30. Contradiction, Harmony, and the Discovery of Truth

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Lecture Notes

Main Topics #

Contradiction as a Gateway to Knowledge #

• Contradiction is not a dead-end but reveals the direction inquiry must take
• The sharpness of contradiction correlates with confidence in the truth of a solution
• Hidden harmony (deeper truth) is concealed beneath apparent contradiction
• Progress in philosophy, science, and theology all proceed by identifying and resolving contradictions

Divine Simplicity and the Problem of Predication #

• God, being absolutely simple, has no real distinction between his essence and attributes
• Goodness and God are identical; therefore God cannot be bad
• Example: If hardness and butter were identical, butter could never become soft
• Our language about God is inadequate because it reflects the composition found in material things
• Both affirmation and negation of divine names are necessary: God is goodness, yet the name “goodness” inadequately captures this because it suggests composition

The Necessity of Natural Philosophy for Theology #

• Understanding change and composition in natural philosophy is foundational for theology
• General knowledge of change is more useful theologically than particular scientific facts
• Example: Knowing that wholes have parts is essential for proving God has no parts; knowing water is H₂O is not theologically necessary
• Definition of eternity requires understanding the definition of time from natural philosophy via negativa (negation of temporal properties)

The Continuity Between Great Thinkers #

• Heraclitus first recognized that conflict/contradiction drives all things forward
• Plato (influenced by Heraclitus and Socrates) began untying apparent contradictions, particularly regarding the immortality of the soul
• Aristotle perfected the art of resolving contradictions through distinction
• Medieval scholasticism (especially Thomas Aquinas) systematized this through questiones disputatae
• Modern physics (Einstein, Bohr, Heisenberg) independently rediscovered this principle

Aristotle’s Reasons Against Infinite Principles (from Metaphysics III) #

• First reason: To doubt well before discovering is necessary; discovery is an untying of previous difficulties
• Second reason: Those who have not considered difficulties cannot know where inquiry should go
• Third reason: One cannot untie a knot one does not see; doubt of the mind about a thing is like being physically tied—both prevent forward progress
• Fourth reason: Those who have seen difficulties are better prepared to judge whether a solution is true

Key Arguments #

The Slave Boy and Hidden Harmony (Plato’s Meno) #

• Socrates asks: How do you double a square by doubling the side?
• Slave boy assumes: If 2×2 = 4, then 4×4 = 16 (which is double of 4, so this should work)
• The contradiction revealed: 4 is double of 2, but 16 is four times 4, not double—contradiction
• This apparent contradiction removes the slave boy’s false knowledge and creates desire to learn
• Hidden under the contradiction: the true method is to take the diagonal
• The hidden harmony (true solution) is better than the apparent harmony (false assumption)

The Distinction Between Contraries and the Subject #

• Hardness cannot become softness (this would violate non-contradiction)
• Yet butter is sometimes hard, sometimes soft—change occurs
• Resolution: The butter (subject) changes, not the contraries themselves
• The butter remains butter while its properties (hardness/softness) change
• This requires a real distinction between form and what has the form

Asking the Right Question Is More Than Halfway to the Answer #

• Heisenberg’s insight: In scientific investigation, formulating the right question frequently accomplishes more than half the work
• Example: Physicists learned to ask questions about apparent contradictions between experimental results
• These contradictions enabled them to ask the right questions about quantum phenomena
• Once the right question emerges (born from contradiction), the answer follows more readily
• The investigator then knows where to direct effort

Important Definitions #

Contradiction (in the sense used throughout this lecture) #

• An apparent irresolvability between two seemingly opposed truths or observations
• Not a violation of the law of non-contradiction, but rather an indication that more precise distinctions are needed
• Functions as a sign that the mind lacks the proper categories or distinctions to understand reality

Hidden Harmony (ἁρμονία κρυπτή) #

• The deeper order and truth concealed beneath apparent contradiction
• Better than apparent harmony because it represents genuine understanding rather than superficial consistency
• Revealed through the untying (λύσις) of contradictions

Apparent Harmony #

• Superficial consistency that masks underlying problems or unresolved contradictions
• Example: Slave boy’s belief that doubling the side doubles the square
• Must be disrupted for genuine knowledge to emerge

The Knot (κόμπος) and Untying (λύσις) #

• Metaphor for how contradiction binds the mind, preventing forward movement
• Just as tied feet cannot progress, a mind bound by unresolved contradiction cannot advance
• Untying the knot is not merely resolving the contradiction but is itself the act of discovery

Via Negativa (Negation of Terms) #

• Method of understanding a thing by denying certain properties
• In theology: We understand eternity by negating temporal properties
• The definition of eternity is understood by negating properties of time that Aristotle identified

Examples & Illustrations #

Butter and Hardness #

• Hardness cannot become softness (contradiction)
• Butter can be hard or soft without contradiction
• Therefore: It is butter that becomes soft, not hardness itself
• Illustrates the necessity of distinguishing subject from properties

The Doubling of the Square #

• False method: Double the side (2 → 4)
• Apparent result: Square doubles (4 → 16)
• The contradiction: If side doubles, square should double. But 16 is 4× the original square, not 2×
• True method: Use the diagonal
• Shows how contradiction removes false confidence and creates desire for genuine knowledge

