51. Proportion in Philosophy, Science, and Theology

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Lecture Notes

Main Topics #

Proportion as a Foundational Principle #

• Proportion (ἀναλογία) operates across all philosophical and scientific domains
• The ability to see hidden likenesses beneath surface differences is essential to scientific and philosophical discovery
• Einstein’s insight: science consists in recognizing superficial similarities versus discovering proportional likenesses hidden under differences

Proportion in Natural Science #

The Inverse Square Law

• Gravity follows the inverse square law: if distance doubles, force becomes one-fourth; if tripled, one-ninth
• This law derives from observing light’s behavior: light spreads evenly and diminishes proportionally to the square of distance
• Geometrical basis: as distance increases, the area receiving light increases proportionally
• Example: doubling distance from light source to face results in face receiving one-fourth the light
• This principle traces back to geometry and the theory of proportions (as found in Euclid)

Proportion in Platonic and Aristotelian Philosophy #

Plato’s Republic and the Soul

• In Republic, Plato demonstrates that the just soul is better off than the unjust soul, apart from rewards and punishments
• In Book IV, Socrates “blows it up” (clarifies the argument) by establishing a proportion between three parts of the soul and three parts of the city
• The disordered soul is compared to a disordered city: reason to rulers, spirited appetite to army, concupiscible appetite to common citizens
• Simpler proportion: reason is to emotions as a man is to a horse—the man (reason) can either give up and let the horse act freely, or continue riding until the horse is tamed and obeys

Aristotle’s Rule of Reason Over Emotions

• Aristotle asks whether reason should rule emotions like a master rules slaves or like a father rules his son
• Master rules for the good of the master; father rules for the good of the son
• When reason rules emotions paternally (for their good), emotions become ordered and the person is better off
• Evidence from observation: children who receive proper parental discipline are happier than those without discipline; similarly, students in well-disciplined classrooms are happier than in uncontrolled ones
• An unordered emotional life is like working at a fast-food restaurant with constant demands: the person is “enslaved” and runs ragged trying to satisfy competing desires

Moral Virtue and the Mean #

Virtue as a Mean Between Extremes

• Aristotle proportions moral virtue to art: just as cooking requires the right amount of seasoning (not too much, not too little), virtue consists in the mean between excess and deficiency
• Example: seasoning food—too much seasoning ruins it; too little leaves it bland
• Example: cooking a steak—it can be undercooked or overcooked; the good lies between these extremes
• Physical beauty follows the same proportion: a nose that is too long (Cyrano de Bergerac) or too short is not beautiful; beauty requires proper proportion
• Mozart discussed the golden mean in his work, though it is not fully understood
• The principle applies universally: in eating, drinking, and all matters, one must avoid both excess and deficiency

Proportion in Theology #

Second Vatican Council’s Use of Proportion

• The Council uses the proportion between the Word of God (the second person of the Trinity) and human language
• Just as the divine Word became flesh and took on human nature, in Scripture the Word of God takes on human language and expresses itself in human words
• This proportion guides proper theological interpretation

Scriptural Examples of Proportion

• “The Lord is my shepherd” is based on a proportion: God is to us as a shepherd is to his flock
• Homer speaks of leaders as “shepherds of the people,” using the same proportion
• “Forgive us our trespasses as we forgive those who trespass against us” contains a continuous proportion: God is to us (whom we have offended) as we are to those who have offended us
• If we do not forgive those who offend us, God will not forgive us for offending Him
• This petition and its corresponding parable (the servant forgiven much but unwilling to forgive others) are structured entirely on this proportional reasoning

Proportion in Literature and Metaphor #

Aristotle on Metaphor and Similes

• The most beautiful metaphors and similes are based on proportions
• Example (Pericles on war): When many young men die in war, saying “spring has been taken out of the year” captures the loss beautifully through proportion
• Example (Romeo and Juliet): When Juliet is found apparently dead on her wedding day, her father says: “Death lies on her like an untimely frost upon the sweetest flower of all the field”—a perfect proportional expression
• This ability extends from the most beautiful metaphors to scientific discovery itself

Key Arguments #

The Universality of Proportion #

1. Proportion operates in natural science (inverse square law)
2. Proportion structures philosophical arguments (Plato, Aristotle)
3. Proportion appears in aesthetics and literature (metaphor and simile)
4. Proportion guides theological reasoning (Vatican II, Scripture)
5. Conclusion: The ability to perceive proportional likeness is fundamental to understanding across all domains of knowledge

The Importance of Careful Proportional Reasoning #

• One must be careful to discern true proportions and not create false ones
• A proportion requires that the likenesses between two ratios be genuine, not forced
• The dialectician must distinguish what is truly similar and what merely appears similar

Proportion and Definition #

• Proportion is useful for arriving at definitions and syllogisms about difference
• Proportion aids in induction and in syllogisms based on proportional likenesses
• Through proportional thinking, one can better understand complex concepts by comparing them to more familiar ones

