Empedocles: The Four Elements, Numerical Ratios, and Change as Change of Place

Orientation #

He recalls last time: Thales, Anaximander, Anaximenes (Miletus), Pythagoras (Samos, then southern Italy), Heraclitus (Ephesus), all around 500 BC (Thales earlier, c. 600 BC, predicting the eclipse of 585 BC); “we went through all the fragments of Heraclitus” and “the natural inclination of our mind to unity and simplicity” in the moderns (prev. lecture). Heraclitus’ “wise, listening not to me but to reason, to agree that all things are one” touched that inclination; Empedocles is “a kind of break” because he gives up the one first matter. Fragments he will “come back to again” and Anaxagoras are pointed to as coming. The previous class traced the drive to unity and simplicity from the Greeks through modern physics, and the next continues with Empedocles’ Love and Strife, Anaxagoras’ Mind, and Empedocles’ theory of cognition.

The class, in order #

1. Opening and where Empedocles stands (“give up the attempt to find one first matter”) #

Point: Empedocles breaks with the monists; the class will try to see his reason for giving up the one matter, even though reason naturally looks for one.

• Before the prayer he quotes Aristotle’s “book on mistakes” (Sophistical Refutations): the deception in question “deceives even the wise,” which “could hardly be stronger.”
• Empedocles is in Sicily (Porto Empedocle). The legend that he jumped into Etna to claim divinity (the “crazy poets” like Shelley wrote of it; compare Oedipus disappearing at the end of Oedipus at Colonus) vs. the local account: he built a tower to observe the volcano, as volcanologists still do, and the tower collapsed; remains of the tower have been dug up.

2. Verse is not poetry (“clothed his philosophy in the garment”) #

Point: Empedocles wrote in verse and used the names of gods, but that does not make him a poet.

• Poets had the authority then that scientists have now: Aristotle notes some will not proceed unless you can quote a poet; poets were seen as inspired by the gods. Parallel: the “social sciences” put on the air of science (hypotheses, tests), a book called Scientific Philosophy.
• Others who put philosophy in verse: Lucretius; Boethius’ Consolation, alternating prosa and verse.
• Distinction: verse/meter vs. a poem, which is “a likeness of something,” a fiction. Boundary cases: Thomas’ Adoro te devote (meter, rhyme, still a prayer); the Our Father possibly in verse in the original (easier to remember); Shakespeare’s exhortation on reason, in meter but “really an exhortation.” “We use the word poem sometimes too lightly for anything in verse.”

3. The four roots, DK 6 (“Here first the four roots of all things”) #

Point: Empedocles takes as first matters the four that had each been taken singly before.

• The gods decoded with the class: bright Zeus = fire; life-giving Hera = air; Hades (god of the underworld) = earth; Nestis “who moistens with tears the springs of mortals” = water.
• Term: from Empedocles on, the pluralists; those before, the monists.
• Fragment on method: man, “having seen only a part of life,” boasts of having seen the whole. So Thales (water), the poets (Mother Earth), Anaximenes (air), Heraclitus (fire) each saw part of the truth; the whole truth is all four as beginnings.

4. Why give up one matter: the either-or argument (“either that matter has some definite quality”) #

Point: as with Thales, descend from the general; the most general question is why abandon one matter, and the reason can only be gathered from what he says later.

1. If there is one first matter, either it has some definite quality or it has none.
2. If it has a definite quality, everything would have that quality (student’s answer): if sugar were the beginning of all things, everything would be sweet; but we live in a world of contraries (sweet/bitter, hard/soft, wet/dry). Thales, Anaximander, Anaximenes already saw this difficulty; the move from earth to water to the unlimited or air is a move toward a matter with no definite quality.
3. If it has no qualities, a greater difficulty: not just contrary qualities but any quality is unexplained, since “you can’t get something out of nothing” (as Empedocles will say). Kool-Aid: you must add to colorless, tasteless water something that has color and taste; water added to water stays colorless. Wine sauce or salad dressing: a new taste from combining, but the ingredients must have some taste.
4. Conclusion (first step): there is more than one first matter, and each must have some quality. “Reasonable,” he says, “not necessarily the truth.”

