Contradiction and the Progress of Knowledge: Heraclitus, Aristotle and the Untying of Knots

Orientation #

He refers back to “the apparent contradiction DK 12 there of Anaxagoras” and to “the definition of nature” and “the confused and the distinct” as already treated (prev. lecture). He says he will “stop, as we will look at those secondary readings” on the role of contradiction, and that Plato’s Phaedo and Bohr/Einstein “in context” will be taken up later. The verified sources locate the handout he reads from as “Texts on Necessity and Difficulty of Beginning Well” (p. 21), “Beginnings of Philosophy in the Senses and Reason” (p. 5) and “The Royal Fragment” (p. 20), with DHB Vol I pp. 36-80 and Vol III p. 904 as the printed volumes. The previous class established that the principles of change must be more than two contraries, and the next continues through the scientists and the theological texts on the handout.

The class, in order #

1. Why this is the first major example (“first major example in our learning”) #

Point: untying the contradiction in change is the first (in the order of learning, not the hardest) example of how knowledge goes forward by untying contradictions.

1. Shakespeare, Troilus and Cressida (Ulysses/Odysseus): “things in motion sooner catch the eye than what not stirs” — change first grabs the senses.
2. Since the natural rises from the senses into reason, change first absorbs the mind.
3. All change seems to be between contraries or opposites, so there is an apparent contradiction in all change: one opposite becoming the other.
4. Therefore this is the first example of contradictions leading to the development of knowledge when we untie them; “ever since this,” philosophers, scientists and theologians have gone forward the same way.

• Heraclitus perhaps first saw this: he calls him “the father of the progress of the human mind” — “quite a title,” but hard to exaggerate. He may not really think day and night are the same, but stresses the apparent contradiction to force deeper thought.
• Heraclitus fragment (on method): “Men do not understand the things they meet every day, even though they think they do” — recalls Socrates. You make men aware they don’t understand by showing they are in an apparent contradiction; a real contradiction is worse, but even the appearance is a sign they have not fully understood. Example: if you can’t solve the Anaxagoras DK 12 contradiction, you don’t understand what is required for the mind to direct itself.
• Aside: valedictorians at Nazianzen graduations claim they were “taught to think for ourselves”; that means directing your own mind, which requires separating what you know from what you don’t, and what is more known from what is less known — an illusion if the professors haven’t done that. Socrates’ compliment to him: “you’re able to move yourself.”

2. The proposition used in theology: God is simple, so God does not change (“what changes is composed”) #

Point: the general proposition learned in Lectio 11 — what changes is composed (of the contrary in the strict sense and the underlying subject); unless there is a real composition between things not identical, change is impossible — is what theology uses. Syllogism:

1. Summa Theologiae I: q. 1 nature of theology, q. 2 existence of God, q. 3 simplicity of God — eight articles each denying a mode of composition, finally “not composed any way.”
2. What changes is composed; God is not composed; therefore (second figure, affirming of what changes, denying of God) God does not change.

• “That’s a very important thing”: in at least some theology, simplicity is shown before one asks whether God changes.
• Knowledge of the general in theology: we know more what God is not than what He is (the beatific vision, St. John: “we will see him as he is”). In affirmative knowledge the more specific is closer (body < living body < animal < man; number < odd number < prime odd number). In negative knowledge the more general negation is closer: “not a dog” vs. “not a quadruped” — the second separates you from more (a student first answered “neither,” then “not a dog”; corrected). Seven: “not four” is less close than “not even.”
• Hence to negate the general you must know the general distinctly; so theology shows God does not change, not that He doesn’t walk, run, crawl or grow.
• Corollary for almost everything shown of God: since God is altogether simple, no real distinction between God and His goodness; so once He is shown good, just, knowing, He can in no way be the opposite. Example: “if hardness and butter were the same thing, butter could never be soft.”
• Language: De Anima III — the soul in the body is turned to what can be sensed or imagined, where form and what has the form are distinct; hence abstract and concrete words. “God is goodness” seems to say He is that by which something is good; “God is good” seems to say He has goodness, implying composition. So Thomas, following Dionysius: no name is adequate to God; we both affirm and deny the names.
• Aside: Weisheipl’s biography — Thomas at the University of Naples, a heterodox place but the only place in the Christian West where Aristotle’s “physics” (Natural Hearing) was available; “divine providence,” since without it the Summa could not be done that way.
• Eternity: Thomas understands Boethius’s definition (Consolation) by what it negates of time and of the now as Aristotle brought them out; De Koninck ended his graduate course on time (second part of Book Four, after place and the empty) with a theological footnote on eternity, via negativa / via negationis.
• General vs. particular: how fast a ball falls is useless in theology; theology shows God has no parts, so you need to know what whole and parts are — not that water is H2O, or that a Manhattan is rye whiskey and sweet vermouth, or that “cat” has letters C-A-T. “It’s more useful to know that a whole has parts than to know that water is H2O.” General knowledge of natural things is the foundation; particular knowledge comes later but is not usually needed in theology.

