Contradiction in Science and Theology: Planck, Bohr, Einstein, Augustine and Thomas, plus Q&A

Orientation #

The recording begins mid-class (“go to science here now”); he is working through a set of numbered readings on the role of contradiction in discovery, having already done Heraclitus, Aristotle and Heisenberg (prev. lecture: “we looked pretty much at the text there from Heisenberg”). At the end he says two examples of untying contradictions were already seen in the course — Anaxagoras on mind self-ruling vs. the ruler separated, and change — and that next time (Thursday this week, since exam week blocks the usual slot) they will “finish this eleventh reading” and begin the next. Verified sources place the readings on p. 20 of the handout “The Royal Fragment” and p. 36 of DHB Vol I, The First Philosophers. The previous class set up contradiction as the engine of progress across philosophy, science and theology; the next returns to Physics I on the third thing underlying contraries.

The class, in order #

1. Planck: the fact that contradicts the theory (“nothing is more interesting to the true theorist”) #

Point: the “father of modern physics” testifies that discovery starts from a fact the theory cannot fit.

• Biography as credential: Planck was told on enrolling in the late 19th century that physics was complete in its principles (“go into biology” if you want fundamental discoveries); yet in December 1900 he proposed the quantum hypothesis, walked in the park with his son saying he had found something as important as Newton. Einstein (1905, photoelectric effect, Nobel) showed light cannot be understood without the quantum; Bohr (1913) showed the atom cannot — so neither matter nor light is intelligible without it. This led to the greatest change in physics: the rejection of determinism (Heisenberg especially).
• The reading: the first impulse to revising a theory is “nearly always” a fact that cannot be fitted — which he glosses “that means it contradicts it”; a few such facts are the hinge of the most important theories; and the key sentence: nothing is more interesting to the true theorist than a fact directly contradicting accepted theory.

2. Gamow: staggering contradictions (“theoretical expectations on the one side”) #

Point: a second witness, from the thirty-year development of quantum theory.

• Gamow: Russian, studied under Bohr at Copenhagen, later in the US; Nobel for explaining things that “do what they don’t have enough energy to do” (to be taken up later). Quantum theory ran from 1900 to the late 1920s; the Copenhagen interpretation was fought over at the Solvay Congresses, with the “showdown” in 1927 when Bohr refuted Einstein.
• The reading: “staggering contradictions” between theoretical expectation on one side and observed fact or even common sense on the other are the main factors in the development of science. He links “staggering” to the “apparently hopeless contradiction” seen earlier.

3. Bohr and Einstein: the dialectical mind (“essentially dialectical rather than reflective”) #

Point: Bohr, the central figure with Einstein, proceeded from paradox to elucidation, and said so himself.

• Aside on the Bohr–Einstein debates: Einstein rejected Copenhagen because it abandoned determinism, “the absolute principle of modern science” (mentioned earlier in the course); he invented thought experiments, Bohr stayed up all night and answered; in 1927 Bohr used Einstein’s own relativity to refute Einstein’s last public objection (the photograph of the two leaving, Einstein smug, Bohr worried).
• Bohr’s 1913 Danish Physical Society lecture: his early hypotheses were provisional, a mixture of Planck’s ideas with the old mechanics; he stresses that his considerations conflict with the “admirably coherent” classical theory, yet that by emphasizing the conflict a new coherence may in time be discovered. “You have to insist upon that contradiction in order to discover the hidden harmony” — Heraclitus’s phrase.
• From his collaborators’ volume: Bohr’s turn of mind was “essentially dialectical rather than reflective” (dialectic = the Greek practice of arguing on opposite sides, raising problems); he needed dialogue to think, and those who sat at his feet compared it to being with Socrates; he pressed a point not to beat his opponent but to make him share the exhilaration of solving the difficulty; he would never outline a finished picture but go through all phases, “starting from some apparent paradox” and leading to its elucidation. Aside: Chesterton’s paradoxical style (“worth doing badly”) likewise makes you start thinking.
• The most revealing text: logical analysis was for Bohr not a mere verification of consistency but “a powerful, constructive tool, orienting the groping mind in the right direction” — the heuristic power of logic. He derives heuristic from Greek heuriskō, “to find / discover”; the power of dialectic to bring out contradictions is a power of discovery, “exactly what Heraclitus and Aristotle have been saying.”
• Bohr’s own discovery: Rutherford’s atom model made clear that atomic stability could not be accounted for by classical laws (he explains “classical/Newtonian” = 17th–19th-century physics, “modern” = 20th), and so pointed to the quantum postulate as the only escape from the dilemma; the sharpness of the contradiction he resolved made him “absolutely confident of the truth” of the postulate. He ties this to Aristotle’s second paragraph: the contradiction tells you where to go, and you know you have arrived when it is untied — the two things “tied together.”
• Bohr in one of his last conversations: no progress in high-energy transformations of matter because no process yet showed “a sufficiently violent contradiction” with current ideas to indicate how to modify them — compared to “expecting the unexpected.”
• Last Bohr reading: contradictions were for him the external appearance of new knowledge (like an orange’s outer shell); in an apparently hopeless contradiction he saw the seed of a wider, more comprehensive order and harmony — the hidden harmony, better than the one before.
• Recap of Heisenberg (done last time): the right question comes from apparent contradictions between experiments — particle behaviour vs. wave behaviour, extended by de Broglie to electrons.