5. Second step: the many matters are distinguished by opposites (“makes sense to divide human beings”) #

Point: a division must be by opposites, and the opposites that yield his four are hot/cold and wet/dry.

• Dividing humans into male and good fails: where do you put Christ, or St. Paul? The same thing can be both. Male/female, good/bad, young/old work; young/male does not.
• Crisscross the two pairs (“the rule of two and three”): fire hot and dry; water cold and wet; earth cold and dry (the cellar is cooler than the house; take the water out of dirt and it is dust); air hot and wet, thinking of steam (“a little forced”).
• Fits the way up and way down: earth, water, air, fire (sun, moon, stars). Air shares hot with fire and wet with water: “something in common with its two neighbors, but not identical.”
• “We don’t know how far Empedocles got”; he was undoubtedly influenced by his predecessors’ choices.

6. Why these opposites and not others (“hot and cold are causes of hard and soft”) #

Point: hot/cold and wet/dry are the most basic sensible contraries, because the others are their effects.

• Student: hot and the others “signify some kind of activity.”
• Hot and cold make butter hard or soft. Wet and dry make the sponge soft or hard as a rock, the loaf of bread crumbly dry or soft again when moistened.
• Colors: white bread in the toaster goes red, then black; metal goes red hot, white hot; a wet garment looks darker; his own hair, wet down in the morning is darker, drying to gray or white through the day. Cooking changes flavor (do not overcook the steak).
• Conclusion: if there is more than one matter, they must be distinguished by opposites; the senses know no opposites more basic than these; therefore these four. “It doesn’t seem like there’s any way to get around that.”
• The theory lasted over 2,000 years as the standard one, to Shakespeare (Cleopatra: “I am fire and air, and my baser elements I give to the earth”; sonnets on the agile elements fire and air and the plodding water and earth). Getting beyond it needed “a very roundabout way with some kind of subtle experiment” suggesting something before water, like hydrogen. “The longest lasting chemical theory in history. Doesn’t mean it’s true.”
• DK 38 touches these two pairs, less clearly than DK 6.

7. Compounds as ratios, DK 96 and the next fragment (“bone equals what W2F4”) #

Point: Empedocles is the first to say compounds like flesh, blood, bones are the elements in different numerical ratios, combining his predecessors with Pythagoras.

• DK 96: earth in its melting pots receives two parts of Nestis (water) and four of Hephaestus (fire); white bones, “by the gluing of harmony.” Chemical formula: bone = W2F4. More of the dry element (fire) than the wet: explains why bone is the driest part of the body (“bone dry”).
• The next fragment: earth, the goddess of love, Hephaestus, water and upper air “in about equal measure,” a little more or less; from these blood and flesh. Different ratio, more of the moist element. (He corrects the translation: “from these,” not “the.”)
• Parallel with modern chemistry: H2O, C6H12O6; carbon dioxide vs. carbon monoxide differ in ratio, and one kills you.
• Gregory the Great: boasting is the first species of pride. Seeing a part and boasting of the whole explains much disagreement: Marx (economic mode of production explains industry, social structure, government, ideas); Freud (sex explains everything, even why you philosophize). Each likely saw part. Empedocles follows his own dictum, gathering the scattered parts; what remains with us: more than one kind of matter, combining in numerical ratios.

8. The group DK 8, 9, 11, 12, 15: change of place the only change (“change of place is the only kind of change”) #

Point: for Empedocles (explicitly, and Anaxagoras too) every apparent inner change is a disguised change of place.

