Heraclitus: Contradiction, Hidden Harmony, Strife and Fire

Orientation #

He picks up from the previous class’s account of Mother Earth, water and air as guesses at the first matter (“we saw before how the first opinion about matter is Mother Earth”) (prev. lecture), and says that when Heraclitus is finished the class will turn to the secondary readings on the modern scientists (“You all got copies”), and after that to Empedocles and Anaxagoras, in whom matter and mover come apart. He also promises to return to Aristotle’s untying of “one contrary becoming another” “when we go back to the readings from Aristotle.” The previous class traced the Presocratics from Thales to the opening of Heraclitus, and the next takes up the “principle of fewness” in modern physicists.

The class, in order #

1. Parmenides and the Socratic method (“a man to be reverenced, and a man to be feared”) #

Point: the Socratic method rests on Parmenides’ axioms of being and unbeing.

• In Plato’s Parmenides, Socrates falls into contradictions under Parmenides’ questioning as others do under his own; Plato shows Parmenides and Zeno teaching Socrates the Socratic method. Whether Parmenides could historically have met Socrates is “beside the point.”
• Socrates’ method: ask what you think, draw out what follows, see whether you contradict yourself; a contradiction is “a sign that there’s some mistake in your thinking.” So the method is based on the axioms Parmenides was first to state explicitly.

2. The dichotomy Parmenides / Heraclitus and why Parmenides wins (“the ball game’s over”) #

Point: the one denies change to keep the axiom of contradiction, the other keeps change and (in words) admits contradiction; forced to choose, reason must choose Parmenides.

• Parallel to the earlier Plato/Aristotle “yes and no” on the central question. Heraclitus: all things flow, day is night, the sleeping are the waking. Historically far more have spoken like Heraclitus (Hegel, the Marxists, who quote him as “a good exposition of the rudiments of dialectical materialism”) than like Parmenides, because our knowledge begins with the senses and what strikes the senses is change.
• Heraclitus’s own methodological fragment: “Those who speak with understanding must be strong in what is common to all.” Two who disagree get nowhere by each saying “you don’t agree with me”; they need common ground — as two scientists with rival hypotheses devise an experiment both can perform where the theories predict differently.
• What Parmenides and Heraclitus have in common: that you must choose. Argument:
  1. Both agree you must choose between the axiom and change.
  2. You must choose only because change involves a contradiction and so contradicts the axiom.
  3. But that reason is itself Parmenides’ principle. So “in thinking you have to make a choice, you’re already admitting Parmenides’ principle” — “the ball game’s over. Parmenides has won.”
• Generalised: anyone who denies the axiom because something he runs into contradicts it “is saying it isn’t so because it is so” — the absurdity of rejecting the axiom on the strength of the axiom. Like his brother Mark’s examination of the famous attempts to prove Euclid’s fifth postulate: each assumes what it is proving, so all are invalid, but their not noticing shows the postulate is obvious even to them. Likewise in ethics: whoever argues that we should live by emotions rather than reason uses reason to decide it and “has already lost.”
• Aristotle’s move: choose Parmenides because the axiom is more certain, but change obviously exists, so the contradictions in change are apparent, not real; his task is to “untie” them. Boundary case: “I find travel restful” — body in motion, emotions at rest; the boy made to sit still gets agitated; no contradiction, since contradiction needs the same thing in motion and not at the same time. One contrary becoming another is left for Aristotle’s readings.
• Reread Heraclitus charitably: perhaps he did not think day is night but wanted to point out that our way of speaking of change (“love turns into hate”, “day becomes night”) seems to admit a contradiction. Evidence: his fragment “We should not act and speak like those asleep” — he plainly sees a difference between waking and sleeping. “Maybe more subtle than we think, Heraclitus.”

3. The hidden harmony is better than the apparent (“out of that apparent harmony into a contradiction”) #

Point: Heraclitus anticipates Socrates’ leading men from apparent harmony through contradiction to the true, hidden harmony.

• Harmony from Greek harmozo, to fit together. Most people live in apparent harmony: they think all they think fits, but some of it contradicts the rest.
• Example (Plato’s Meno, slave boy): side twice as long gives a square twice as big? Take side 2: area 4; side 4: area 16. Three thoughts — 4 is double 2; 16 is not double 4; the square with side twice as long is twice as big — do not fit. The weak point is the third, so it is false; the hidden harmony is that the diagonal gives the side of the double square.
• Fragment “Men do not understand the things they meet every day, although they think they do”: you think you understand the wet becoming dry; but “becomes” means comes to be, so the wet would be dry, hence wet and not wet, dry and not dry — “you don’t even understand what you’re talking about.” He flags this as “a marvelous introduction” to the role of contradiction in the development of knowledge, to be treated later.