Manhattan and Water #

• Water is H₂O; Manhattan has rye whiskey and sweet vermouth
• These facts are true but not theologically useful
• Theology proves God has no parts without needing to know specific compositions of material things
• Distinguishes between useful and unnecessary knowledge depending on one’s field of inquiry

The Questiones Disputatae Structure #

• Medieval scholarly method: Arguments on one side, arguments on the other side (sed contra)
• Master resolves the contradiction by untying the knot
• Example texts: Thomas Aquinas’s Questiones Disputatae de Veritate, de Caritate, de Spe, etc.
• In de Spe: Thomas clarifies that hope is a greater virtue than faith (though charity is greatest)
• This method persists in the Summa Theologiae but in abbreviated form

The Development of Mozart’s Quartets #

• Mozart’s early Vienna Quartets show influence of Haydn’s Opus 17 and 20
• After hearing Haydn’s Russian Quartets (where each instrument had its own role), Mozart’s understanding deepened
• He then wrote six perfect quartets dedicated to Haydn
• Haydn’s recognition: “Your son is the greatest composer I know”
• Illustrates how genuine mastery requires assimilating and then surpassing what one has learned
• Parallel to how Aristotle perfected what Plato began

Aristotle’s Natural Philosophy as Foundation for Theology #

• Thomas Aquinas could only develop his theological synthesis because Aristotle’s Physics and natural philosophy became available at the University of Naples
• Without understanding Aristotle’s definition of time and motion, medieval theology could not properly understand the definition of eternity
• This is an example of divine providence: the recovery of Aristotle’s works enabled the perfection of scholastic theology

Mozart’s Violin Concertos (K. 207-219) #

• Composed within about a year when Mozart’s father pressured him to write them
• First two are good; third is much better; fourth and fifth are “incredible”
• Shows development and mastery emerging through production
• Comparable to Shakespeare’s progression from Titus Andronicus to the great tragedies

Questions Addressed #

How Can Divine Simplicity Be Reconciled with Our Language About God? #

• Problem: We say “God is good” (suggesting composition: God + goodness) or “God is goodness” (suggesting God is merely the source of goodness in others, not himself good)
• Aristotle’s solution (following Dionysius): No name is adequate to God; both affirmation and negation of names are necessary
• The resolution: God truly is good, and goodness is not distinct from God (simplicity), yet our language—adapted to material composition—inevitably suggests composition
• Significance: This inadequacy of language is not a defect in theology but a reflection of God’s transcendence

How Does Contradiction Function in the Progress of Knowledge? #

• Contradiction indicates the direction inquiry must take (toward its resolution)
• Contradiction confirms arrival at truth when it disappears
• Contradiction enables the formulation of the right question, which is more than halfway to the answer
• This is true across philosophy, science, and theology

What Is the Role of Dialectic in Discovering Truth? #

• Dialectic (presenting arguments on both sides) reveals difficulties and contradictions
• Difficulties must be seen before they can be untied
• The untying of difficulties is itself the discovery of truth
• Therefore, dialectic is not merely preliminary but integral to the discovery process
• This justifies the medieval use of questiones disputatae throughout theological and philosophical inquiry

How Do We Know We Have Found the Truth? #

• When the contradictions that initiated inquiry disappear, we know we have arrived at truth
• The sharper the contradiction that was resolved, the more confidence we have in the solution
• We can judge the adequacy of a solution by whether it addresses all the arguments that seemed to contradict it

Notable Quotes #

“War is the father of all things; the king of all things.” — Heraclitus (DK8)

“The hidden harmony is better than the apparent harmony.” — Heraclitus (DK54)

“If you do not expect the unexpected, you will not find it. For it’s hard to be found and difficult.” — Heraclitus (DK18)

“All of the essential ideas in science were born in a dramatic conflict between reality and our tints of understanding.” — Einstein

“Just the sharpness of the contradiction made me absolutely confident in the truth of the quantum postulate.” — Niels Bohr

“In an apparently hopeless contradiction, he conceived the germ of wider and more comprehensive order and harmony.” — Description of Bohr’s method (page 3)

“Asking the right question is frequently more than halfway to the solution of the problem.” — Werner Heisenberg (History of Quantum Theory)

“To doubt well before is necessary for those wishing to discover it. For the discovery afterwards is an untying of the difficulties before.” — Aristotle (Metaphysics III)

“No name is adequate to talking about God.” — Thomas Aquinas (following Dionysius)

“To ask the right question is to go in the right direction.” — Duane Berquist (elaborating Aristotle’s point)

“The man who’s seen the difficulties, the contradiction, knows where he’s going.” — Duane Berquist (summarizing Aristotle’s Metaphysics III)

Connections to Broader Philosophical Tradition #

Philosophical Lineage #

• Heraclitus recognized that conflict/war drives all things forward
• Plato (in the Phaedo) began untying contradictions about soul and change
• Aristotle perfected the method of resolution through precise distinctions
• Augustine and Medieval Scholastics inherited this method
• Thomas Aquinas systematized it in the questiones disputatae and Summa Theologiae
• Modern Science (Einstein, Bohr, Heisenberg) independently rediscovered this principle

Why Understanding Change Is Foundational #

• Change involves apparent contradiction: a thing becomes what it was not, yet remains itself
• This paradox is the starting point for all deeper understanding
• The resolution (subject + contraries) becomes the model for resolving other contradictions
• In theology: Understanding composition in material things helps us understand why God, being simple, cannot change