• Contrast: Aristotle’s nature as cause of many kinds of change: place, growth, alteration of quality, and a fortiori generation and death.
• Same tendency in modern science, which begins with change of place: Galileo (free fall), Kepler (planets), Newton (uniting them); then the attempt to reduce other changes to it. Challenged with quantum theory in the 20th century. “It’s not unique to the Greeks.”
• DK 8: no birth of any mortal thing, no end in death, only mixing and exchange of what has been mixed; birth is a name given by ignorant men.
• DK 9: when mixed in the shape of men, beasts, bushes, birds, men say it is born; separated, “wretched death.” “They do not name these things rightly, but I also follow the custom.” Compare the scientist who says “the sun rose at six” while holding the earth turns.
• Berquist’s class: cigars passed out when it is “born,” a black armband when it “dies”: ridiculous, since the students were only mixed in one combination and then separated into other rooms. So one should not go to the funeral house and say “so and so has died” but “I see a new mixture.”
• Bertrand Russell: takes us as a mixture of atoms and molecules, yet spends his last years at conferences against atomic war, as if it were more than a rearrangement of molecules. “Something in the back of his mind” says it is more, but he cannot understand how.

9. DK 11, 12, 15: fools and far-reaching minds (“you can’t get something out of nothing”) #

Point: the reason nothing really comes to be or perishes is that something cannot come from nothing or be cut into nothing.

• DK 11: fools, with no far-reaching minds, think what was not comes to be, or that anything is destroyed utterly.
• DK 12: “impossible that anything comes to be from what in no way is.” Basement dry yesterday, flooded today: not something from nothing; the water changed place from soil or clouds through a crack you could not trace.
• The other side, clearer in Anaxagoras: “what is cannot cease to be by being cut,” since you cut a thing into what it is made of; cut into nothing means made of nothing. “It will always be there where anyone ever puts it.” Log on the fire: not annihilated; the ashes under the grate and the specks in the sky are what was in it. Magician: the rabbit was up his sleeve; a “magic show of the natural world” is ridiculous.
• DK 15: a wise man would not guess that mortals are only while they live and are nothing before being fastened together and after being unfastened.
• Yet if Empedocles’ wife or son died, or a baby were born, he would react as we all do, knowing it is more than a rearrangement; “he can’t quite understand how this is possible.”
• Distinction: change of place, an outward change, vs. inward change of quality or substance. Aristotle’s main contribution: to understand how inward change is possible, tied to “the ability that is matter, the potency that is matter.” “The difficulty is in it, not in us”; still very hard to understand.

10. Quantum theory and potency (“a quantitative version of the potency”) #

Point: the place where “only change of place” broke down is where Aristotle’s potency reappeared.

• The atom first imagined as a miniature solar system; but an electron going from orbit to orbit should emit energy continuously, and instead it jumps: the electron is not moving from place to place; the change is more inward.
• Heisenberg, who saw most of all how radical quantum theory was: it introduced a quantitative version of Aristotle’s potency; nearly every lecture of his Gifford lectures talks of it; it first appeared, he says, in the 1924 paper of Bohr, Kramers and Slater as “something entirely new.”
• De Broglie (father of wave mechanics): a 19th-century physicist would say the colors were all inside the white light and the prism separated them (Empedocles’ way: separation, a change of place); today they exist in the white light “only as a possibility.”
• Aside: his friend Warren Murray asked Heisenberg whether he was Platonist or Aristotelian; as a mathematical physicist (Plato’s Timaeus) “more a Platonist,” but always coming back to Aristotle and potency.

11. How other changes get reduced to change of place (“changing its shape on the TV screen”) #

Point: without potency, one is almost forced to explain any apparent change as a change of place too fine to follow.

• Change of shape: the Michigan marching band at halftime forms a boat (Anchors Aweigh), then the state of Michigan; “Perkos” claims a new kind of change; “Fool, put your glasses on”: 150 changes of place.
• Change of quality: sugar stirred into Berquist’s bitter coffee while he is out; the coffee is still bitter and the sugar still sweet, too small to see; what he tastes is sugar that changed place.
• Water on the stove, cool then warm, in the same place: “where did that heat come from?” If there was no heat in the water, something from nothing. Einstein, The Evolution of Physics: the caloric theory, a substance hot by nature flowing from the hot body into the cold one, “just like the sugar.” Later, the kinetic theory: molecules vibrating faster and faster; hot is the gross appearance of hyperactive molecules, eventually bubbling and shooting out.
• The joke he tells students: if this is true, teaching must be a change of place from his mind into theirs, so the more he teaches the dumber he gets; the theory “doesn’t explain even teaching.” His answer: he cannot get dumber, they get smarter because they are able to know and the ability is actualized. “What is this ability? Kind of an odd thing to try to understand.”
• Change of place is the change most known to us; even Aristotle, descending from change in general, studies change of place first. But without ability or potency no other change seems possible; all one can do is mix and separate things that always were and will be, “the thinking of the early Greeks and of the early modern scientists.” That is why he takes the five fragments together.

