Anaximenes, Pythagoras and Heraclitus: Air, Form, and the Problem of Change

Orientation #

He picks up from Anaximander’s unlimited (“as you saw last time” (prev. lecture)) and finishes the three Milesians, then begins Pythagoras and Heraclitus, promising to look at each Heraclitus fragment individually and to return to whether Heraclitus really thinks there is a contradiction in change. The verified handout page (On the Natural Fragments, p. 12) and DHB Vol I p. 125 are the pages read from. The next class continues with Parmenides and further Heraclitus fragments.

The class, in order #

1. Opening talk before the fragments (“no evidence at all for intelligence in the universe”) #

Informal talk before class, none of it argued: a scientist quoted as seeing no evidence of intelligence in the universe; his diagnosis that science is so complicated one cannot see the simplest things, unlike knowledge based on common experience; Warren Murray’s report that scientists now doubt life exists elsewhere, the odds being “astronomical”, so “Mother Earth is coming back” as the one place of life.

• Aside: after death the soul lives for a time entirely in an immaterial world we know little about; we know angels “kind of negatively”.
• Aside: a couple converted through the Rosary (“a compendium of the Gospel,” as the Pope says); Charlie Swisher of the package store, the minister throwing hosts in the waste basket as a convert’s turning point, the Seventh-day Adventist store and cigarettes, and Charlie’s “I believe what they tell me to believe in the church” (“blood brothers”).

2. Anaximenes: soul as air, and why we call spirits by the name of breath (“just as our soul, being air, holds us together”) #

He reads the fragment: as our soul, being air, holds us together, so breath and air surround the whole world; Anaximenes is “influenced by air”, which is tied up with life even more immediately than Thales’ water.

• Homer’s battle scenes: souls flit down to Hades; a wind blows one man’s soul back into his body. Dante tries to hug the air-like shades. Both show that when people imagine the soul (which cannot be imagined) they picture a finer, air-like human figure.
• Word history: Greek psuche (whence “psychology,” originally the study of the soul) comes from the word for breath or air; Scripture says God breathed into the clay; Latin spiritus from breath. We carry “breath/spirit” over to substances not sensible at all (God, angels) because air is a material substance that is nearly insensible: you cannot see it, though you can feel it in a bag or when it blows.
• Shakespeare, The Tempest: the actors “were all spirits, and melted into air, into thin air.”

3. Why air rather than water: two reasons from Anaximander (“why did Anaximenes say air instead of water”) #

Point: Anaximenes could be led by Anaximander’s thinking to a better guess than water, while keeping something more concrete than the bare negative “unlimited”.

1. “Unlimited” can mean in quantity or in quality. Thales was already after a qualityless matter, able to take on all qualities; Anaximander went further and removed all qualities, since water is wet, cool, and even a drop has a globular shape. But the unlimited may be “too abstract, too remote from the senses.”
2. Quantitatively: air is everywhere, lakes are not; air goes “up and up, on all sides of us.” So air is the better guess for something unlimited in quantity.
3. Qualitatively: air is more transparent than water; water is definitely wet and, nearly everywhere, cool, whereas air is not definitely wet or dry (student: in the desert it is dry; he: even in the desert we think water cool). So air is less limited in quality. Conclusion: two reasons for air over water, both suggested by Anaximander, yet with the advantage of being “concrete.”

4. The third reason: earth, water, air, from the thick to the thin (“the thick is made out of the thin”) #

Point: comparing the three guesses (poets’ Mother Earth, Thales’ water, Anaximenes’ air) shows an order that makes air the best guess for first matter.

