Anaxagoras: Everything in Everything, All Things Forever Equal, and Q&A on Good and Evil

Orientation #

He refers back to “the example I was giving you last time,” the conservation of energy (prev. lecture), and to having said before that Anaxagoras’ Mind caught Socrates’ attention. He announces next time: the “great fragment on the mind,” DK 12, and a brief comparison of Heraclitus, Empedocles and Anaxagoras on the mover using “the moderns on the mover” in the secondary reading. The previous class treated Empedocles’ Love and Strife and his materialist cognition, the next takes up DK 12 on Nous and its apparent contradiction.

The class, in order #

1. Great and small are toward something (“each thing to itself is both great and small”) #

Point: the end of the fragment is confused, because great and small belong to the category pros ti (toward something), not to quantity, which is absolute in itself.

• Aristotle’s Categories example: a hundred people at dinner in my house is a big dinner party; a hundred people at the World Series is a tiny crowd; “the same number, absolutely speaking.”
• A seven-foot man is tall compared to us, small compared to a redwood.
• Betelgeuse: as a beginning astronomy student he was awed that the whole solar system fits inside it; now “it’s all relative” (think of the molecules in a glass of water). Same for the thimbleful of star weighing a ton; same for his children impressed that Daddy can count to 100, then to 1,000, then not impressed at all.
• Homo sapiens (“the wise ape”) vs Pythagoras/Socrates’ “God alone is wise”: Heraclitus’ proportion, as ape is to man so man is to God, and as child to man so man to God. Man is wise compared to the ape, not compared to God.
• Aside opening the recording: number said of the Trinity means something quite different, since there is nothing continuous in God.

2. Quantity in pure math vs quantity of natural things (“there are limits in the quantities of natural things”) #

Point: the fragment reveals an understanding of the continuous (and maybe of its connection to number), but Aristotle will later show, against Anaxagoras, a difference he calls the second difference between quantity in math and in natural philosophy.

1. First difference: math considers quantity in separation from matter and motion, from all natural bodies; nothing prevents dividing forever.
2. Because Aristotle saw the first difference, he was open to discovering the second: there can be limits in the quantity of natural things due to their natures, not foreseeable from pure math. To be seen in the second, third and fourth arguments against Anaxagoras.

3. DK 6 and DK 8: nothing cut off with an axe (“neither warm from the cold nor the cold from the warm”) #

Point: without the idea of ability, “nothing is separated from anything” becomes even more radically true, because Anaxagoras has everything actually inside everything.

• Distinction: able-to-be vs actually. A clay sphere is able to be a cube (so not cut off), but actually a sphere is never a cube.
• If the lion ate me, my matter would become a lion; if the worms ate me (Hamlet on Polonius: “not where he eats, but where he is eaten”), a worm; dust. So there is something in me that “in a way is my enemy,” able to be other than me; I am cut off actually, but not completely.
• Aristotle’s further problem: if the things are infinite in multitude, they cannot be known “in word or in deed.”

4. DK 9, 15, 16: separation by circular motion (“does man himself use circular motion to separate things”) #

Point: partial separation comes from a circular motion, which he will attribute to the greater mind; two things support this.

1. Evidence in the world: the whole sky appears to revolve around us (a remnant of circular motion); heavy earth settled at the centre, then water, air, fire at the periphery (the sun and stars: “what else could it be?”).
2. Man uses circular motion to get force and to separate: the rock on a string whirled to break a window; his friend Jim Franzak the Golden Gloves boxer teaching him to turn into the punch; the cyclotron accelerating particles to split things; the altar-boy picnic ride where his baseball hat flew off and was ground up while he, the heavy thing, stayed at the centre. Student adds that biologists separate the same way (centrifuge). So “greater mind is like the lesser mind.”

• What he stresses: this is still really change of place.

5. Coming to be is mixing, perishing is separating (“The Greeks do not rightly take coming into being and perishing”) #

Point: at the top of page 8 Anaxagoras says what Empedocles said (“far-reaching mind… you fool”): nothing comes to be or perishes; things are mixed and separated from existing things.

• Reason: real coming-to-be would get something out of nothing; real perishing would cut something up into nothing. (I can cut you up until the pieces cannot be found, but not into nothing.)
• New baby at the hospital: “a new mixture”; funeral: “a separating.” Something in us says this is wrong, but they cannot see how else to avoid something out of nothing.
• Distinction: chairs brought from the next room (actually there) vs chairs got out of trees (not actually there, but something in the tree able to be a chair). Neither is something out of nothing, but they are not the same. Without ability it is like getting blood from a turnip: there would have to be blood in it.

6. All things are forever equal (“it is necessary to know that all things are neither more nor less”) #

Point: from “neither more nor less” (never more, else something came from nothing; never less, else something went out of existence; “not possible for more than all to be”) he concludes all things are forever equal, and this, he tells students, underlies the whole modern mathematical science of nature.