3. Student: has anyone else untied this contradiction? Plato’s Phaedo (“student of what Cratylus, as well as of Socrates”) #

Point: Plato, student of Cratylus (student of Heraclitus) and of Socrates, comes close in the Phaedo, so there is real continuity between Heraclitus, Plato and Aristotle.

• First argument for immortality: an induction that change is between contraries (Heraclitus began this in the fragment seen; Plato is fuller; Aristotle has it here), then a syllogism.
• Last argument: Socrates denies one opposite can become the other; an interlocutor objects he said the opposite at the beginning; Socrates: one of two opposites cannot become the other, but a third thing maybe can — “getting close to the distinction of Aristotle,” though he frames it as whether one opposite is in the definition of the third thing.
• Example: hard is not in the definition of butter, so hard butter can become soft and remain butter; virtue is in the definition of justice (or courage), so justice can never be a vice. “Not exactly the same distinction,” but a certain proximity. The more you read Plato the more you see Aristotle got from him.
• Digression: Mozart and Haydn — the Vienna quartets (Köchel below 200) imitate Haydn’s Op. 17 and 20; after hearing Haydn’s Russian quartets (each instrument its own role, a true ensemble of four voices) Mozart wrote the six “Haydn” quartets (from about K. 387); Haydn to Leopold: “as an honest man before God … your son is the greatest composer that I know”; Mozart’s dedication letter (“father sending his sons into the world”) and another letter: “he taught me how to write the quartet.” Similar leaps: the five violin concertos in about a year (around K. 200), the third to fifth far better; Shakespeare from Titus Andronicus (“this disgusting play”) to the great tragedies; Mozart’s 36th to 38th symphony — there is no 37th, which was Michael Haydn’s with a Mozart introduction.

4. The handout: Heraclitus’s fragments applied to knowledge (“the hidden harmony is better than”) #

Point: the readings (two philosophers, Heraclitus and Aristotle; 20th-century scientists pp. 2-5; theology from mid-p. 5) show that despite important differences in how philosophy, science and theology proceed, contradiction plays a fundamental role in all three; “you don’t get it from the horse’s mouth” — Einstein or Bohr themselves point to a contradiction as starting point.

• “War is the father of all things, the king of all things”: war is a conflict. Compared with Einstein’s last sentence (p. 5), a universal affirmative: all the essential ideas in science were born in a dramatic conflict between reality and our terms of understanding. DK 8 says the same.
• DK 54, “the hidden harmony is better than the apparent harmony”: harmony (Greek, “fit together”) is the opposite of contradiction. Meno slave boy: in apparent harmony thinking doubling the side doubles the square; 2x2=4, 4x4=16, but 16 is not double 4 — let out into a contradiction; Socrates to Meno: haven’t we done him a good turn? Error removed, and now he wants to know. Hidden under the contradiction is the true way (the diagonal) — the hidden, true harmony, separated from the apparent by a contradiction.
• Bohr (p. 4, last): difficulties (= contradictions) were for him “the external appearance of new knowledge”; in an apparently hopeless contradiction he conceived the germ of a wider, more comprehensive order and harmony — while other physicists stayed in apparent harmony, unaware of contradictions in their thinking.
• Applied to nature: “nature loves to hide”; nature is defined by motion (the beginning and cause of motion and rest in that in which it is first, as such and not by happening), and change itself is an apparent contradiction with something of nature hidden underneath.
• “If you do not expect the unexpected, you will not find it; for it is hard to be found and difficult” — “extremely important”, to be seen repeated (perhaps independently) by the scientists. It sounds itself like a contradiction, as he liked; the answer: a fundamental contradiction leads you to expect the unexpected. Bohr (p. 3, bottom): “just the sharpness of the contradiction made me absolutely confident of the truth of the quantum postulate”; no progress on high-energy particle transformations because no “sufficiently violent contradiction with what could be expected from current ideas” has been found — note “expected.”
• Last fragment: dispute. The Middle Ages dominated by quaestiones disputatae — Thomas’s De veritate (21 questions, many articles), De potentia, De anima, De caritate, De spe: arguments on both sides, then the master unties; if truth is on one side he answers all on the other, if on both he answers both. Aside: in De spe, a text Orin Murray showed him, Thomas is clear hope is a greater virtue than faith (Paul: charity greatest). The Summa, “for beginners,” abbreviates: about three objections, one sed contra — the same dispute in essence.