• Timon of Athens: Timon digging for roots calls earth “Common Mother… whose womb immeasurable and infinite breast teems and feeds all”; even the poets think Mother Earth infinite, but air is far more so.
• Order 1, from more sensible to less: an emptied room, “there’s nothing in there,” though full of air. Air is less sensible and so less known than water, a fortiori than earth. This explains why Mother Earth was guessed first, not which guess is better.
• Order 2, from thick to thin: Lear’s “strike flat the thick rotundity of the earth” against “thin air”; water gets into basements, earth does not come through walls, air comes through the roof. Argument:

1. Matter is that out of which something is made (later defined as a cause: “that from which something comes to be and is in it”).
2. The thick is made out of the thin, not vice versa: a fat book from thin pages; pie dough in layers.
3. So the thinnest, finest thing is the best guess for the first matter. Student objection: the thick gives you “more to take from.” Reply: ripping pages out is taking parts from a whole; matter is like the parts, the whole is more like the form. Confirming cases: molecule vs. atom vs. elementary particle (the smallest is the best guess, and quarks would be better still if they exist); paragraph, sentence, words, letters (letters are not made of words).

• Greek stoicheia means both elements and letters of the alphabet (Latin likewise): out of letters words, sentences, paragraphs, chapters; the first “out of which” is the letters. Learning Greek begins with the alphabet.
• Exam question he flags as a favorite: why is Anaximenes’ guess better than Thales’? Two answers: more unlimited quantitatively and qualitatively (from Anaximander), and it is the thinnest, the thick being put together from the thin.
• Aside: the cynical Minnesota professor making freshmen write the alphabet “to show you how dumb you are.”

5. Pythagoras and the second kind of cause: form (“this kind of cause is called form”) #

Point: coming from mathematics, where there is no matter, Pythagoras looks in nature for a different cause, form, meaning not shape but order or ratio.

• Biography: from Samos to southern Italy (Greek cities and temples there; Greek grape names, Greco, Aglianico from Hellenico); Plato, disgusted with Athens after Socrates’ death, studied with the Pythagoreans in Italy; Empedocles will be in Sicily.
• Geometry example (drawn): when straight lines intersect, opposite angles are equal. Why? Because the lines are straight. A straight line meeting a straight line makes two right angles or angles equal to two right angles; x + b = two right angles, x + a = two right angles; equals to the same are equal; subtract equals; hence a = b. “All follows from the fact that the lines are straight”; bent lines would not give it. That is the form of the lines as cause.
• Custom shapes thinking: Pythagoras looks for what he is used to, so he differs from the three Milesians.
• His most famous sensible discovery: harmonious sounds come from objects in simple ratios; the octave (do above and do below) from objects in the ratio 2:1. His St. Mary’s demonstration: two strings tuned alike, a wedge at exactly half, whole string and half string give the octave. Other harmonies also have simple ratios.
• The Pythagoreans “got carried away”: simple numerical ratios under everything. He notes (from Heisenberg) Bertrand Russell’s remark that Pythagoras is perhaps the most influential man; certainly so for the mathematical science of nature.
• Raphael’s School of Athens: Plato carries the Timaeus, Aristotle the Nicomachean Ethics; the Timaeus is a mathematical view of the natural world put in the mouth of Timaeus, presented as a Pythagorean, with a geometrical theory of the four elements and no matter. Heisenberg as a young man was inspired by it to seek mathematical symmetry in atomic physics.
• Schrödinger perfected the mathematics of wave mechanics (going back to de Broglie), published the same year as Heisenberg’s quantum mechanics, then showed their equivalence; yet he says the modern atom “consists of no stuff at all,” comparing it to Plato’s Timaeus. Aside: the Moscow communists, whose philosophy is dialectical materialism, were upset that modern science seemed to have no matter.
• Preview of the causes: matter (Milesians); form (Pythagoras); Heraclitus will introduce a third, the mover or maker; Empedocles uses matter, form and mover; Socrates and Plato a fourth; Aristotle brings it all together.
• Pythagorean ethics: justice an even number (“getting even,” “are we even now?”); Aristotle in On the Soul I reports the opinion that the soul is a self-moving number, surely Pythagorean; “I got your number”; his own attraction to five, “likeness is a cause of love.”
• Plato’s Timaeus made Plato a model when the Renaissance turned to mathematical science of nature; Galileo even writes in dialogue form.

