79. False Imagination, Natural Understanding, and the Examined Life

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Lecture Notes

Main Topics #

False Imagination and Deception #

False imagination (falsigraphic) is the main cause of deception in our knowing powers. It occurs in two ways:

• Imagining something other than it is (e.g., falsely imagining points in a line are actually present rather than in potency)
• Trying to imagine what cannot be imagined (e.g., the soul, infinity, God, angels)

When we try to imagine what is essentially unimaginable and follow that false imagination, we are inevitably deceived.

Examples of False Imagination #

The Soul: The soul cannot be imagined because it is not a body. Yet we falsely imagine it as:

• An air-like substance
• A shadowy thing in the shape of a man (as Homer represents souls in the Odyssey)
• A ghost-like form (as Dante poetically represents it in the Inferno)

The average person is deceived by these false imaginings about the soul’s nature.

Geometry: Even in geometry, where things can be imagined, false imagination deceives us:

• Men imagined that two lines always have a ratio expressible as the ratio of numbers to numbers, until discovering the incommensurability of the diagonal to the side of a square (a scandalous discovery requiring Euclid’s fifth book on general ratios)
• The horned angle: A straight line tangent to a circle at a point creates an angle smaller than any rectilineal angle. False imagination suggests we could fit a straight line between the circle and tangent because space seems infinibly divisible, but we cannot

Physics and Potency/Actuality: Modern physicists falsely imagine that everything obtainable from an elementary particle must be actually in it (following Anaxagoras’s error). This leads them to imagine:

• Every elementary particle is composed of all others (Heisenberg’s formula)
• Infinite regression of smaller particles within particles
• This contradicts the experimental fact that each elementary particle has definite mass and size

The root error: inability to understand potency (ability, capacity) as distinct from actuality (act, realization).

The Three Foundations of Natural Philosophy #

Berquist identifies three statements foundational to all philosophy:

1. There are some statements we naturally know (natural understanding/noesis)
2. We have a natural desire to know what we don’t naturally know (wonder)
3. We come to know unknown things through what we naturally know (complete dependence on the natural)

Modern philosophy has revolted against all three by:

• Denying natural understanding exists
• Replacing wonder with desire for power over knowledge
• Abandoning the natural foundation

The Unexamined Life #

Plato’s statement in the Apology: “The unexamined life is not worth living for a human being” is an exhortation to practical philosophy and examination of conscience.

Why? Because examination of life is made by reason. An unexamined life is one not examined by reason, therefore not based on reason, therefore not truly human.

Socrates examined the Athenians on their preference for:

• Goods of the body and external goods
• Over goods of the soul

This examination revealed their life was based on a mistake. This is irritating to those living such a life—no wonder they executed him—yet necessary for genuine human flourishing.

Natural Understanding and the Revolt Against It #

Why do moderns deny natural understanding?

• Pride: Desire to imagine freely rather than be bound by nature
• Moral concerns: If you listen to nature, you’ll hear moral responsibilities (as noted by a student in class)

Yet this creates an ironic problem: If there are no statements we naturally know, then no statement can be known at all. Those who deny natural understanding cannot even know their own denial.

Wonder and the Examined Life #

Wonder arises not merely from not understanding something, but from encountering what is contrary to expectation:

• We don’t wonder why objects fall (happens daily, expected)
• We wonder why a magnet moves objects without contact (contrary to expectation that bodies move only by contact)
• We wonder at the horned angle (contrary to expectation that space between curves can always fit a line)

This connects to Einstein’s reflection: people don’t wonder about things happening all the time even when they don’t understand them. Newton knew he didn’t know why stones fall, but we don’t wonder because it’s ordinary.