4. Opposites that agree: the bow (“a harmony of opposites, as in the case of the bow and the lyre”) #

Point: things that seem opposed may be working together.

• Pushing a glass forward with one hand and pulling it back with the other: cross-purposes, both frustrated. The bow: right hand pulls back, left pushes forward, yet together they send the arrow with more force (and direction) — through the armour at Agincourt. “A hint that maybe there are things that seem to be opposed that are not really opposed.”

5. The opposite is useful; from differing, the most beautiful harmony (“the whole American way of life is based on this one statement”) #

Point: opposition serves truth, justice and beauty.

• Legal system: prosecutor and defender; one lawyer alone would give more convictions or more acquittals, but not justice. Political: one-party states in the twentieth century have usually been tyrannies; an opposing party exposes the other’s corruption (aside: Massachusetts is too much one-party). Economic: a monopolist charges what he likes; a competitor forces lower prices and better products. Debates likewise. So Heraclitus’s “opposition” is what jolts men out of apparent harmony to seek the hidden one.
• Character: brought up on easy street, character does not develop; hardiness comes from opposition. He tells the girls to play hard to get; “even God … with the saints … plays hard to get, so to speak.”
• “From those differing comes the most beautiful harmony”: stars against the black sky (all black or all lit would be garish); his mother’s diamond ring under candlelight; jewellers show a diamond on black cloth; Rembrandt’s man with the helmet, beautiful by contrast of light and dark, not flooded or all shadow; sunrise and sunset more beautiful than noon.
• Aside: on this line Heraclitus would find homosexual marriages ugly, “‘cause they’re not from opposites.”

6. War the father of all: the mover as a cause (“war is the father of all things”) #

Point: “father” names a third kind of cause, the mover or maker, not form or matter.

• Latin materia from mater: Mother Earth was the first opinion about matter; father is the mover. Aristotle will later use “father” as the example of the third cause. Why God is called Father not Mother: God is not a cause as matter but as mover or maker. Fitting that the thinker who most stresses change should look for the mover.
• “War is common and strife is justice, and all things come into being by strife”: source of Marxist dialectical materialism — matter is the origin, but things develop by a war of opposites in matter. Connection with dialectic in Aristotle’s Sophistical Refutations: reasoning from probable opinions to contradictory conclusions, as Socrates in the Meno argues both that virtue can and cannot be taught; and the medieval quaestiones disputatae (Thomas’s De veritate, De malo, De potentia), ten or fifteen arguments each side, “a war” the master resolves. The same idea is taken over by moderns, including biologists.

7. “Listening not to me but to reason”: what listening to reason means (“Is there a reason out there besides your reason?”) #

Point: to listen to reason is to listen to what is common to, and natural to, reason.

• “It is wise, listening not to me but to reason, to agree that all things are one”: reason itself seeks unity, since reason seeks order and order is based on unity; the modern scientists in the secondary readings show the same tendency.
• Puzzle: there is my reason, your reason, the next man’s; what is reason apart from these? Answer via Augustine: “If you see it and I see it, it’s not mine, it’s not yours” — what is common to your reason and mine is what reason naturally knows. Ties to “strong in what is common to all” and to “Wisdom is to speak the truth and to act in accord with nature, giving ear thereto.” Common ⇄ natural.
• Parmenides saw this: whatever he says he comes back to the axiom; its denier is a “two-headed mortal” — joke: here two heads are not better than one; a two-headed mortal is a monster, and a monster is the opposite of the natural. So denying the axiom is unnatural. What reason naturally knows: his “natural understanding”, Aristotle’s nous, Latin intellectus.
• The whole is larger than the part: anyone who says he doesn’t know it is lying — give him part of his salary, part of his dinner, part of his car. Sophistical objection he sets students: animal is only part of what man is (his mother disliked “man is an animal”), yet animal includes dog, cat, horse — so a part is more than the whole? Solution: two wholes — the universal whole, said of its parts and always said of more than any one; the composed whole, e.g. the definition, always put together from more than one part. Animal vs man/dog/horse is universal whole to particulars; animal in the definition of man is the other whole.

8. Fire as first matter — and as mover (“all things are exchanged for fire”) #

Point: fire is a worse guess than water in qualities but the thinnest of all, and Heraclitus is really reaching for a matter that is also a mover.