6. Heraclitus of Ephesus, the central thinker (“Nature loves to hide”) #

Point: Heraclitus is “the central thinker” by analogy to the centre of a circle, where all the radii, going off in different directions, meet.

• Ephesus: Paul’s epistle, John and the Blessed Mother, the idol-makers’ riot. Political fragment: the Ephesians cast out Hermodorus for being better than they; “they ought to cast themselves out and turn the city over to beardless lads”, a proportion showing their irrationality. Parallel: the Athenian voting to ostracize Aristides, “tired of hearing him called the Just.”
• Lines of influence: Hegel goes back to Heraclitus; Plato was a student of Cratylus, student of Heraclitus (Aristotle in the Metaphysics says Plato held Cratylian views even in old age; Plato’s dialogue Cratylus), and through Plato Aristotle.
• “Nature loves to hide”: first reason, nature is within, and what is within is hidden.

7. Heraclitus on change: the river (“It is not possible to step twice into the same river”) #

Point: by insisting on change Heraclitus fixes the mind on what comes first in our knowledge, since our road runs from the senses into reason.

• Troilus and Cressida: “things in motion sooner catch the eye than what not stirs.” Waving at the airport, blinking lights and sirens, stage performers jumping about, professors walking; conversely, to hide in the bushes, don’t move.
• His argument: if you don’t understand change you don’t understand changing things; then not unchanging things either, since these are known by negation of change; hence “you don’t understand anything.” (“Before this course you understood nothing.”)
• The river fragment and “all things flow, nothing remains”: stepping into the Mississippi today and tomorrow is not the same water; “the situation is fluid.” Cratylus went further: not even once, since the surface water changes before the foot reaches the bottom.
• Negative influence on Plato: if all is changing, how know it? “Understand” suggests something must stand still; and if the way we know must be the way things are, one cannot understand what doesn’t stand still. Some Heracliteans: you can say nothing, only point (“where is Berkeley? in front of that chair”, already moved).
• Max Born (handout p. 2, to be read later): worked with Einstein in Berlin (the Einstein-Born correspondence), with Bohr and Heisenberg on the Copenhagen interpretation, put Heisenberg onto matrix mathematics, Nobel prize, explained what the wave means. His title The Restless Universe and his line that it is strange we have a name for what does not exist, rest: Heraclitus’ universe at the centre of modern physics.

8. The apparent contradiction in change: the fragments (“We step and do not step into the same rivers”) #

Point: Heraclitus’ second famous theme, that change makes something both be and not be; he speaks as if it were a contradiction, whether he really thinks so is left for later.

• DK 49A: we step and do not step into the same rivers (he crossed the Mississippi and the Hudson many times, yet the waters differ); we are and are not (you have changed since last class, lost some hair, yet are the same person).
• DK 6: the sun is new every day; “he’s not the same person I married.”
• DK 126 (with 88, “the most important”): the beginning of an induction (argument from many particulars to the general) that change is between contraries: what is warmed is cold, what cools is warm, what dries is wet, what is moistened is dry (you don’t moisten the ocean), hardened is soft, softened is hard, sickened is healthy, healed is sick. Socrates’ first argument for immortality in the Phaedo likewise starts with such an induction; Aristotle will bring it out; found among Greeks, Chinese, modern scientists.
• The contradiction: we all say one opposite becomes the other (hard becomes soft, young become old); becomes means comes to be; so one opposite is the other. DK 88: the same in us is living and dead, awake and asleep, young and old, each changing into the other. Yet deny it and the sick could never be healthy, “you can’t come to be something you can’t be.”
• DK 57: Hesiod, teacher of most men, did not know day and night, “for they are one”: day becomes night, so they are the same; but then it would be light and not light, dark and not dark.
• DK 84A: changing, it rests. “I find travel restful,” though travel is motion; the boy made to sit still becomes restless.

9. Two ways off the centre: Hegel and Parmenides (“Change is an illusion”) #

Point: from Heraclitus’ apparent contradiction, thinkers depart in opposite directions.

