29. The Third Principle: Resolving Contradiction in Change

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Lecture Notes

Main Topics #

The Problem of Change and Apparent Contradiction #

• When we say “the hard becomes soft” or “the healthy becomes sick,” we appear to claim that the hard is soft—which violates the principle of non-contradiction
• Heraclitus identified this apparent contradiction as fundamental to all change
• The untying of this apparent contradiction is the discovery of a third thing necessary for change

Why Two Contraries Are Insufficient #

• From the previous reading, we know that beginnings (principles) are contraries, meaning at least two are required
• However, two contraries alone cannot account for change without generating logical impossibility
• If density made rareness dense, then rareness itself would be dense—a contradiction
• Therefore, there must be a third thing (subject/substrate) apart from the contraries themselves

The Third Principle: Subject with Potency #

• The third thing is that which possesses the contraries but is identical to neither
• Example: Butter is neither hardness nor softness, yet can possess both properties at different times
• This third thing has the capacity (potency/ability) to be either contrary, but not both simultaneously
• When actually one, it remains capable of becoming the other

The Critical Distinction: “As Such” vs. “By Happening” (Accidentally) #

• As such (κατὰ τὸ εἶναι): What something is in its essence or nature
• By happening/accidentally (κατὰ συμβεβηκός): What incidentally belongs to a thing without being its essence
• Hardness as such cannot become softness; but the subject (butter) as such can become soft
• A carpenter “as such” builds houses; playing violin is accidental to being a carpenter
• This distinction prevents the contradiction that would arise from confusing the property with its subject

From Confused to Distinct Knowledge #

• Aristotle proceeds from confused knowledge (the undifferentiated word “hard”) to distinct knowledge
• Distinct knowledge recognizes the real distinction between:
  • The hardness (the quality)
  • That which possesses hardness (the subject/butter)
• Unless there is a real distinction between the subject and its properties, change would be impossible
• This parallels the first reading’s principle: we know sensible wholes before distinguishing their parts

Aristotle’s Four Arguments Against Unlimited Principles #

First Argument (from Knowledge and Nature’s Efficiency):

• We naturally desire to know causes
• If causes were unlimited, they would be unknowable
• Nature does nothing in vain; therefore, causes cannot be unlimited

Second Argument (from Genus and Contraries):

• In any one genus, there is only one pair of contraries (e.g., white and black in color, not yellow and black)
• Contraries are defined as species furthest apart in the same genus
• Since substance is one genus (the fundamental genus), there can be only one pair of contraries as first principles

Third Argument (from the Principle of Fewness):

• Limited principles (like Empedocles’ four elements: earth, air, fire, water, plus love and hate) can explain perpetual coming-to-be
• Unlimited principles would require infinite complexity
• Fewer causes are better if sufficient

Fourth Argument (from Hierarchy of Causes):

• Not every pair of contraries can be first principles
• Some pairs (hard/soft) cause other pairs (black/white)
• If principles were unlimited, we would have an impossible hierarchy

The Principle of Fewness (Simplicity) #

• Core formulation: Fewer causes are better if they are sufficient
• Nature does not affect “the pomp of superfluous causes”
• “More is in vain when less will serve” (Newton)
• This principle underlies all natural science from the Greeks through modern physics (Einstein)
• Not that fewer is always better in absolute terms, but that we should not multiply causes beyond necessity

Key Arguments #

The Main Argument for a Third Principle #

The Logical Problem:

1. We ordinarily say “the hard becomes soft”
2. If this means the hard comes to be soft, then the hard would be soft
3. This would mean the same thing is both hard (its nature) and soft (what it becomes)
4. This violates the principle of non-contradiction

The Solution:

1. The hard as such does not become soft
2. Rather, a third thing (the subject) becomes soft
3. This third thing is neither hardness nor softness essentially
4. It can possess either property at different times

Examples Demonstrating the Argument:

• Butter: Is neither hardness nor softness; can be hard or soft
• Air: Is neither light nor darkness; can be illuminated or dark
• Cloth: Is neither wetness nor dryness; can be wet or dry

The Method of Contradiction in Knowledge Development #

Pattern Identified:

• Apparent contradictions in our thinking prompt deeper understanding
• The resolution of contradictions reveals previously hidden distinctions
• This is the first major example of how human reason advances

Historical Examples:

• Anaxagoras on Mind: Apparent contradiction between mind being self-ruling and the ruler being separate; resolved by distinguishing what the mind knows from what it doesn’t know
• Socrates and the Slave Boy: Socrates reveals the slave boy’s contradiction (thinking he knows what he doesn’t) through questioning, moving him from false confidence to genuine inquiry
• Heraclitus on Change: Identified the apparent contradiction in change itself

Important Definitions #

Contraries (ἐναντία) #

• Species furthest apart in the same genus (the same general kind of thing)
• In color: white and black (not yellow and black)
• In ethics/habit: virtue and vice (not confidence and incompetence)
• Cannot both exist in the same thing at the same time
• At least two are required for any subject to admit of change

The Subject (ὑποκείμενον) / Substrate #

• That which possesses the contraries without being identical to either
• Remains the same throughout the change of contraries
• Has the capacity (potency) to possess either contrary
• When actually possessing one, remains capable of possessing the other
• Examples: butter, air, cloth, wax, etc.