His words #

• “book on mistakes”: Sophistical Refutations.
• monists vs. pluralists: one first matter vs. more than one; “many” means “more than one.”
• roots: Empedocles’ name for the four first matters.
• either-or syllogism: eliminate both alternatives (matter with a quality, matter with none).
• “the rule of two and three”: crisscrossing two pairs of opposites to yield four.
• the way up and the way down: the ordering earth, water, air, fire (from Heraclitus, prev. lecture).
• “W2F4”: his formula for Empedocles’ bone.
• change of place vs. inward change: outward change vs. change of quality or substance, coming into or going out of existence.
• far-reaching mind: Empedocles’ phrase for tracing where matter went, opposed to the “fool.”
• ability [ed.: potency]: “the ability that is matter”; Aristotle’s answer to how inward change is possible.
• caloric: the substance hot by nature in the early modern theory of heat.

Texts #

Read in class

• Empedocles DK 6 (four roots: Zeus, Hera, Hades, Nestis)
• Empedocles DK 96 (bone) and the fragment following it (blood and flesh)
• Empedocles DK 8, 9, 11, 12, 15 (no birth or death; fools; nothing from what is not; wise man)
• Empedocles, fragment on method: men see a part of life and boast of having seen the whole
• Handout: Note for Book One, Reading Nine, p. 8 (verified source)

Mentioned

• Empedocles DK 38
• Aristotle, Sophistical Refutations (“deceives even the wise”)
• Aristotle on those who will not proceed without quoting a poet (no locus given)
• Anaxagoras, fragment: what is cannot cease to be by being cut (locus not given)
• Heraclitus, “wise, listening not to me but to reason…” (prev. lecture)
• Lucretius; Boethius, Consolation of Philosophy; Thomas, Adoro te devote; Shakespeare, Oedipus at Colonus (Sophocles), Antony and Cleopatra (inferred, “I am fire and air”), sonnets on the elements
• Plato, Timaeus
• Heisenberg, Gifford lectures; Bohr, Kramers, Slater 1924 paper; de Broglie on the prism; Einstein, The Evolution of Physics
• Gregory the Great on boasting as the first species of pride
• DHB Vol III, The School of Aristotle, p. 382 (verified source)

His questions #

• Why would Empedocles give up the attempt to find one first matter? Either the one matter has a quality (then everything would have it, but the world is of contraries) or none (then no quality could arise, something from nothing); so more than one matter, each with a quality.
• What is the difficulty in saying the first matter has some definite quality? Everything would have to have that quality (sugar and sweetness).
• Would it make sense to divide human beings into male and good? No: Christ or St. Paul would fit both; divide by opposites (male/female, good/bad).
• By what opposites would you distinguish earth, air, fire and water? Hot and cold, wet and dry, crisscrossed: fire hot-dry, water cold-wet, earth cold-dry, air hot-wet.
• Is there any reason these opposites rather than hard/soft, black/white, sweet/bitter? Hot/cold and wet/dry cause hardness, color and flavor (butter, sponge, bread, toaster, hair); the senses know none more basic.
• Hephaestus was the god of what? Fire; so bone is two parts water, four parts fire.
• Where did that heat in the water come from, if there was no heat in it? On the “change of place only” view it must have come from somewhere (caloric, or faster molecules); on Aristotle’s, from the water’s ability. He leaves how to understand that ability as very hard.
• What’s going on when he teaches, if all change is change of place? Not a transfer making him dumber; the students’ ability to know is actualized.