1. The characteristic expression of nature is the equation, from “equal.”
2. Algebra example: 2(x+y) = 2x + y is marked wrong because a y has gone out of existence; the reverse, 2x + y = 2(x+y), is wrong because a y came from nothing. In algebra you may only mix and separate (x+x+2y etc.); nothing comes to be or dies.
3. This fits the view that change of place is the only change: if we change seats, the number in the room is neither more nor less; to get more people you must “kill somebody or convert somebody.”

• He notes Anaxagoras goes from neither-more-nor-less to equal, as Aristotle does in “the tenth book of wisdom” [ed.: Metaphysics X]: equal is after more or less in meaning; two lines are equal when one is neither longer nor shorter.
• Connection to the Phaedo: Socrates’ recollection argument that equality is not got from sensible things, since two chairs approach equality but fall short, so you must already know equality to judge them unequal. His comparison: Lafayette, back in America after Washington’s death, judging the statues and paintings “not exactly what he was”; he needed a knowledge of Washington not from the paintings (aside on Lafayette’s friendship with Washington and Washington’s agents trying to extricate him in the French Revolution). But sensible things certainly are larger and smaller than each other; if equal is got by negating more and less, “the argument would collapse.” In English unequal looks like the negation of equal, which hides this.

7. Conservation laws and whether knowledge increases (“Is there more knowledge in the world now”) #

Point: the conservation laws (energy, from last time) say the amount is always equal day to day, only in different forms (kinetic, potential, heat), to be understood the way algebra is understood: mixing and separating. (Joke: the kids’ energy is taken from the parents.)

• Objection he raises: does learning a theorem of Euclid, or his teaching, increase knowledge, or is knowledge only moved from him to you? The materialist would say you are only rearranging atoms and molecules in your head, with corresponding loss elsewhere. Left open; he calls the statement “interesting” especially in light of modern science.

8. Stopping before the fragment on Mind (“see if you can see the apparent contradiction”) #

Point: the next three fragments begin to make mind responsible for the circular motion and separate from the mixture; DK 12 is left for next time.

• Assignment: what Anaxagoras says of the greater mind he gets from knowing the human mind; some things said of the greater mind hold of ours in a lesser way. Look for an apparent (not real) contradiction, “the key to something very important”; in all his years only one student has found it. This fragment caught Socrates’ attention, and Plato and Aristotle admired it.
• Aside: the Pope’s address at the Consistory on the danger of modern science disposing the mind unfavourably to faith, and on man vs the other animals: “reason first, then go to love, proper order.”

9. After class: is size relative? (“large and small are relative”) #

Point: a student asks whether size is relative; he corrects: not size (quantity is absolute in itself, whether known or not), but large and small are toward something, nothing in themselves.

• A large pea is small compared to a mountain; a large apple would be a very small man. Aristotle’s way: the same thing is called large and small in comparison to different things.
• Student: if the whole universe shrank to a teacup in proportion, we would never notice. He: “that’s what they say… seems to be correct,” though it did not have to be true.

10. Descartes’ cogito and how the Greeks build on each other (“you have to be before you can think”) #

Point: a student suspects “I think therefore I am”; he finds nothing wrong with it.

• Being is before thinking, so if you think you must be; it is seeing before and after in the thing. Whether what I think is true in reality is another matter, not involved in the statement. Some say it is not reasoning in the full sense, the mind moving so quickly that it sees one involves the other.
• One should be suspicious of the moderns: each has his own mistakes, though “guilty of having some insight.” The Greeks build on each other: Cajetan’s phrase (quoted in the encyclical, “the 13th quote”) that Thomas seems to have inherited the mind of all the Fathers, so reading Thomas is reading what is good in Gregory, Augustine, Chrysostom; likewise Aristotle inherited the mind of Plato and his predecessors; already Empedocles combines earlier thoughts on matter with numerical ratio and adds the mover.
• Aristotle in the Politics: try to say some things better than predecessors, others as well as they did, and add what one can; note what they said, why they said it, and give reasons where it is wrong. Moderns say the opposite without noting the Greeks said otherwise or why (Descartes on confused vs distinct, reversing Aristotle without recalling his arguments).
• Illustration from his other class on the four causes (matter, form, mover, end): the order Aristotle distinguishes them is the historic order and, more important, the order in which reason can best be forced to admit there are four. The Greeks, being first, begin with what is more known to us; once there are books and a printing press one begins by chance with whatever book or Professor X one meets, and moderns start where the last modern left off, never getting back to what is more known to us.

11. A student on learning by breaking down the text (“teaching an imaginary person”) #

Point: writing out and dividing a text forces understanding; Thomas’s commentaries divide Aristotle’s text and see its order, which works because Aristotle is orderly. His own habit: thinking things out by explaining to an imaginary person.