Potency (δύναμις) and Actuality (ἐνέργεια) #

• Potency: The ability or capacity to be something
• Actuality: The state of being something in fact
• The subject is in potency to both contraries but in actuality to only one at a time
• This distinction allows us to understand how change occurs without contradiction

Privation (στέρησις) #

• The lack of a form that something is naturally capable of possessing
• Cold is understood as privation of heat
• Important for completing the three principles of change

Examples & Illustrations #

The Butter Example #

• Butter is neither hardness nor softness itself
• Butter can be hard; butter can be soft
• Hardness cannot become softness (that would be a contradiction)
• But butter (as such) can become soft
• Distinction: When butter is hard, being hard is what it is “as such” at that moment; when it becomes soft, the softness is what happens to it

The Day and Night Example #

• Question: Does darkness become light? Does light become darkness?
• Answer: No—that would be a contradiction (light cannot be lack of light)
• Rather: The air (the third thing) becomes illuminated or becomes dark
• The air is capable of both states but not simultaneously

The Carpenter and Musician #

• A carpenter “as such” builds houses
• If an individual carpenter plays violin, that is accidental to his being a carpenter
• We do not say “carpenters play violins” even if some individual carpenters do
• A child asking “what do carpenters do?” should be answered: what carpenters “as such” do, not what particular carpenters happen to do

The Last Drink Example #

• A person desires another drink because it appears good (seems like continuing the good time)
• Not because it appears bad (making one sick)
• The good as such is what is desired
• The bad is desired only as apparently good, not as bad
• Demonstrates how the “as such” distinction resolves apparent contradictions in desire and action

The Circle vs. Straight Road #

• A wealthy man wants to run forever
• On a straight road: requires an infinitely long road
• On a circular road: finite road allows infinite running
• Illustrates the principle of fewness: fewer resources (finite road) achieve the same result (perpetual motion)

The Blocks vs. Finished Toy (Christmas Gifts) #

• A bag of building blocks can be made into something, knocked down, rebuilt indefinitely
• A finished toy breaks in a week; then you need to buy another, and another
• Blocks exemplify Empedocles’ principle: limited elements with the capacity for infinite recombination
• Shows how limited principles with potency are superior to unlimited ones

The Twin Brother Thought Experiment #

• How do we know the lecturer doesn’t have an identical twin teaching on Thursdays while he teaches on Tuesdays?
• In the absence of evidence for two people, we assume one
• Only contradictory evidence (seeing both simultaneously) would force us to posit two
• Illustrates the principle that we do not multiply entities beyond necessity

Notable Quotes #

“Only a two-headed mortal could think this [that something can both be and not be].” — Parmenides (referenced through Aristotle)

“Nature affects not the pomp of superfluous causes; more is in vain when less will serve.” — Isaac Newton, Principia

“Fewness in truth.” — Shakespeare (Troilus and Cressida, through Ulysses)

“Fewer causes are better if they are enough.” — Paraphrase of foundational principle discussed by Einstein and evident in Greek natural philosophy

“Things in motion sooner catch the eye than what stirs not.” — Shakespeare (Troilus and Cressida, Ulysses)

“Men do not understand the things they meet every day, even though they think they do.” — Heraclitus (DK, Fragments on Method)

“The untying of the apparent contradiction is the discovery of how the mind does in fact rule itself.” — Duane Berquist (paraphrase of argument on Anaxagoras)

Questions Addressed #

How Can Change Occur Without Contradiction? #

Problem: If the hard becomes soft, then the hard is soft—which violates non-contradiction.

Solution: The hard (as such) does not become soft; rather, the subject (butter) becomes soft.

Key Insight: We must distinguish between:

• The property (hardness/softness) which cannot change into its opposite
• The subject (butter) which can change from possessing one property to possessing the other

Why Are Two Principles Not Sufficient? #

Answer: Two contraries alone cannot account for change without logical impossibility.

Reason: The contraries themselves cannot change; only what possesses them can change. Therefore, a third thing (subject) is necessary.

Consequence: All changeable things are composite—composed of subject and property.

How Many Principles Are Necessary and Sufficient? #

Answer: Three principles are both necessary and sufficient:

1. The subject (substrate)
2. One contrary (form/actuality)
3. The other contrary (privation/absence of form)

Necessity: Demonstrated by the contradiction arising without a subject.

Sufficiency: Demonstrated by the principle of fewness; these three suffice to explain all change.

What Drives the Development of Human Knowledge? #

Answer: The recognition and resolution of apparent contradictions.

Mechanism:

1. We encounter an apparent contradiction in our thinking or in nature
2. We recognize it as impossible
3. We seek to untie (resolve) the contradiction
4. The resolution reveals a deeper distinction or third principle previously hidden
5. Our knowledge becomes more distinct and comprehensive

How Is Philosophy of Nature Used in Theology? #

Example: In theology, we establish that what changes is composite. In God’s theology, we establish that God is simple. Therefore, we can syllogize that God does not change.

Significance: General knowledge about change is more useful in theology than particular knowledge about specific physical phenomena.