Important Definitions #

Ἀναλογία (Analogia/Proportion) #

• A relationship of likeness between two ratios or relationships
• Enables understanding of complex matters through comparison with simpler, more familiar matters
• Not mere resemblance but a deeper structural similarity

Continuous Proportion #

• A proportion in which the middle term appears in both relationships
• Example: God : us :: us : those who offend us
• Used to reason from one domain to another in theological and ethical matters

Examples & Illustrations #

Natural Science: Light and Distance #

• If a light source is doubled in distance from a face, the face receives one-fourth the light
• If tripled, the face receives one-ninth the light
• This demonstrates the inverse square law through proportional geometric reasoning

Plato’s Horse and Rider #

• Reason is to emotions as a man (rider) is to a horse
• If the rider gives up, the horse acts freely
• If the rider persists, the horse becomes tamed and obedient
• This illustrates how reason’s rule over emotions leads to order and harmony

Discipline and Happiness #

• Children receiving proper parental discipline are happier and more content than undisciplined children
• Students in well-disciplined classrooms are happier than in chaotic, undisciplined ones
• This shows that reason’s rule (for the good of the emotions) benefits the emotions themselves, not just external order

The Enslaved Pizza Worker #

• A worker at a pizza place in summer, overwhelmed with customer demands, running from one request to another
• This is like a person enslaved to uncontrolled sensory appetite
• The constant, competing demands leave one frazzled and unable to achieve peace

Cooking and the Mean #

• Seasoning: too much pepper ruins the soup (family joke); too little leaves it bland
• Cooking a steak: undercooked or overcooked is bad; the good lies between
• Physical features: Cyrano de Bergerac had a nose too long; others have noses too short—beauty requires proportion

Death as Frost Upon a Flower #

• When Juliet is found dead on her wedding day (when joy was expected), her father laments: “Death lies on her like an untimely frost upon the sweetest flower of all the field”
• This proportional comparison captures the tragedy perfectly: just as frost destroys the sweetest flower at its peak, death has taken the sweetest life at its happiest moment

The Shepherd and the Flock #

• Homer spoke of leaders as “shepherds of the people”
• The proportion: the leader’s care for the people :: the shepherd’s care for the flock
• This same proportion appears in Scripture: “The Lord is my shepherd”

Forgiveness as Continuous Proportion #

• God : us (offenders against God) :: us : those who offend us
• If the proportion holds in the lower ratio, it should hold in the upper
• Therefore, if we forgive those who offend us, God will forgive us; if we do not, He will not

Notable Quotes #

“When you go back to Newton and its contemporaries… gravity seems to be like light spreading out evenly.”

“Einstein said very often: science is the way it’s seen… to see a likeness, you know, a superficial likeness that’s nothing, but to see one hidden under all these differences, right? That’s really very important in scientific work.”

“When reason rules the emotions, it’s for the good of the emotions… they’re better off.”

“If you don’t correct the child, eventually the child becomes unruly… but those households in which the parents discipline the children as a parent should discipline a child, not as a master rules a slave, but as the father should discipline the son, in those households the children are actually happier and more contented.”

“The most beautiful metaphors and similes… are based on what? Proportions.”

“All the way from the most beautiful metaphors to what discovery right in science and in philosophy this ability to see a proportion is very important right and it’s not easy to see sometimes.”

“When he speaks of these he speaks of a consideration here of likeness right because he had very careful of proportion in what way are these two ratios like right and not to try to make them like in a way that they’re not.”

Questions Addressed #

What is the role of proportion in natural science? #

• Proportion explains why the inverse square law governs both light and gravity
• Scientists discover laws by recognizing proportional relationships between different phenomena

How does proportion help in understanding the soul and virtue? #

• The proportion of the soul’s three parts to the city’s three parts clarifies Plato’s argument about justice
• The proportion of reason to emotions (as man to horse, or father to son) clarifies how virtue involves the rule of reason

Why does proper discipline make people happier? #

• When reason rules emotions for their own good (not for the ruler’s benefit), emotions become ordered
• Ordered emotions allow peace and contentment; disordered emotions are like slavery
• This is observable in children and students

How does proportion function in theology? #

• Just as the divine Word took on human flesh, the Word of God takes on human language in Scripture
• Forgiveness operates according to the proportion: if we forgive others, God forgives us; if we don’t, He doesn’t
• The “Lord is my shepherd” works through the proportional relationship between divine care and human dependence

What makes a metaphor beautiful? #

• Beautiful metaphors are based on true proportional likenesses, not forced similarities
• The more hidden and profound the proportion discovered, the more beautiful and powerful the metaphor

Dialectical Tools Applied #

• First Tool (selecting probable opinions): The ability to recognize proportions depends on identifying probable opinions that reveal genuine likenesses
• Second Tool (distinguishing senses of words): One must be careful not to equivocate when establishing proportions—the terms must maintain consistent meanings
• Third and Fourth Tools: Proportion aids in arriving at definitions (through proportional clarification) and in constructing syllogisms based on proportional reasoning