4. Einstein: necessity, aim, and the wall of contradictions (“break down the wall of contradictions”) #

Point: Einstein, “from the horse’s mouth,” gives the same two marks — knowing where you are going and knowing you have arrived.

• The Evolution of Physics (Galileo to his own work) on relativity: it arose “from necessity” — because the mind cannot accept a contradiction — from “serious and deep” contradictions in the old theory with no escape; and the strength of the new theory lies in its consistency (freedom from contradiction) and the simplicity with which it solves the difficulties. So: contradictions disappearing is the sign of arrival, as with Bohr.
• Second paragraph: how to reconcile the two contradictory views of matter (particle and wave) is one of those fundamental difficulties which, once formulated, “must lead in the long run to scientific progress” — “magnificent.” Einstein leaves it to the future whether the quantum solution is enduring; Berquist: “Zarathustra, I’m ashamed of you, Einstein” — he could not refute it and would not accept it; a recent string-theory book (The Elegant Universe) treats the struggle as over, though a few (Bridgman) still cling to mechanical views.
• Reading “on page 264”: science forces us to create new ideas — better stated, the contradiction forces us. Their “aim” (if you can aim, you know where you are going, as Aristotle said) is to break down the wall of contradictions blocking scientific progress: Einstein’s image is a wall to knock down, Aristotle’s is feet tied by a knot to be loosed — same idea. Then a universal affirmative: all the essential ideas of science were born in “dramatic conflict between reality and attempts at understanding” — “dramatic” recalls Aristotle on a good plot as tying and untying the knot.

5. Theology I: Christ’s question about David’s Lord (“How is it that David, moved by the Spirit”) #

Point: despite all differences among philosophy, science and theology, contradiction plays the same fundamental role; the first witness is “the greatest authority I could take.”

• Matthew 22: Christ asks the Pharisees whose son the Christ is; they answer David; he cites the psalm “the Lord said to my Lord” — if David calls him Lord, how is he his son? An apparent contradiction between two passages of Scripture: a son is not the lord of his father.
• Difference from Heisenberg: there, contradictions between experiments; here, between passages of a divinely written text. It also resembles the examination discussion (from earlier in the course): Christ shows they do not understand what they claim to know, so “no one dared to ask him any further questions.”
• Hidden under the contradiction: Christ is God (Lord of David) and man (descended from David). If you don’t expect the unexpected you will never find it. Parallel: “the Father is greater than I” vs. “the Father and I are one” — as man, and as God.
• Socratic note: Thomas’s division of Matthew places ch. 22 among the chapters showing why they wanted to kill him — as with Socrates, for showing men they did not know what they claimed to know.

6. Theology II: Augustine and the heretics (“the necessity of defending them forces us”) #

Point: the Fathers came to deeper understanding by being forced to defend articles the heretics denied.

• Reading (via Vatican II’s order: biblical themes first, then the Fathers, then history of dogma, then Thomas): Augustine — even heretics profit the proficient, per Paul “there must be heresies”; the wise son “uses the foolish as his servant.” How is the heretic Augustine’s servant? The “hot restlessness of heretics” stirs questions about many articles; “the necessity of defending them forces us” (the same two words as Einstein) to investigate more accurately, understand more clearly, proclaim more earnestly; the adversary’s question becomes the occasion of instruction.
• Illustrations: the predominance of contra titles in Augustine; Thomas’s remark that after the Pelagian heresies Augustine spoke more carefully and exactly on grace (the Pope: Augustine’s mind on grace is the Church’s), so his understanding develops as he refutes.
• The ad hoc character of the Fathers and councils: each defends the article denied in his time (Trent on sacraments and justification against Luther; an earlier council on “Mother of God” vs. “Mother of Christ” — denying the title in effect divided Christ into two persons). Vatican II’s phrase “individual truths of revelation” touches this.