5. Aristotle’s reasons for raising difficulties: the knot (“impossible for those ignorant of a knot to loosen it”) #

Point: Metaphysics III is all dialectical disputation on the main questions of wisdom, untied from Book IV on; at its start Aristotle gives four or five reasons for doing this. Reasons (first paragraph, two connected reasons):

1. Doubting well before is necessary for those wishing to discover, for the later discovery is an untying of the previous difficulties (he prefers “doubt well … discover … untying” to “raise difficulties … resolve … loosening”); it is impossible for those ignorant of a knot to loosen it.
2. The doubt of the mind shows something about the thing: the mind in doubt undergoes the same as those tied; in both cases it is impossible to go forward. The mind can’t accept the contradiction and is stopped — but the very untying is the discovery of what was hidden (C. S. Lewis: “find the loose end”).

• Usage: “tied up” borrowed for a busy man, a tied game untied by a home run; Poetics describes the plot as tying and untying the knot (elsewhere beginning, middle, end). Arden Cymbeline: some count fifteen or twenty knots untied in the last scene, really three or four. Difference: in tragedy tying takes longer than untying; in the Metaphysics Book III ties, Books IV-XIV untie, so untying takes longer. Likeness: many poets tie interesting knots but fail to untie them well; even more so in philosophy — the young philosopher is better at seeing difficulties than untying them, and some “drown, intellectually speaking.”
• Example: an article in Laval Théologique et Philosophique, “Du paradoxe du devenir par contradiction” — an apparent contradiction in becoming much harder than today’s, untied only in Physics VI; Hegel sees it but thinks it real (change is contradiction), whence Marx’s dialectics and Lenin’s “dialectics is the study of contradictions in the essence of things”; the same problem arose in medieval theology of the Eucharist and Thomas, with Aristotle, untied it. Second paragraph, two more reasons:

3. Those who investigate without first considering difficulties are like those who do not know where they ought to go — the direction is toward untying the knot.
4. The other side of the coin: they do not know whether what is sought has been found; the goal is clear to the one who has raised the difficulties — you know you’ve arrived when you can untie them. To be seen repeated in Bohr and Einstein.

6. Heisenberg: asking the right question (“more than halfway to the solution”) #

Point: Heisenberg (Physics and Philosophy, Gifford lectures, “history of quantum theory,” p. 4) complements Aristotle’s third reason: Bohr’s theory opened a line of research; “from this time on the physicists learned to ask the right questions,” and asking the right question “is frequently more than halfway to the solution” — “a very profound observation”, contrary to what we’d expect (that questions come early and answers take long). Drawn as a line from ignorance to knowledge with a halfway mark: more effort lies before the right question than after.

• Meno, second conversation: Socrates only asks questions and the doubling comes out of the boy’s answers, so it seems the boy’s own knowledge; but Socrates asks the right questions and does most of the work; “they will seem to teach themselves” — the perfection of teaching.
• His own experience: a question carried from undergraduate days (Cassirer [unclear in recording]) through teaching at St. Mary’s; ten years later, in a class of Monsignor Dionne [ed.: “Dion”] reading Thomas, he asked the right question and “bang, I was there”; Dionne: “I know where you’re going, Duane.”
• Heisenberg, Physics and Beyond: around 1926 he and Bohr talk all day, get on each other’s nerves, sick; Bohr goes skiing; one night Heisenberg recalls a conversation with Einstein, asks the right question, and the calculation comes out.
• “Every investigation takes the direction of the questions asked,” so the right question is the right direction; witness on the stand disliking where the questions are going. Heisenberg’s second paragraph: practically all the right questions concerned strange apparent contradictions between experiments; describing atomic events in Newtonian terms led to contradictions — “a beautiful way of complementing Aristotle.”
• Applied to Anaxagoras: how does the mind rule itself? Not two minds nor two parts (the mind “the thinnest of things”), but a distinction between what it knows and doesn’t, more known and less known — reached by asking the right questions because we saw the contradiction. Einstein the greatest and most famous 20th-century scientist; Bohr more influential, his Copenhagen institute training Heisenberg, Dirac, Pauli.