• Economic comparison “goods for gold and gold for goods”: don’t exaggerate — you don’t turn money into what you buy.
• Compared with earth, water, air: by definiteness of quality fire is worse than air and even water (definitely hot and dry). By thinness, fire “cuts” — paper in air is not cut up, in fire it is ashes; fire gets right inside the charcoal, “the most penetrating thing”; the thin is what cuts — so possibly the best guess.
• Why fire: he needs a mover as well as matter; fire is both. Heisenberg: substitute “energy” for fire; and by E = mc² you get mass, hence matter, from energy, so energy is both matter and mover in modern science.
• “That gives you a nice hint”: what makes fire a good mover — being hot (hot air rises; fire makes the water shoot out of the pan) — makes it a bad matter, since everything made of it would have to be hot. So matter and mover need separating: more in Empedocles, entirely in Anaxagoras. We know confusedly before distinctly. Marxists prefer Heraclitus because once mover separates from matter you are “on the way to God.”
• Caution on Heisenberg: energy is an abstract mathematical notion; in mathematics there is no matter and no motion (Schrödinger); such knowledge “shadows matter and motion but doesn’t contain them.”
• Syllogism comparison: universal equations are like premises (both called “deduction”). Every B is A, every C is B, so every C is A — Barbara, three A’s for universal affirmatives. Aristotle says premises are sometimes as the matter, sometimes as the mover of the conclusion: C and A, out of which the conclusion is made, are in the premises like matter; B, the middle term, is no part of the conclusion but brings C and A together — like the matchmaker who arranges the couple but is no part of the marriage. Matter and maker are more distinguishable there than in the equations, and not at all in Heraclitus’s fire. Student asks the connection to physics: deducing from equations is calculating, from premises reasoning; the Greek word syllogism comes from “to calculate” (“I reckon”, “I figure”), since calculating is more obvious to us.

9. Beginning and end common in the circle (“Dust thou art, and to dust thou shalt return”) #

Point: circularity of beginning and end recalls Anaximander and, in a higher way, God.

• Straight line: beginning and end differ; circle: you return where you started. Matter is a beginning that is also the end (Ash Wednesday). But God is beginning as Father/mover and end as purpose, not destruction: things go out from God and tend back to him. Shakespeare: “he that made us with such large discourse, looking before and after, gave us not that capability and godlike reason to fust in us unused” — reason given to be used, and being godlike, its use returns us to our maker.

10. The way up and the way down; the deaths of the elements (“the way up and down is one and the same”) #

Point: Heraclitus is already transcending fire alone and anticipating Empedocles’ four.

• The picture: earth in the middle, water on it, air above, sun and stars (fire) at the periphery; things come by condensing and rarefying — water to steam and back, water to ice “almost like earth”, heat enough and it is fire. Same way, opposite directions.
• “Death of earth is water coming to be, of water air, of air fire, and in reverse”; “the same thing is death to souls to become water” — very concrete words of life and death; solid to liquid to gas in our terms.

11. The everlasting fire and the random heap (“a heap piled up at random”) #

Point: a mindless matter-mover should yield a heap, not a cosmos — Heraclitus leaves a problem that Anaxagoras’s mind answers.

• “This universe … no god or man has made … everlasting fire, kindled in measures and extinguished in measures”: quoted by Marxists as anticipating eternal matter.
• Cosmos vs universe: cosmos, a beautiful ordered whole (hence cosmetics); universe, turned into one. Order based on unity, matching “all things are one.” Yet he calls the most beautiful cosmos a heap piled up at random. Perhaps he is puzzled: if the origin is mindless matter or matter-mover like fire, the result should be mindless — the fire raging through the twin towers left a heap, not an ordered whole. So all thinkers so far imply a heap.
• Aside with Warren Murray: Latin mundus, first meaning “elegant”; the string-theory book The Elegant Universe; the scientist sees an ordered whole that “suggests mind, as Einstein would say.”
• Anaxagoras will first bring in a mind responsible for the cosmos — Socrates’ enthusiasm in the Phaedo; Aristotle: “a sober man among drunk men.” Heraclitus is “forcing us”: opposition is useful; why a cosmos if there is no mind?
• Handout p. 8, Anaxagoras DK 12: the first thing said of mind is that it is unlimited. Heraclitus’s last fragment anticipates this: one could not find the ends of the soul, “so deep is the reason it has” — something infinite about the soul. “We’ll have to find out.”