7. Theology III: Thomas and the mysteries of salvation (“illumine the mysteries of salvation as completely as possible”) #

Point: the council sends students to Thomas for two things, both done by starting from contradictions.

• The decree: students should penetrate the mysteries “with the help of speculation under the guidance of Thomas” and “perceive their interconnections.” Every article of the Summa Theologiae (and more fully the Quaestiones Disputatae) begins with a contradiction and unties it; and the Summa looks at all the articles of faith together in order, which the Fathers’ ad hoc writings do not.
• Cajetan: Thomas seems to have inherited the mind of all the Fathers. Example, the suitability of the Incarnation (not the only way, the most appropriate), where Thomas is really quoting Augustine’s dialectic: God should be followed but cannot be seen, man can be seen but is not a perfect model — so God became man; man’s sin is in a way an infinite crime (rejecting the infinite good) so man cannot make infinite reparation, God can but did not sin — so God became man.
• Close of the formal class: this is “a little introduction to the role of contradiction”; two striking examples already met in the course — Anaxagoras (mind self-ruling vs. ruler separated) and change. Scheduling: exam week, so meet Thursday this week; finish the eleventh reading, then the next.

8. After the reading: pillars, metaphors, dialectic, the good (“metaphors are two-edged swords”) #

Loose conversation, in order:

• Thomas on the Ephesians as “pillars of the church” (unusual, since usually the apostles are), by faith, hope and charity, matched to three Old Testament pillars: cloud = faith (seeing darkly in a mirror, the cloud of unknowing), fire = charity, smoke = hope, because smoke rises from fire as charity perfects hope. Student: “where there’s smoke there’s fire”; Berquist: it does not mean hope goes up in smoke — metaphors cut both ways (fire for charity or lust; the lion for Christ or the devil). Student: smoke is like prayer — yes, Augustine and Thomas take up prayer with hope.
• Student remarks that Ockham thinks dialectically too, and that one should purposely think up disputes. Berquist: these knots and untyings are fundamental for the whole development of the mind, not just philosophy of nature.
• Sophistical Refutations: four kinds of argument — demonstrative/teaching, dialectical, examination, sophistical; dialectic there is “reasoning from probable opinions to contradictory conclusions,” which shows how dialectic is a tool of discovery. Student: the per accidens vs. as such distinction is the hinge; “that’s where most errors lie.”
• His introduction-to-philosophy sequence: Meno then Euthyphro; Euthyphro teaches asking the right question (pious because it pleases the gods, or pleasing because pious?), which he transfers to the good (good because wanted, or wanted because good? — wanted because good). Objection: “the good is what all desire” cannot be a definition if the bad is sometimes desired, since a definition by effect must still be convertible and separate the thing from everything else. Solution: the good as such is desired, the bad only under the appearance of good — e.g. Raskolnikov in Crime and Punishment murdering for the false good of being above the law.
• Student asks for exercises to learn the art of spotting contradictions; no method given, but puns (Shakespeare’s, his mother’s “I see through the blind man”) produce small paradoxes that make you stop and examine a word’s meaning; “all humor, I guess, involves a contradiction.”
• Student: the Catholic faith seems steeped in this — one passage of Scripture appearing to contradict another; Berquist: Augustine says there is more in Scripture we do not understand than we do, and each such thing leads the mind.
• Asides: correcting 20–30 exams to Mozart (Zaide, Seraglio) or harpsichord; Górecki’s Amen; Mozart’s masses lengthening the Amen to annoy a bishop who liked short masses; a student’s report that Thomas regretted the burning of heretics’ books.

9. After class: infinite reparation and irreparable evils (“I can do more harm to you than I can do good”) #

• Student objection to the Augustinian argument: the sin was infinite only because directed at God, who is infinite; then reparation directed at God is infinite in the same respect, so the argument seems to shift the sense of “infinite” — as if I had to be infinite. Berquist does not resolve it directly; he compares it to the earlier puzzle that God is chiefly responsible for the good you do and you for the evil, “which seems quite unfair.” Left open.
• Student: was the infinite sin original sin? Berquist: any mortal sin has a kind of infinity, rejecting an infinite good. Analogy: if I murder you I can take your life but not restore it — I can do you more harm than good; in mortal sin I have killed myself spiritually by separating from God, as God is to the soul what the soul is to the body (a likeness, not an identity). Student pushes: the murderer is more dead than the victim in a state of grace? Berquist: my rejection of God is worse than my killing you; some evils are irreparable (Bin Laden cannot rebuild what was destroyed; Othello, learning his wife’s innocence, sees no way to be forgiven; a written note, being premeditated, is harder to reconcile than hot words).