7. The last reason: judging like a jury; Thomas on dialectic (“two parties in a lawsuit”) #

Point: the one who has heard all the reasons of those disagreeing, like two parties in a lawsuit, is better prepared to judge — this concerns judging, not just discovery; a jury hearing only one side may have more or less conviction but is less apt to judge what is true.

• Thomas’s commentary: for these reasons Aristotle uses dialectic in almost all his works; Book III is unique as a universal dialectic, the other parts being more particular; there is an affinity between dialectic and wisdom, and Thomas gives three reasons (not stated here).
• Summary: witnesses from two philosophers, Aristotle “the philosopher” and Heraclitus “the central thinker in human thought,” central because he sees something of this. The recording cuts off at “Now, let’s.”

His words #

• untying / breaking down a contradiction; the way knowledge goes forward
• father of the progress of the human mind; central thinker in human thought — Heraclitus
• what changes is composed — the proposition of Lectio 11
• second figure — the syllogism affirming of what changes, denying of God
• negation of the general — closer than a negation of the particular
• Natural Hearing [ed.: Physics]
• via negativa / via negationis
• abstract word and concrete word — reflecting form vs. what has the form
• harmony — Greek, “they fit together”; hidden harmony vs. apparent harmony
• expect the unexpected
• quaestiones disputatae; sed contra
• to doubt well before / discover / untying the difficulties — his preferred rendering of Metaphysics III
• knot; tie up / untie — Aristotle’s near-metaphor, also for plots (Poetics)
• the right question — Heisenberg; “every investigation takes the direction of the questions asked”
• universal dialectic vs. particular dialectic — Thomas on Metaphysics III

Texts #

Read in class:

• Heraclitus fragments on the handout: “men do not understand the things they meet every day”; “war is the father of all things”; DK 8; DK 54 “the hidden harmony”; “if you do not expect the unexpected”; the fragment on dispute
• Einstein, last sentence of the passage on handout p. 5
• Niels Bohr, handout p. 3 (bottom) and p. 4 (last)
• Aristotle, Metaphysics III, opening paragraphs on raising difficulties (two paragraphs of the handout)
• Heisenberg, Physics and Philosophy, “history of quantum theory,” handout p. 4
• Verified handout sources: “Texts on Necessity and Difficulty of Beginning Well” p. 21; “Beginnings of Philosophy in the Senses and Reason” p. 5; “The Royal Fragment” p. 20 Mentioned:
• Aristotle, Physics I Lectio 11; Physics IV (place, the empty, time); Physics VI; De Anima III; Poetics
• Thomas, Summa Theologiae I qq. 1-3 (q. 3, eight articles); De veritate, De potentia, De anima, De caritate, De spe; commentary on Metaphysics III (inferred)
• Anaxagoras DK 12; Plato, Phaedo, Meno; Boethius, Consolation of Philosophy; Dionysius
• Shakespeare, Troilus and Cressida, Titus Andronicus, Cymbeline (Arden)
• Weisheipl’s biography of Thomas; Heisenberg, Physics and Beyond; C. S. Lewis essay; “Du paradoxe du devenir par contradiction,” Laval Théologique et Philosophique; Lenin on dialectics; St. John on the beatific vision; St. Paul on charity
• DHB Vol I pp. 36-80; DHB Vol III p. 904 (verified printed volumes)

His questions #

• Which is closer to you: “you’re not a dog” or “you’re not a quadruped”? “Not a four-footed animal” — it separates you from more.
• Is there any real distinction in God between God and His goodness? No, they are identical, because He is altogether simple; so goodness itself could never be bad.
• Can justice ever be a vice? No — virtue is in the definition of justice, unlike hard in the definition of butter.
• Harmony is the opposite of what? Contradiction; harmony means things fit together.
• How can you expect the unexpected? A sufficiently violent contradiction leads you to expect something unlike current ideas.
• Why does Aristotle raise all the difficulties before (Metaphysics III)? You can’t go forward tied; untying is discovery; you know where to go; you know when you’ve arrived; you judge better having heard both sides.
• Is asking the right question really more than halfway? Yes — the Meno, his own ten-year question, Heisenberg in 1926.
• Has anyone besides Aristotle untied the contradiction of change? (student) Plato comes close in the Phaedo, via whether an opposite is in the definition of the third thing.