12. The three meanings of bad (“sin is nothing, and the man who sins becomes nothing”) #

Point: from the fifteenth reading (Aristotle’s critique of Plato), the key to understanding bad.

1. First meaning: a lack, a non-being of something one is able to have and should have.
2. Second: to have a lack (a blind man, an ignorant mind); bad because blindness, ignorance, is bad, as it is good to be wise because wisdom is good.
3. Third: what causes a lack (poking out an eye; what keeps the mind ignorant).

• A bad human act is not simply a lack but an unreasonable act, lacking the ordering and measuring of reason (eating or drinking too much is unmeasured).
• Hence Augustine’s “sin is nothing, and the man who sins becomes nothing”: a lack is a nothingness; “a little bit of an exaggeration,” since sin is an act lacking the order it should have. Once the first meaning is understood one sees why there can be nothing bad in God.

13. Temperance vs chastising the body (“it’s always a question of prudence”) #

Point: a student asks why Thomas says natural temperance eats what is needed while the supernatural virtue chastises the body; he answers that the mean is not the same when ordered to a higher, supernatural good.

• The vow of chastity seems excessive humanly, but not in view of seeing God face to face.
• Caution: Bernard of Clairvaux himself thought some penances excessive; it is a matter of prudence (foresight). In the Dark Night of the Soul any attraction to material things keeps the soul from turning wholly to God; St Paul carried to the third heaven, “within the body or not, I know not.” The recording ends mid-sentence on what the mean is.

His words #

• towards something (pros ti): the category of great and small; not quantity, which is absolute in itself.
• ability: what Anaxagoras lacks; something in me able to be lion, worm, chair-in-tree [ed.: potency]; he also says “potency” once.
• cut off (with an axe): Anaxagoras’ phrase for separation, which he takes as absolute.
• mixing / separating: what Anaxagoras calls coming to be and perishing.
• all things are forever equal: his gloss of “neither more nor less”; the basis of the equation and of conservation laws.
• second difference: limits in quantity of natural things due to their natures, beyond pure math; the first difference is math’s abstraction from matter and motion.
• tenth book of wisdom [ed.: Metaphysics X]: where equal is after more or less in meaning.
• greater mind / lesser mind: Anaxagoras’ Nous and the human mind.
• bad: (1) a lack of what one is able to and should have; (2) having a lack; (3) causing a lack.
• unreasonable act: a bad human act, lacking the ordering and measuring of reason.

Texts #

Read in class

• Anaxagoras, DK 6 and DK 8 (nothing cut off with an axe, warm from cold)
• Anaxagoras, DK 9, 15, 16 (separation by circular motion)
• Anaxagoras, “top of page 8”: the Greeks do not rightly take coming to be and perishing
• Anaxagoras, fragment on “neither more nor less… forever equal” (locus not stated)

Mentioned

• Anaxagoras, DK 12 (fragment on mind, next time)
• Aristotle, Categories (hundred people example)
• Aristotle, arguments 2-4 against Anaxagoras (work not named)
• Aristotle, “tenth book of wisdom” [ed.: Metaphysics X] (inferred)
• Plato, Phaedo (recollection, equality)
• Aristotle, Politics (saying things better than predecessors)
• Empedocles fragment (“far-reaching mind… you fool”; coming to be as mixing)
• Heraclitus (ape : man :: man : God)
• Shakespeare, Hamlet (Polonius at supper)
• Descartes (cogito; confused and distinct)
• Cajetan on Thomas, quoted in “the encyclical” (13th quote)
• The Pope’s address at the Consistory
• Aristotle’s critique of Plato, “the 15th reading” (meanings of bad)
• Augustine (“sin is nothing”)
• Thomas, Summa (temperance; vow of chastity)
• Bernard of Clairvaux; Dark Night of the Soul; St Paul, third heaven (epistle not named)
• Secondary reading, “the moderns on the mover”

His questions #

• Is great and small to itself or to another? To another; it is in the category of towards something, not quantity.
• If the lion ate me, my matter would become what? A lion; there is something in me able to be lion, worm, dust, but not actually.
• Were there already chairs out in the trees? Potentially, yes; not actually, unlike chairs in the next room.
• Why does he say the whole modern mathematical science of nature is based on “all things are forever equal”? Because it is expressed in equations, and in algebra nothing comes into or goes out of existence, only mixed and separated.
• Is there more knowledge in the world now because of my teaching, or are all things forever equal? Left open; the materialist would say only atoms are rearranged.
• Does it follow that if the universe shrank to a teacup we would never notice? “That’s what they say”; seems correct.
• Is there anything wrong with “I think therefore I am”? No; you must be before you think; whether what I think is true is another question.
• What are the first, second and third meanings of bad? A lack; having a lack; causing a lack.
• Isn’t the vow of chastity, or bodily chastisement, excessive? Not in view of a higher supernatural good; but a question of prudence, and Bernard thought some penances excessive.