10. After class: shape as a quality about quantity (“quality about quantity”) #

• Student, puzzled by property/characteristic/attribute all pointing to quality, and by the fourth species of quality, “shape or form,” which seems to be quantity. Berquist: yes, figure is the fourth species of quality in the Categories, “quality about quantity,” tied to the determination or limit of quantity. Euclid shows figures of different shape can be equal: early on by superposition, later (triangles and parallelograms on the same base between the same parallels; a parallelogram on half the base equals the triangle) without superposition — same quantity, different quality; the student notes using this in Proposition 47.
• Aside: pasta shapes — same matter, different form, yet tasting different; a family story about a one-way ticket and repeated airport searches; Gregorian masses and endowed chantries (recording cuts off).

His words #

• “apparently hopeless contradiction” / “staggering contradictions” — the contradiction that is the seed of discovery
• “hidden harmony” — Heraclitus’s phrase for the more comprehensive order found by untying the contradiction
• dialectic — arguing on opposite sides, raising problems; in Sophistical Refutations, reasoning from probable opinions to contradictory conclusions
• heuristic — from Greek heuriskō, to find or discover; the “heuristic power of logic”
• classical/Newtonian physics vs. modern physics — 17th–19th century vs. 20th century, as the physicists use the words
• “the wall of contradictions” (Einstein) vs. the knot that ties the feet (Aristotle) — same idea, different metaphor
• “examination discussion” — showing someone he does not know what he claims to know
• “ad hoc character” — the Fathers’ and councils’ defence of only the articles then denied
• suitability of the Incarnation — not the only way, the most appropriate way
• the good as such / the bad as such — the bad desired only under the appearance of good
• synecdoche — the name of the part given to the whole (“souls” for men, in The Tempest and Scripture)
• fourth species of quality — shape or figure, “quality about quantity,” the limit of quantity

Texts #

Read in class

• Max Planck, reading in the handout (work not named)
• George Gamow, reading in the handout (book title alluded to, not named)
• Niels Bohr, lecture to the Danish Physical Society, Dec. 1913, and reminiscences from a volume by his collaborators
• Albert Einstein, The Evolution of Physics (readings, including “page 264”)
• Matthew 22, Christ’s question about David’s Lord
• Augustine, reading on heretics (work not named)
• Second Vatican Council, decree on priestly training, the paragraphs on dogmatic theology (Optatam Totius, inferred)

Mentioned

• Heisenberg, Gifford lectures (history of quantum theory); Bohr’s three volumes of essays on atomic physics
• Heraclitus; Aristotle on tying and untying (the “second paragraph” read earlier); Aristotle on drama’s plot
• The Elegant Universe; Bridgman
• Thomas Aquinas, division of Matthew; Summa Theologiae; Quaestiones Disputatae; on the reasons for the Incarnation; commentary on Ephesians; Cajetan’s commentary
• Aristotle, Sophistical Refutations; Aristotle, Categories (inferred, for the species of quality)
• Plato, Meno, Euthyphro; Dostoevsky, Crime and Punishment; Shakespeare, The Tempest, Othello; Euclid (Proposition 47)

His questions #

• Where does the first impulse toward revising a physical theory come from (Planck)? From facts that cannot be fitted into the theory, i.e. that contradict it.
• What is heuristic? From Greek heuriskō, to find or discover; dialectic’s power to bring out contradictions is a power of discovery.
• How did Bohr know both where to go and that he had arrived? The contradiction with classical laws pointed to the quantum postulate, and its sharpness, once resolved, made him confident of its truth.
• Why did Einstein say relativity arose “from necessity”? Because the mind cannot accept a contradiction.
• If David calls the Christ Lord, how can he be his son? Hidden in the contradiction: Christ is God (David’s Lord) and man (David’s descendant).
• In what sense is the heretic Augustine’s servant? The necessity of defending the article forces deeper investigation, understanding and proclamation.
• Why does Vatican II send students to Thomas? To illumine the mysteries as completely as possible and perceive their interconnections — both done by starting from contradictions.
• Is something good because it is wanted, or wanted because it is good? Wanted because good; the bad is desired only as it appears good.
• Why does the argument for infinite reparation seem to shift the sense of “infinite”? (student) Left open; compared to the puzzle of responsibility for good and evil.
• Is shape quantity or quality? A quality about quantity, its limit or determination; equal figures may differ in shape.