Key Arguments #

The Problem of Imagination in Geometry #

1. In geometry, we can and must use imagination to resolve figures
2. Yet false imagination can deceive us even in geometry
3. The horned angle demonstrates this: it’s geometrically real but seems impossible to imagine because we falsely imagine space between the curves where none exists
4. Therefore: You cannot judge by imagination alone, particularly in matters transcending imagination (nature of angels, nature of God, the soul)

The Incommensurability Discovery #

1. Men naturally imagined all ratios could be expressed as number to number
2. The diagonal of a square to its side proved incommensurable (irrational)
3. This was a shocking discovery requiring rethinking all geometry
4. Led to Euclid’s fifth book on general ratios not reducible to numerical ratios
5. Lesson: Natural expectations can be systematically wrong; wonder corrects them

Anaxagoras’s Error Repeated in Modern Physics #

1. Anaxagoras knew you cannot get something from nothing
2. Therefore everything obtained from matter must already be in matter
3. But he imagined it actually present rather than in potency
4. This led to infinite regress (everything infinitely small) and contradictions
5. Modern error: Heisenberg and elementary particle physics repeated this exact mistake
6. They observed that all elementary particles can eventually be obtained from each other
7. Therefore they imagined each must contain all others actually
8. Yet this contradicts the fact that each has definite, finite mass and size
9. Root cause: Inability to understand the distinction between potency and actuality

Important Definitions #

Potency (δύναμις/dynamis) vs. Actuality (ἐνέργεια/energeia) #

Potency: Ability, capacity, or power to be or become something

• A line contains infinite points in potency, not actuality
• When we cut a line, we make actual what was in potency
• The points are not already there waiting to be found

Actuality: The realization or manifestation of a capacity

• A point becomes actual only through division of the line
• The sum of infinite actual points is impossible
• But infinite division is actual (as process) while individual points remain potential

Key distinction: Failure to understand this distinction leads to false imagination and contradictions. Modern physicists imagine potentiality as if it were actuality.

False Imagination (falsigraphic, falsely drawn) #

The representation or mental picturing of something:

• Other than it is (false in content)
• That cannot be pictured (false in kind)

Natural Understanding (noesis) #

Knowledge that reason naturally comes to know through basic experience, not through demonstration. Distinguished from epistemic knowledge (ἐπιστήμη/episteme), which is reasoned out.

Wonder (thaumazein) #

The natural desire to know the causes of things, particularly aroused by what is contrary to expectation rather than merely by what is unknown.

Examples & Illustrations #

The Horned Angle #

A straight line tangent to a circle at a single point creates an angle between the line and curve that is smaller than any rectilineal angle (an angle formed by two straight lines).

Why it seems impossible: False imagination suggests that since space is infinitely divisible, we should be able to fit a straight line in the space between the curve and tangent line. But we cannot.

Lesson: Geometry can contain truths contrary to sensory expectation; wonder arises from encountering the unexpected.

Euclid’s Fifth Theorem (Book II) - The Rectangle Problem #

If a line is cut into equal and unequal segments, the rectangle on the equal segments is greater than the rectangle on the unequal segments.

Practical example:

• A 5×5 square: perimeter 20, area 25
• A 4×6 rectangle: perimeter 20, area 24
• A 2×8 rectangle: perimeter 20, area 16

Ancient application: Crooked geometers in ancient times sold land by perimeter rather than area, thus defrauding customers who believed more fence meant more land. Some estimated island area by sailing time around it, not realizing more indentation could make a smaller island take longer to circumnavigate.

Lesson: What we expect (more fence = more land) can be systematically false; geometry teaches reality.

The Baby’s Smile #

A smile is a natural sign that can indicate:

• Joy or pleasure
• Amusement
• Affection or love

Key observations:

• Babies naturally smile yet also learn to smile
• A smile to the baby brings a smile back
• The baby recognizes that an adult is communicating with it
• The first morning smile is particularly rich (baby hasn’t seen you in hours)
• Smiles are more interesting than laughter because more ambiguous
• A frown naturally distresses a baby

Lesson: We can observe natural signs and natural knowledge even before language develops. The smile and frown (unlike symbolic colors like white/black) are naturally understood across cultures.

