Empedocles' Love and Hate, Chance vs. Mind, and Anaxagoras on Matter and the Continuous

Orientation #

He continues from “the next two fragments” of Empedocles, treating fragments he refers to by handout page (pages four to six, with Democritus on page nine and Anaxagoras DK 12 on page eight); the verified sources place the readings in Natural Fragments of the First Philosophers pp. 32–33 and the Note for Book One, Reading Nine. He says Anaxagoras’s great fragment DK 12 on Mind will be looked at “later on”, and that “we’ll go back to Aristotle” for his long critique with eight arguments against Anaxagoras on matter. The previous class treated Empedocles’s four roots and reduction of change to mixture and separation; the next continues Anaxagoras on quantity and Mind.

The class, in order #

1. Does the empty exist? (“Nor does anything of the whole become empty”) #

The point: Empedocles denies the empty; Democritus (DK 9, handout last page) affirms atoms and the empty as what truly exists (while denying sense qualities “like the modern philosopher”). A famous question with two answers, yes or no.

• Empedocles’s reason (as he reconstructs it): the empty is really nothing; to say the empty exists is to say nothing is something. Test: does empty space have length, width, depth? If something there has them, it is not empty; if nothing is there, nothing has length, width, depth, “which is absurd.” So affirming the empty involves a contradiction.
• Democritus’s motive, like Heraclitus: admit an apparent contradiction (“what is not is”) to save the reality of change. His argument: without the empty the universe is packed completely tight, like an overfull suitcase you sit on to close; things could not move at all, “like fish in ice.”
• Aristotle follows Empedocles: the empty does not exist; his answer to Democritus is that motion can be circular without the empty. Beer can full of beer: the beer can still rotate, since as one part comes in another leaves at the same time.
• Early modern scientists followed Democritus (the word atom borrowed from him; empty space between planets, galaxies, even inside the atom) because they thought motion required it. With Einstein in the 20th century a tendency back to Empedocles and Aristotle: fields everywhere (magnetic, gravitational), and these are “something real,” not a mathematical device.

2. A third kind of cause: love and hate (“contrary effects have contrary causes”) #

The point: DK 17, 21, 23 expand on mixture and separation but introduce the mover.

1. There are contrary effects in the world: earth, air, fire, water coming together and separating.
2. Contrary effects have contrary causes, “a highly probable statement.” Butter becoming hard and becoming soft: you would look for contrary causes, and eventually find them to be the hot and the cold (refrigerator or backyard vs. warm room or stove).
3. Like effects have like causes. Among human beings, love brings people together, hate separates them.
4. Conclusion: there must be something like love and hate in the natural world, a cosmic love and cosmic hate, named after gods and goddesses (Aphrodite for love). Our less poetic version: force of attraction and force of repulsion between pieces of metal, “basically the same idea.”

• The cycle: love brings them together, hate separates them, and this goes on forever. He reads: “I shall tell something double… at one time it grew from the many to be one only… a double birth of mortals, a double death… in no place do these things stop taking turns forever.”
• On “truly learning causes the mind to grow”: he asks whether Empedocles has any change besides change of place for the mind to grow; a student starts to answer, and he lets it drop as the fragment goes on describing the same coming together and separating.
• Reads: “look at her with your mind… calling her by the name of Joy or Aphrodite.”
• Tally: Empedocles now has three kinds of cause: matter (four in kind: earth, air, fire, water), form (the ratio from Pythagoras), and the mover (what Heraclitus was reaching for with “war is the father of all things” and in choosing fire over a more passive matter), which is love and hate.
• Aristotle and Thomas note he is “a little bit along the Manichean line”: a good and a bad principle. But an interesting fragment Aristotle uses for several reasons says there is no hate in gods, which will raise contradictions with his other positions (page six).

3. Good order in animals: chance or mind? (“all these crazy combinations”) #

The point: the “fundamental dichotomy” between Empedocles and Anaxagoras on the cause of the good arrangement of parts in animals and plants (biting teeth in front, chewing teeth in back; stomach, arms, legs in the right places; the cat’s and even the tree’s parts).

