28. Modern Physics, Mathematics, and the Problem of Knowledge

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Lecture Notes

Main Topics #

• The Mathematical-Physical Paradox: Modern physics describes nature using mathematics that contains neither matter nor motion, yet claims to explain material things in motion
• Contrasting Epistemologies: Aristotelian natural philosophy seeks order in things themselves vs. modern experimental science that orders only experience
• The Making-Knowing Relationship: Kant’s principle that we can only know what we make, and its radical consequences when applied universally
• Marxist and Scientific Implications: How the same epistemological principle appears in both Marx and modern physicists, despite different philosophical orientations
• The Crisis of Modern Knowledge: The psychological and intellectual consequences of enclosing the human mind in a world entirely of its own making

Key Arguments #

The Mathematical Paradox #

• Planck and other quantum physicists showed that mathematics describing atoms contains no matter and no motion
• Yet mathematics is used to explain matter in motion in nature
• This represents a strange kind of knowing: using tools that contain neither the subject matter nor the modes of being being studied

Bohr’s Definition and Its Implications #

• Bohr states: “The task of science is to extend the range of our experience and reduce it to order”
• This can mean either: (1) ordering things themselves (Aristotelian), or (2) ordering only our experience of things (Kantian)
• When examined closely, modern science appears to do the latter—ordering experience, not reality
• This parallels Kant’s claim that we cannot know things-in-themselves, only phenomena as they appear to us

The Kant-to-Marx Connection #

• Kant: We know only phenomena (what appears in our experience), not things as they are
• Kant applies this to experimental science: We must make things (experiments) to know them
• Marx draws the radical conclusion: If man knows only what he makes, then man is the beginning and end of all knowledge
• Modern physicists (Weizsäcker) reach similar conclusions despite not being Marxists

Weizsäcker on Experimental Science #

• Knowledge proves itself only in successful experiments
• Experimentation means exerting power over nature
• Possession of power is the ultimate proof of truth
• At the remotest reaches of nature, only what is of our own making (or could be) is comprehensible to us
• This creates a closed epistemological system: we know nothing we have not made

The Problem of Closure #

• If one’s only experience is experimental/mathematical science, the mind becomes closed
• The modern person tries to live in a world entirely of their own making
• Such a world is necessarily inferior to the person and can never satisfy them
• This intellectual solitary confinement produces the “anxiety of the modern mind”

Important Definitions #

• Mathematical Description: A formal, abstract representation using purely mathematical language, distinct from physical reality
• Experimental Science: Knowledge gained by making things happen under controlled conditions
• Phenomena vs. Noumena: Kant’s distinction between things as they appear to us vs. things as they are in themselves
• Power/Exertion: In modern physics, the ability to manipulate and control nature through experiment

Examples & Illustrations #

The Atom and Wave Mechanics #

• Planck perfected the mathematics of wave mechanics used to describe atoms
• Showed mathematical equivalence between wave and quantum mechanics
• Yet he could testify: there is no stuff (matter) in these mathematical descriptions
• This disturbed Marxists who believe matter is fundamental to all things

The Greeks and Grammar #

• The Greeks understood their own language well enough to formulate grammar rules
• Romans imposed Greek grammatical categories on Latin, creating the abative case that doesn’t exist in Greek
• This shows the difference between understanding something in itself vs. forcing external categories upon it
• English grammar became even more confused by trying to imitate Roman categories

Modern Art and the Crisis of Meaning #

• Norman Rockwell paintings are now accepted in museums despite earlier dismissal
• People like them because they speak to natural human values
• Modern art, by contrast, doesn’t confirm people in natural understanding—it requires special initiation
• Example: a composition where musicians sit silently for 10-15 minutes—purely self-referential, not about anything beyond itself

Geometric Construction and Making #

• Euclid reduces all geometric objects to the point, then constructs upward
• A point moving makes a line; a line rotating makes a circle
• To know geometry, you must construct—make—these things
• This shows there is some truth to Kant’s principle, but only in the context of liberal arts where making is involved

Questions Addressed #

How can mathematical descriptions contain neither matter nor motion? #

Mathematics is a purely formal language; it describes relationships and structures abstractly. While useful for organizing experience, it necessarily abstracts away from the physical reality it aims to describe.

Does modern science know things themselves or only our experience of them? #

The evidence suggests modern science knows only its own constructions (experiments, measurements, mathematical orderings) and projects these onto reality. True natural philosophy, by contrast, seeks to understand order in things themselves.

What is the consequence of claiming “we know only what we make”? #

If applied universally, this principle means man is the beginning and end of all his knowledge. He becomes practically self-creating and self-sufficient, which is a definition of God. This is why Berquist calls it “practical atheism.”

Why does living in a world of one’s own making cause mental anguish? #

Because such a world is necessarily inferior to the person who made it and can never satisfy human intelligence, which naturally seeks truth about reality beyond itself. This creates psychological and intellectual confinement.

Notable Quotes #

“There is no matter there. That’s why the communists…were getting nervous about modern physics, because matter seemed to be disappearing from the scientific picture of the world.” — Berquist, on mathematical descriptions of atoms

“You’re studying matter in motion with mathematics that contains neither matter nor motion. They have a very strange kind of knowing.” — Berquist, on the paradox of mathematical physics

“We reverence ancient Greece as the cradle of Western science.” — Einstein (quoted by Berquist)

“Science is the Greek way of looking at things. No one has ever had science who has not come in contact with the Greeks.” — Schrödinger (quoted by Berquist)

“The thinking of our experience proves itself only in action in a successful experiment. To experiment means to exert power upon nature. The possession of power is then the ultimate proof of the correctness of scientific thought.” — Weizsäcker (quoted by Berquist)

“In those remotest reaches of nature, only that is still comprehensible to us which is of our making, or which at least could be of our making.” — Weizsäcker (quoted by Berquist)

“The source of the mental anguish…is that they’re trying to live in a world entirely of their own making…A world that’s inferior to them…It’s like solitary confinement.” — Berquist

Connections to Prior Lectures #

• Builds on earlier discussion of Greek contraries and Heraclitus as the “father of the progress of the human mind”
• Extends the principle that Greek thought reverenced order in things themselves
• Shows how modern methodology has inverted this principle
• Relates to natural philosophy’s role in providing foundations for theology (God’s simplicity vs. creatures’ composition)