• Hegel (a follower of Descartes) and Marx after him, Lenin after Marx: there is a contradiction in change; Lenin defines dialectics as the study of the contradiction within the very essence of things (quote promised later). Hegel used Heraclitus to refute all the rest.
• Parmenides: it is impossible for day to be night, the sleeping to be awake, the hard to be soft; if that is what change involves, there is no such thing; change is an illusion. He is the first to make explicit the axiom of contradiction, “the axioms of being and non-being”: something cannot both be and not be, and something must either be or not be. Aristotle in “the fourth book of wisdom” [ed.: Metaphysics IV] adds “at the same time, in the same way.” Class ends here: “Change is an illusion. Great question.”

His words #

• “influenced by air”: Anaximenes’ guess governed by breath as life.
• psuche: soul, from the Greek for breath or air.
• spiritus: Latin, from breath; carried over to immaterial substances.
• “unlimited in quantity / in quality”: two senses of Anaximander’s unlimited.
• “concrete”: his word for air against the “negative notion” of the unlimited.
• “the thick out of the thin”: rule for finding first matter.
• matter: “that from which something comes to be and is in it.”
• stoicheia: elements, also letters of the alphabet.
• “form”: not shape but order, ratio; second kind of cause.
• “mover or maker”: third kind of cause (to come with Heraclitus).
• “central thinker”: Heraclitus, by analogy to the centre of a circle.
• induction: argument from many particulars to the general.
• “change is between contraries” / “change is by contraries”.
• “becomes means comes to be”.
• “axioms of being and non-being”: cannot both be and not be; must either be or not be [ed.: principle of non-contradiction and excluded middle].
• “fourth book of wisdom” [ed.: Metaphysics IV].

Texts #

Read in class

• Anaximenes fragment, soul as air / breath and air surround the world (handout p. 12, verified; DHB Vol I p. 125, verified).
• Heraclitus DK 49A, DK 6, DK 126, DK 88, DK 57, DK 84A (quoted and discussed); the river fragment and “all things flow”; “Nature loves to hide”; the Hermodorus fragment.
• Shakespeare, The Tempest (spirits melted into thin air); Timon of Athens (Common Mother); Troilus and Cressida (things in motion catch the eye); Lear’s “thick rotundity of the earth” (play not named). Mentioned
• Homer, Iliad battle scenes; Dante, Divine Comedy; Scripture on God breathing a living soul.
• Plato, Timaeus, Cratylus, Phaedo (first immortality argument).
• Aristotle, On the Soul I (soul as self-moving number); Metaphysics (Plato and the Cratylians; “fourth book” on the axiom).
• Raphael, School of Athens; Heisenberg on the Timaeus and on Russell; Schrödinger on the atom having no stuff; Max Born, The Restless Universe (handout p. 2, promised); Lenin on dialectics (quote promised); Galileo’s dialogues; St. Paul, Ephesians and Corinthians.

His questions #

• Could Anaximenes have been influenced by Anaximander to guess air rather than water? Yes: air is more unlimited than water both in quantity (everywhere, up on all sides) and in quality (transparent, not definitely wet or cool).
• Which is more unlimited in a quantitative sense, water or air? Air, which seems to be everywhere.
• Is the first matter the thickest of things or the thinnest? The thinnest, since the thick is made out of the thin.
• Is matter like the whole or like the parts? Like the parts; the whole is more like the form.
• Whose guess is best: molecule, atom, or elementary particle? Sentence, words, or letters? The smallest, since it makes up the rest.
• What kind of cause do you look for in geometry? Form, as order or ratio: opposite angles are equal because the lines are straight.
• Why does nature love to hide? Because nature is within, and what is within is hidden.
• If I step into the Mississippi today and tomorrow, is it the same river? Not the same water; so we step and do not step into the same river.
• What is it that becomes warm, cools, dries, is moistened, hardened, softened, sick, healthy? Its contrary; inductively, change is between contraries.
• Does Heraclitus really think one opposite is the other? Left open (“that’s another question, we’ll come back to that”).
• Would justice be an even or an odd number? Even: getting even, equality.