• Anaxagoras (who brought philosophy to Athens, friend of Pericles, had to leave on a charge of impiety, perhaps a way of getting at Pericles): he saw the likeness between the order in the parts of animals and plants and the order in the parts of a chair, a book, a building, made by man. The cause of order in artificial things is human mind. Like effects have like causes. So a like cause of the order in natural things: another, greater mind, greater because responsible for far more intricate order. DK 12’s last sentence: “Every mind is similar, both the greater and the lesser.” He calls it “the marvelous reasoning there of Anaxagoras.” Socrates in the Phaedo was very impressed, though he thought Anaxagoras could have developed its consequences more.
• Empedocles explains the order with only mindless causes, hence by chance. Mindless love bringing things together would produce any old combination: he reads “foreheads without necks… bare arms bereft of shoulders… eyes wandered in need of foreheads”; “when God was more mixed with God” (i.e. earth, air, fire, water, named as gods) “these things fell together in whatever way”; creatures with two faces, cattle with faces of men, men with heads of oxen (mermaid, centaur). Eyes might come out in my stomach or under my feet.
• Aristotle supplies the rest: all the crazy combinations perished because they could not survive (a mermaid with human lungs cannot live in the sea, and without legs cannot hunt on shore, “even though in Columbus’s voyage there’s report of having seen mermaids”). Love keeps bringing things together; eventually, one in a million or a billion, it put them together the good way, and that one survived. “A remarkable imagination”: the good order we see everywhere is not basically the way nature is. Warren Murray described this to a modern biologist, who said, “Oh, that’s my theory.”
• Heraclitus, thinking of his mindless fire and the other mindless causes: the cosmos is “a heap piled up at random,” like the remains of the World Trade Center, all order gone. Anaxagoras is “much more reasonable”; Aristotle: Anaxagoras seemed “like a sober man among drunk men” (a student asks who said that: Aristotle).
• Aside: a bumper sticker seen that day, “Surgeon General warning: television may be dangerous to your literacy.”

4. Empedocles on how we know (“By earth we see earth”) #

The point: the last two fragments touch how we know. “By earth we see earth, by water water… love by love, and hate by hate”: we know them because we have them in us.

• Is it true that the thing known must be in the knower before it is known? Could I remember you without having your shape and color inside me in some sense? There seems to be truth in it.
• Two difficulties. (a) Aristotle: there is no hate in God, since hate causes corruption and God is eternal (a good insight; St. John says God is love). But on this fragment God then would not know hate, and we would know something God does not, “laughable to all the Greeks.” (b) More basic: there is metal in the chair; why doesn’t the chair know metal? Wood in the wooden chair, why doesn’t it know wood?
• So: in what way is the thing known in the knower? Not as rows of little bone or flesh statues in my head, not as Michelangelo puts your shape into wood or marble; my eye does not change its shape to yours. Aristotle and later thinkers: it is in there immaterially. I receive the shapes and colors of others without losing my own; they remain the shape of another, so knowing is spoken of as receiving the form of another as other. Boundary case: if reception were material, the Pietà would know the person of whom it is the statue; it does not, but I do.
• The higher the knowing, the more immaterial; reason is completely immaterial. This belongs to the study of the soul. Empedocles sees some truth but cannot understand the way it is in there; he still thinks of thought as material, whereas Anaxagoras first starts to think of mind as immaterial, followed by Plato and Aristotle.

5. Thought as blood (“the blood around the heart in men is thought”) #

The point: if thought is material and we are made of bone, flesh and blood, blood is the most reasonable guess.

• Reason 1: thought seems a kind of movement (“discourse,” from running, as in Shakespeare); blood circulates, flesh and bone are stationary.
• Reason 2: thought seems subtle and penetrating (a good mind has “insight,” penetrates). Handkerchief test: dry bone or dry flesh would not go through; blood would. So thought is the most penetrating, blood. Anaxagoras will call mind the thinnest of all things.
• Reads: “nourished in the sea of blood, which goes in two directions… the blood around the heart in men is thought.” Same thinking as modern biologists who identify thought with brain waves or electrons: whatever is the finest matter you can think of.
• Aside: his sophomore high school biology teacher Mr. Gado, who called the class “boneheads” (the worst guess); stories of his brutality; where he met Warren Murray, who knew a lot of science. “So that’s the great Empedocles… but not the greatest, Anaxagoras.”

6. Turning to Anaxagoras (“Anaxagoras is trying to understand ability”) #

The point: Anaxagoras will be taken first on matter, later on the mover.

