Mind (Nous) #

• The contrast: Against Empedocles’s view of mindless matter producing rare good combinations by chance, Anaxagoras argues for a greater mind
• The principle: Like effects have like causes; order in artificial things (produced by human mind) resembles order in natural things
• The inference: Therefore, the order in nature must be caused by a mind greater than human mind
• Against chance: Even if combinations happened by chance, survival requires an ordered environment, and reproduction of good traits cannot be explained by chance
• The second law of thermodynamics problem: Random action tends toward disorder, yet we observe increasing order in nature
• Aristotle’s praise: “Anaxagoras introduced mind as a cause of the order in the natural world. He seemed like a sober man among drunk men.”

Key Arguments #

The Induction to Infinitesimal Parts #

1. Everything in nature eventually comes to be from everything else (empirical observation)
2. Nothing comes from nothing (principle)
3. Therefore, everything must be contained in everything
4. Things keep coming to be forever (empirical observation)
5. Therefore, there must be an infinity of pieces of everything in everything
6. Finite objects cannot contain infinite pieces of finite size
7. Therefore, these pieces must be infinitely small

The Argument Against Points Composing a Line #

1. Points have no parts (definition)
2. For two points to touch and compose a line, they must either: (a) have part touching part, (b) have part touching whole, (c) have whole touching part, or (d) have whole touching whole
3. Since a point has no parts, (a), (b), and (c) are impossible
4. Therefore, two points can only touch by whole touching whole (coinciding)
5. Two coinciding points have no more length than one point
6. One point has no length
7. Therefore, any number of coinciding points produce no length
8. Therefore, a line cannot be composed of points
9. Therefore, a line must be divisible forever

The Argument for the Greater Mind #

1. Order in artificial things is caused by human mind (observation)
2. Order in natural things resembles order in artificial things (observation)
3. Like effects have like causes (principle)
4. Therefore, order in nature is caused by a mind like human mind but greater
5. Alternative explanation (chance) fails to account for consistent, universal good order

Important Definitions #

Continuous (συνεχές): That which is divisible forever; its parts meet at a common limit or boundary; includes line, surface, body, time, and place

Discrete quantity: That whose parts do not meet anywhere; includes number

Point (στιγμή): The limit or boundary of a line; that which has no parts; defined by Euclid as having no parts

Seeds (σπέρματα): The infinitesimal pieces of all things; Anaxagoras calls the mixed infinitesimal parts of everything in everything by this name

Nous (νοῦς): Mind; the cause of order and distinction in the natural world; characterized by being unlimited in ability to know, self-ruling, and unmixed with matter

Potency/Ability (δύναμις): The state of being able to be something without actually being it; what Anaxagoras struggles to express clearly

Examples & Illustrations #

The Grass-to-Everything Chain #

Grass → Cow (eats grass) → Man (eats cow) → Lion (eats man) → Worms (eat lion) → Birds (eat worms) → Cat (eats bird) → Daisies (from cat’s decay). This demonstrates that everything eventually comes from everything else.

The Infinitesimal Parts Problem #

How do you fit an infinity of pieces of different things (hair, flesh, bone, etc.) inside a finite blade of grass? Answer: Make them infinitely small, like how a finite line contains infinitely many points.

Testing Points Composing a Line #

If you physically try to put points together, they must touch somehow. But a point has no parts, so they can only coincide (become one). Two coinciding points have no more length than one point (zero length). Therefore points cannot compose a line.

Survival and Environment #

Even if good combinations happened by chance, a child of two bears should be just as likely to be bad as good (since the combination is random). But we observe consistent reproduction of good traits. This requires something beyond chance—an ordered environment and a governing principle.

Questions Addressed #

How can everything come from everything? #

Answer: Through the principle that nothing comes from nothing. If everything eventually comes from everything else (as empirical observation shows), then everything must already be contained in everything as infinitesimal parts.

How can infinitely many things fit in a finite object? #

Answer: By being infinitely small. Just as a finite line contains infinitely many points (though points themselves have no length), finite objects contain infinitely many infinitesimal parts.

Can a line be composed of points? #

Answer: No. Points have no parts and cannot touch in any way that produces length. Two points can only coincide, and coinciding points have no length. Therefore, a line must be divisible forever without reaching a smallest part.

What explains the consistent order in nature if only chance operates? #

Answer: A greater mind (nous) must exist. The order in natural things resembles the order in artificial things (caused by human mind). By the principle that like effects have like causes, a greater mind must cause natural order.

Why would chance alone be insufficient? #

Answer: (1) Survival requires an ordered environment, not just random combinations; (2) Good traits in offspring cannot be explained by chance if parents’ combination was random; (3) The second law of thermodynamics suggests random action tends toward disorder, yet we observe order; (4) The odds against good combinations infinitely outweigh the odds for them.