Einstein’s Magnet #

When young Einstein’s father brought home a magnet, Einstein wondered at it because:

• A magnet is a body
• Yet it moves other bodies without contact
• He expected bodies move only through contact
• Therefore: The unexpected (action at distance without contact) aroused wonder

Contrast: We don’t wonder why stones fall, though Newton knew he didn’t know why. Falling is ordinary, expected. Einstein was trying to understand it but wonder wasn’t aroused because it happens all the time.

Babe Ruth’s Home Run #

Babe Ruth pointed to the bleachers before hitting a home run, then hit it exactly there. This demonstrates:

• The satisfaction from accomplishing something contrary to expectation
• Similar to the horned angle or incommensurability discoveries
• The human desire for wonder and its fulfillment

The Politician Friend Roy Monroe #

Berquist recounts telling his friend about discovering the horned angle while reading Euclid:

• The friend laughed in disbelief that this could be interesting
• When Berquist explained the horned angle (an angle smaller than any rectilineal angle), the friend’s reaction shifted
• The friend experienced wonder at something contrary to expectation
• Lesson: Encountering the unexpected can transform someone’s attitude toward philosophy and geometry

Notable Quotes #

“The unexamined life is not worth living for a human being.” — Plato, Apology

Berquist emphasizes this as the opening exhortation to practical philosophy. It is acceptable for trees and dogs to live unexamined, but not for humans whose nature includes reason.

“You can’t judge by imagination here.” — Thomas Aquinas (on the nature of angels and God)

From Thomas’s commentary on Boethius’s De Trinitate, establishing that imagination cannot resolve matters transcending bodily forms.

“It’s kind of hard to understand… there’s a chair in ability, what else do you mean?” — Berquist, on the difficulty of understanding potency/capacity in nature

Illustrating how modern minds, accustomed to actual forms, struggle to grasp what is potential.

Questions Addressed #

How can the soul be understood if it cannot be imagined? #

False approach: Imagine it as air-like, shadowy, ghost-shaped (deceiving ourselves)

Correct approach: Reason grasps what imagination cannot. The soul is form without matter, not a body of any kind. We cannot resolve our imagination because the imagination necessarily grasps only bodily forms.

Why did ancient geometers falsely imagine about ratios and areas? #

They naturally expected that more fence (perimeter) would enclose more land (area), and that all ratios could be expressed numerically. Geometry revealed these natural expectations to be wrong, but only through careful demonstration.

How could modern physicists make Anaxagoras’s ancient mistake? #

They observed that all elementary particles can be obtained from each other and correctly reasoned “something cannot come from nothing.” But they falsely imagined this meant all particles must be actually present in each other, rather than present in potency. This led to infinite regress contradicting experimental evidence.

Why do modern philosophers deny natural understanding exists? #

Two possible motives:

1. Pride: Desire to imagine freely, to break free from nature’s constraints
2. Moral avoidance: If you acknowledge natural understanding, you must acknowledge natural responsibilities and moral law

Yet this creates a self-refuting position: to deny natural understanding is itself to claim knowledge, which assumes some natural understanding exists.

What is the relationship between wonder and expectation? #

Wonder is aroused not by mere ignorance but by encountering what is contrary to expectation. We don’t wonder at ordinary falling objects though we might not understand gravity. We wonder at magnets moving objects without contact, at incommensurable ratios, at horned angles—things that violate our natural expectations.

Connections to Broader Course Themes #

• To natural philosophy: The importance of listening to nature and natural understanding throughout the course
• To Aristotle’s metaphysics: The fundamental distinction between potency and actuality, and how confusion about it leads to modern errors
• To logic and epistemology: The role of natural axioms and self-evident truths as foundations for all reasoning
• To morality: The connection between natural understanding and moral responsibility; the modern revolt from both