• Aristotle is sometimes hard on Anaxagoras about matter, sometimes says Empedocles is better there, other times “if you listen to what Anaxagoras is trying to say.” Later: Aristotle’s long critique, recounting the whole argument and giving eight arguments against his position on matter. Anaxagoras’s position reveals the difficulties of those who cannot quite understand ability [ed.: potency]: “everything is inside of everything in infinitely small pieces.”
• His way of speaking came back in the mid-20th century study of elementary particles, with the same difficulties.
• Student: did Aristotle know him? He was probably dead by then; came to Athens under Pericles. The impiety charge: saying the sun is a stone on fire (the sun being Apollo). Likely source: a large meteor that fell in northern Greece; falling stars are meteors, rocky things that burn in the atmosphere, occasionally reaching the ground still burning (one in the southwestern United States, passed down among the Indians, later confirmed from the air).
• Aristotle did not think the sun was fire: it would have burned out long ago; the amount of energy reaching us at 93 million miles, a tiny fraction of what it emits, century after century, undiminished, is incredible; a pupil of Heisenberg, Weizsäcker, is supposed to explain why it can go on so long. Even the great fire of London ended; New York is still smoking. So the sun and stars must be something quite different from ordinary fire.

7. Everything comes to be from everything (“How could hair come from what is not hair”) #

The point: reconstructing Anaxagoras’s argument on matter.

1. Inductive observation: start anywhere and eventually get everything else. Grass eaten by the cow gives more cow (not out of nothing); Berquist eats steak, more man out of grass; Berquist is a Christian, so given to the lions, more lion; the lion is food for worms; the bird gets the worm; the cat gets the bird; the cat pushes up daisies. So everything eventually comes to be from everything.
2. Common Greek thought: you can’t get something out of nothing; “you can’t get blood out of a turnip.” DK 10: “How could hair come from what is not hair, and flesh from what is not flesh?”
3. So there must already be a bit of cow, man, lion, worm, bird, cat, daisies in the grass. Before laughing: 20th-century elementary particle physics found that from any particle you eventually get all the rest, hence the well-known formula “every elementary particle is composed of all the rest” (as water is composed of hydrogen and oxygen), the same conclusion.
4. Added observation (seen with Anaximander): things keep coming to be forever, every spring. So there must be an infinity of things in the original grass; to fit an infinity in a finite blade they must be infinitely small, like the modern mathematician’s line composed of an infinity of points.

• DK 1: “All things were together, unlimited in number and in smallness” (unlimited or infinite, in multitude and in smallness); “nothing was clear because of smallness.” He is trying to get at everything being in there in ability by making them infinitely small, but still makes them actually there; he does not have the idea of ability. A throwback to Anaximenes and Anaximander in the air and ether and their unlimited character. Each particle containing all the rest, and each of those all the rest, smaller and smaller.
• The next fragment: “many things of all kinds… the seeds of all things”; DK 4: nothing distinct from another because so small.

8. No smallest of the small (“what is cannot cease to be by being cut”) #

The point: DK 3 states the infinite divisibility of the continuous, and he shows why a line cannot be composed of points.

• Two definitions of the continuous. Logic (Aristotle, Categories): quantity divided into discrete (number) and continuous (line, surface, body, sometimes time and place), by their parts: in discrete quantity the parts meet nowhere (do the three and four in seven have a boundary? no); in continuous quantity they meet (parts of a line at a point, of a circle at a line, of the chalk at a surface). Natural philosophy (Natural Hearing Book Six): the continuous is that which is divisible forever. Number is not: the abstract one cannot be divided, it is simpler than a point; the modern mathematician who divides the one in arithmetic is thinking of the continuous.
• Why divisible forever: cutting a line gives two shorter lines (cuttable again), or nothing (impossible), or points. The only alternative to test: is a line composed of points? Either-or syllogism. To compose a line the points must touch. Four ways two things touch: part to part (two overlapping circles), part to whole and vice versa (one circle inside the other), whole to whole (coinciding), edge to edge (circles touching at a point; the edge is not a part). Points have no parts (Euclid’s definition; the end of a line has no length), so the first two are out; a point cannot be distinguished from its edge (that would make it a little circle), so the fourth is out. Points can touch only by coinciding, and coinciding points have no more length than one point, which is none; so even an infinity of points gives no length. Hence dividing a line gives two shorter lines, and there is “no smallest of the small, no shortest of the short.” The same holds for the square (its side shorter and shorter) and the circle (rotating a line about an endpoint). This contradicts what modern mathematicians say in grade school and high school.
• The Natural Hearing Book Six argument that time and distance are both divisible forever: the faster body covers the same distance in less time; in that less time the slower covers less distance; in that lesser distance the faster takes less time; alternating shows both divisible forever.
• Anaxagoras sees something of this, though “to be complete” one must add that you cannot cut into points.
• “Something greater than the great”: how does no smallest of the small give no greatest of the great? As you divide the line, the number of lines gets greater. Number arises from the division of the continuous; strictly, one is not a number (number is a multitude composed of units): one line is not yet a number, divide and you have the first number, two, divide again, three. If you never reach an indivisible line, you never reach a greatest number.