His words #

• axioms of being and unbeing / axiom of contradiction: the impossibility of something both being and not being; the basis of the Socratic method.
• two-headed mortal: Parmenides’ name for one who denies the axiom; a monster, the opposite of natural.
• apparent harmony vs hidden (true) harmony: thinking one’s thoughts fit when they don’t; what fits when the contradiction is exposed. harmozo, to fit together.
• the opposite is useful: opposition as serving truth, justice, character, beauty.
• father: the cause that is mover or maker; materia from mater for matter.
• dialectical: Marxist sense (war of opposites in matter) vs Aristotle’s reasoning from probable opinions to contradictory conclusions (Sophistical Refutations; he says “Sufficient Refutation” [ed.: ASR]).
• quaestiones disputatae: disputed questions with arguments on both sides.
• listen to reason: listen to what is common to your reason and mine, i.e. what reason naturally knows.
• natural understanding: his name for Aristotle’s nous, Latin intellectus [ed.: the virtue of understanding first principles].
• universal whole vs composed whole: said of more than any part vs put together from more than one part (definition).
• Barbara: mnemonic for the syllogism with three universal affirmatives; middle term as maker, extremes as matter.
• reasoning vs calculating: syllogism from the Greek “to calculate”; “reckon”, “figure.”
• cosmos vs universe: beautiful ordered whole (cosmetics) vs turned into one; Latin mundus, “elegant.”
• “brevity is the soul of wit”: said of “the opposite is useful.”

Texts #

Read in class

• Heraclitus, fragments from the handout “On the Natural Fragments”, p. 17: hidden harmony; men do not understand what they meet every day (methodological collection); that which is opposed agrees with itself, bow and lyre; the opposite is useful; from differing the most beautiful harmony; all things by strife; war the father of all; war is common and strife is justice; listening not to me but to reason, all things are one; all things exchanged for fire; beginning and end common in the circle; the way up and down; deaths of earth, water, air; death to souls to become water; this universe no god or man has made; the most beautiful universe a heap piled up at random; one could not find the ends of the soul.
• Heraclitus, methodological fragments (other collection): “strong in what is common to all”; “not act and speak like those asleep”; “Wisdom is to speak the truth and act in accord with nature.”
• Anaxagoras, DK 12, handout p. 8: “mind is unlimited” (opening only).
• Shakespeare, Hamlet (inferred), “large discourse, looking before and after … godlike reason to fust in us unused.”
• Verified source: Aristotle, Physics I with Aquinas’s commentary lectio 2, and his “Note for Book One of Natural Hearing, Reading 2” (p. 5) matched a few minutes of the audio; the transcript itself only refers forward to “the readings from Aristotle.”

Mentioned

• Plato, Parmenides (Socrates questioned by Parmenides and Zeno); Meno (slave boy; virtue teachable or not); Phaedo (Socrates on Anaxagoras).
• Aristotle, Sophistical Refutations (dialectical reasoning); Aristotle on Anaxagoras as a sober man among drunk men (unlocated); Aristotle on premises as matter and as mover of the conclusion (unlocated).
• Aquinas, Quaestiones disputatae De veritate, De malo, De potentia.
• Euclid, fifth postulate; his brother Mark’s study of attempted proofs.
• Augustine (unlocated), “If you see it and I see it, it’s not mine, it’s not yours.”
• Heisenberg (fire = energy), Einstein (E = mc²; order suggests mind), Schrödinger (no matter in mathematics); Hegel, Marx; the secondary-readings anthology (“You all got copies”).
• Rembrandt, the man with the helmet; The Elegant Universe (string-theory book); Ash Wednesday formula.

His questions #

• If you had to choose between Parmenides and Heraclitus, whom would it be more reasonable to choose? Parmenides — the axiom is more certain — but you must also keep change (student’s answer, which he accepts and Aristotle follows).
• Why do most thinkers in history side with Heraclitus? Our knowledge begins with the senses, and what strikes the senses is change.
• Despite all the disagreement, what do these two have in common? That you must choose — and the reason you must choose is Parmenides’ own principle, so Parmenides has won.
• Is “I find travel restful” a contradiction? No: the body is in motion, the emotions at rest; not the same thing at once.
• Which of the slave boy’s three thoughts is the weak point? That the square whose side is twice as long is twice as big.
• With the bow, are the two hands working at cross purposes? No; together they drive the arrow forward with greater force.
• What kind of cause is Heraclitus talking about when he says “father”? The mover or maker — not form, not matter (matter is “mother”).
• What does it mean to listen to reason, if there is only my reason and yours? To listen to what is common to both, which is what reason naturally knows.
• How have I deceived you with “a part is more than the whole”? By confusing the universal whole with the composed whole (the definition).
• Is fire a better guess than air and water, or not? Worse in definiteness of quality, possibly better in thinness (it cuts); its real advance is to be matter and mover at once.
• Are the premises the matter or the maker of the conclusion? C and A are like matter; the middle term B is like the maker.
• If the origin of all things is a mindless matter or matter-mover, what should the universe be? A heap piled up at random — so why is it a cosmos? Left for Anaxagoras’s mind.