40. Aristotle's Critique of Anaxagoras and the Principle of Fewness

Subscribe in Podcast App | Download Transcript

Lecture Notes

Main Topics #

Anaxagoras’s Position #

• Claims everything is mixed in everything (flesh, blood, bone, etc.)
• Based on two premises: (1) nothing comes from nothing, and (2) everything comes to be from everything
• Proposes an infinity of infinitely small pieces of everything within everything
• Names things by what they have most of (the “Anaxagorean way of naming”)
• Example: Book of Psalms is called sapiential because it contains mostly wisdom literature

The Fundamental Problem: Act vs. Potentiality #

• Anaxagoras confuses what is actual with what is potential
• Everything is in ability within matter, but not in act
• Example: In a piece of clay shaped as a sphere, the cube form is in ability but not in act
• When we speak of the shape changing, we implicitly recognize genus (shape) as prior to differences (sphere/cube), revealing that these distinctions are more knowable than matter itself
• John Locke makes the same error attempting to make a general triangle contain all differences actually

Key Arguments Against Anaxagoras #

Argument 1: Unknowability of Infinite Causes #

• If beginnings are unlimited, they cannot be known
• Nature gives humans a natural desire to know causes
• Nature does nothing in vain; therefore causes must be knowable
• Analogy: one cannot know a word with infinite letters, even the best speller would never finish
• This connects to the principle that natural desires correspond to possible objects

Argument 5: Infinite Infinities (Peculiar to Anaxagoras) #

• Not only are there infinite pieces of everything in everything
• But within each infinitely small piece, there must be infinite pieces of everything
• This creates infinities of infinities infinitely—impossible complexity
• This violates the principle that nature prefers simplicity and unity
• Example: Max Born noted that genuine physicists believe in unity and simplicity of nature despite appearances; the periodic table of ~100 elements is already considered too many—infinities of infinities is absurd

Argument 8: The Principle of Fewness (Comparative) #

• Empedocles explains eternal becoming with only four elements (earth, air, fire, water) and two principles (love and hate)
• Anaxagoras requires an infinity of components to achieve the same result
• Therefore, the simpler explanation is preferable
• This principle has been fundamental to natural science from Galileo, Kepler, Newton through Einstein

The Principle of Fewness (Principle of Simplicity) #

Definition and Application #

• Fewer causes are better if they are sufficient to explain phenomena
• Newton: “Nature is pleased with simplicity; it affects not the pompous, superfluous causes”
• Historical examples:
  • Galileo sought the simplest explanation for accelerated motion
  • Kepler spent ten years finding the simplest geometric figure (the ellipse) for planetary motion
  • The circle is simpler than multiple circles stacked on circles
  • The ellipse with two foci is simpler than Ptolemaic circles upon circles

Modern Applications #

• Debate over day/night causation: both ancients and moderns assume one sun rather than a new sun each day
• With one sun, circular motion explains eternal recurrence; with new suns daily, an infinity would be required
• Recycling principle: resources are finite, so circular (recursive) systems are preferable to linear systems
• The principle of parsimony: prefer one teacher returning each day to hundreds of identical look-alikes with identical training

Important Distinctions #

Natural vs. Mathematical Quantity #

• Mathematical quantity: divisible indefinitely without natural limit; can serve infinite customers (mathematical lines)
• Natural quantity: has definite limits due to the nature of the thing; eventually exhausts (water molecules, biological entities)
• Example: Mathematical retail of lines never needs restocking; selling chairs has finite supply
• Example: The Canteen of Water—mathematically can divide forever, but actually runs out due to molecular size limits

The Anaxagorean Way of Naming Things #

• Name things by what they have most of (either absolutely or in comparison)
• This naming convention reveals that some aspects are more fundamental than others
• When asked if shape or clay changed when sphere becomes cube, people say “shape changed,” implying genus is the more fundamental subject

Examples & Illustrations #

The Grass-to-Everything Example #

• Cow eats grass → more cow from grass
• Man eats cow → more man from cow
• Lion eats man → more lion from man
• Lion dies → produces worms
• Worms become birds → more birds
• Birds become cats → more cats
• Cats die and decompose → daisies grow
• Conclusion: everything must be in everything to allow this continuous transformation

Modern Physics Parallel #

• Accelerating elementary particles into one another produces results with more mass than the original particles
• Unlike water → hydrogen + oxygen (where results are smaller)
• Yet Heisenberg says: “Every elementary particle is composed of all the rest”
• This echoes Anaxagoras’s error of making actual what should be only potential

Christmas Toys and Exercise #

• Anaxagorean way: buy finished toys (must buy new ones constantly when they break)
• Empedoclean way: buy a bag of blocks (can build, destroy, rebuild forever with limited resources)
• Man exercising: must run infinitely long straight line daily to keep running forever
• Wise approach: run in a circle (finite circuit, can continue forever)

The Smallest Piece Problem #

• Arguments 2, 3, 4 form a chain (domino effect):
  • Argument 2: If parts fall below any size, wholes would too; but experience shows definite size limits; therefore smallest pieces exist
  • Argument 3: If smallest piece of flesh exists and is finite in body, infinite pieces cannot be extracted; generation would stop
  • Argument 4: If smallest piece of flesh exists and cannot contain bone, then not everything is in everything

Notable Quotes #

“Everything is mixed in everything, because he saw, and you can say by induction, everything coming to be from everything.” — Aristotle, on Anaxagoras’s reasoning

“Nature is pleased with simplicity; it affects not the pompous, superfluous causes.” — Isaac Newton

“The genuine physicist believes often in the unity and simplicity of nature, despite any appearance of the contrary.” — Max Born, The Restless Universe

“We know matter only through the forms of matter. We don’t know matter by itself.” — Heisenberg

Questions Addressed #

Why Can’t Anaxagoras’s Position Work? #

• Makes actually present what should only be in ability (potentiality)
• Requires infinite causes when finite ones suffice
• Creates logical impossibility (infinite infinities)
• Violates the principle of natural limits based on the natures of things

How Does the Principle of Fewness Apply? #

• If Empedocles can explain eternal becoming with four elements and two principles
• And Anaxagoras requires infinite infinities for the same result
• Then the mind naturally inclines toward the simpler explanation
• This principle is not arbitrary but reflects how nature actually works

Why Is the Order of Arguments Important? #

• Arguments 1-7 critique Anaxagoras’s position itself
• Argument 8 is comparative, showing Empedocles as superior
• Arguments 1, 5, 8 share the principle of fewness and can be grouped together pedagogically
• Arguments 2-4 form a chain showing natural limits exist
• Arguments 6-7 address particular difficulties with substance/accident confusion