His words #

• the empty; Empedocles denies it, Democritus and the early modern scientists affirm it (empty space); Einstein’s fields go back to denying it [ed.: the void]
• contrary effects have contrary causes; a “highly probable statement”
• like effects have like causes; a famous probable proposition
• three kinds of cause: matter, form (ratio), the mover(s), love and hate
• “along the Manichean line”: a good and a bad principle
• the thing known must be in the knower before it can be known
• immaterial reception; receiving the form of another as other
• discourse; from a word for running, so thought as motion
• ability; what Anaxagoras is trying to reach with infinitely small pieces [ed.: potency]
• unlimited; his rendering, “infinite you could use too” (the Latin word), in number (multitude) and in smallness
• discrete vs. continuous quantity; parts not meeting vs. meeting
• the continuous is that which is divisible forever (Natural Hearing [ed.: Physics] Book Six)
• either-or syllogism [ed.: disjunctive syllogism]
• four ways of touching: part to part, part to whole, whole to whole, edge to edge
• number is a multitude composed of units; one is not a number

Texts #

Read in class

• Empedocles, fragments on the empty (“Nor does anything of the whole become empty or overfull”), DK 17, 21, 23 (love and hate), the fragments on crazy combinations (handout page six), “By earth we see earth,” and “the blood around the heart in men is thought”
• Anaxagoras, DK 10, DK 1, DK 3, DK 4, and the next fragment on “the seeds of all things”
• Handout: Natural Fragments of the First Philosophers, pp. 32–33 (verified); Note for Book One, Reading Nine, p. 1 (verified)

Mentioned

• Democritus, DK 9 (atoms and the empty; sense qualities denied)
• Anaxagoras, DK 12 (Mind; “every mind is similar, both the greater and the lesser”)
• Empedocles, fragment that there is no hate in gods (used by Aristotle)
• Heraclitus: “war is the father of all things”; the cosmos “a heap piled up at random”
• Aristotle, Categories (discrete and continuous quantity by their parts) (inferred)
• Aristotle, Natural Hearing Book Six (the continuous; faster and slower bodies)
• Aristotle’s critique of Anaxagoras with eight arguments (locus not stated)
• Plato, Phaedo (Socrates on Anaxagoras)
• St. John: “God is love”
• Euclid’s definition of the point
• DHB Vol I pp. 145–146; DHB Vol III p. 375 (verified)

His questions #

• Does the empty exist? Two answers: Democritus yes, Empedocles (and Aristotle, and Einstein’s fields) no, because it would make nothing something.
• Does empty space have length, width and depth? If something there has them it is not empty; if nothing is there, nothing has them, which is absurd.
• Do contrary effects have the same cause or contrary causes? Contrary causes (student: “Contrary”); e.g. hot and cold for butter hardening and softening.
• What brings people together and what separates them? Love and hate; so a cosmic love and hate for earth, air, fire and water.
• What is the cause of the good order of parts in animals and plants? Anaxagoras: a greater mind, like the human mind that orders artificial things; Empedocles: chance, the bad combinations perishing.
• Could I remember you if I didn’t have your color and shape inside me? No; so the thing known is in the knower, but immaterially, not as a statue.
• There’s metal in the chair; why isn’t the chair then knowing metal? Because the known is in the knower in a way other than something is in matter.
• Is thought bone, flesh or blood? Blood, since thought is a movement and the most subtle and penetrating.
• Is a line composed of points? No: points can touch only by coinciding, and coinciding points have no length.
• How can you reason from no smallest of the small to no greatest of the great? Dividing the continuous forever makes the number of parts grow forever; number arises from division of the continuous.