Anaxagoras on Matter and Mind: Infinite Division, the Continuous, and Why the Ruler Must Be Separate

Orientation #

He continues from last time: “I guess we are talking about the position of Anaxagoras about matter on page seven there,” repeating briefly Aristotle’s report of Anaxagoras’ argument from the first book of “Natural Hearing” (prev. lecture). Verified: about ten minutes of the class are read from his handout “Natural Fragments of the First Philosophers,” p. 33, and from the “Note for Book One, Reading Nine” on Physics I, lectio 9. The class breaks off mid-sentence at “at this point, there is an apparent —”.

The class, in order #

1. The argument for everything in everything (“how could hair come from what is not hair?”) #

The point: recap of why Anaxagoras posits an infinity of infinitely small pieces of everything in everything.

1. By induction, everything in nature comes to be from everything else — the cow eats grass, man eats the steak, the lion eats Berquist, the worms eat the lion.
2. Nothing comes from what it is not in: “how could hair come from what is not hair?” You cannot get money out of his pocket if there is no money there; you cannot get blood out of a turnip.
3. So cow, man, lion, worm, bird, cat and daisies must all be in the original grass.
4. Things keep coming to be forever, so the pieces of each must be infinite in number.
5. An infinity of pieces fits inside a finite blade of grass only by being infinitely small — as modern mathematicians speak of a finite line composed of an infinity of points. DK 1: “All things were together, unlimited in number and in smallness,” nothing clear because so small. Aristotle sees this as an attempt to express ability or potency, where nothing is distinguished from another — all the shapes in the wood are there in ability, not seen as distinct. Parallel: 20th-century elementary-particle physics, “every elementary particle is composed of all the rest” — taken literally it drives the same regress, smaller and smaller without limit. Asides: the rest of DK 1 may show influence of Anaximenes and Anaximander on the infinite; the next fragment calls the pieces “the seeds of all things.”

2. Two definitions of the continuous (“divisible forever”) #

Point: DK 3 is a good introduction to the philosophy of the continuous.

• In the Categories (chapter on quantity): continuous quantity (line, surface, body, time, place) is that whose parts meet at a common limit — the two halves of a straight line at a point, of a circle at a line, of a body at a surface; discrete quantity (number) has parts that meet nowhere — in seven, the three and four do not meet.
• In Physics VI: the continuous is what is divisible forever; halving a line always yields smaller lines, never an end. Anaxagoras sees something of this: “Nor is there a smallest of the small, but there is always a smaller, for what is cannot cease to be by being cut.”

3. Why a line cannot be cut into nothing or into points (“the only way two points can touch”) #

Point: a disjunctive proof that cutting a line always leaves shorter lines. The three alternatives on cutting: shorter lines, two points, or nothing.

• Nothing is excluded: you cut a thing into what it is made of, so a line cut into nothing would be made of nothing — something out of nothing.
• Points excluded by the argument from touching. Ways of touching: part touches part (two circles), part touches whole, whole touches whole — and perhaps limit touches limit. But a point has no parts (Euclid: “that which has no parts”), so part-touching is out; and to distinguish a point from its edge or limit is to make it a small circle. So two points can touch only by the whole of one touching the whole of the other, i.e. by coinciding; then two points have no more length than one, which is no length. Ten, a hundred, a million, an infinity of points likewise. So a line — length without breadth — cannot be put together from points. (“Composed is Latin for put together from.”) Therefore the line is divisible forever.

4. Do points exist? (“are there bodies that don’t go on forever?”) #

Point: how he answers the student who doubts that points exist — by descent through the dimensions. A body does not go on forever, so it has an end, the surface; the surface can have no depth, or you have not reached the end. The surface of the door ends in something with length but no width — a line. The line ends in something with no length — the point; Euclid’s third definition points out that the limit of a line is a point. Student question: must “exist” be understood in a certain way? — Yes: the point exists as an accident exists, not as a substance; you could not cut a surface off without taking some depth, i.e. cutting a body from a body, nor could the surface exist by itself.

5. Why there is also something greater than the great (“number arises from the division of the continuous”) #

Point: the unending greatness follows from the unending smallness by way of number. Student answer accepted after a correction: what grows as you keep cutting is the number of lines. So number arises from the division of the continuous; the continuous is divisible forever; therefore numbers can increase forever — his answer to the child who asks whether one finally comes to a highest number (his grandchildren counting to a hundred). Anaxagoras “saw something of this.” Criticism: “each thing to itself is both great and small” shows he does not understand relation — Aristotle’s pros ti, Latin ad aliquid, toward another. Nothing is double in itself. This matters for understanding the Trinity later on: John’s “the Word was pros God” — toward God — is the beginning of what Augustine, Boethius and Thomas see, that the distinction of persons is a relative distinction.

6. Share of everything: actually, or in ability? (“false imagination”) #

Point: Anaxagoras’ “all things have a share of everything” is true in ability, false as he imagines it. There is something in Berquist able to be a lion, a shark, worms, dust (“dust thou art”) — not a little bit of lion actually in him. Our mind has a hard time with this ability that is matter, and imagines it as actual, then has trouble fitting it in: a common error, false imagination — “as Weizsäcker says, when you imagine something, you make it actual in your imagination.” Same with p. 8: things not “cut off with an axe,” warm from cold — true if it means what is actually warm is able to be cold, not that a thing is actually both. Difficulty Aristotle raises: to know a thing you must know what it is put together from (a definition from genus and differences, a name from its letters); a word with an infinity of letters would never be known — yet Anaxagoras gave his whole life to the study of nature, and said it is better to be born, to contemplate the universe.

7. Separation by circular motion (“the speed makes the force”) #

Point: the mixed things are separated by a violent circular motion, whose cause will turn out to be a greater mind. Circular motion as separator is familiar to us: whirling a stone in a sling to break a window; the cyclotron (“it runs in a circle”) accelerating before it shoots; his friend Jim Franzak the ex-Golden-Gloves boxer teaching him that the power of a punch comes from the circular twist; kicking sports; many of our drills. The text: the speed far exceeds anything now among men; the thick, moist, cold and dark came together where the earth is, the thin, warm and dry went outward to the ether. Evidence: the heavens still apparently revolve about us, less violently than once; at the altar boys’ picnic his light baseball cap flew off in the ride and was ground up, but he, being thick and heavy, did not. DK 16 on the heavy things solidifying.

8. No coming to be, only mixing and separating (“thus they would be right to call coming to be mixing”) #

Point: DK 17 — like Empedocles, the only real change is change of place. “The Greeks do not rightly take coming into being and perishing”; nothing comes to be or perishes, but is mixed and separated. Death and birth are emotionally charged, unscientific words. But something in us says a child’s coming or a friend’s death is more than a change of place, even though we say “he’s gone.” His test case: learning. Is knowledge moved from the professor’s head to the student’s? Then the professor would have less, and “they should pay you less and less the longer you teach.” Nor is it plausibly a rearrangement of molecules — was that your experience? You now know what you did not know; did you get it out of nothing, if the professor knows as much as before? Experience contradicts the position, but how it takes place is hard to understand.

9. All things forever equal, and the modern equation (“two times x plus y”) #

Point: DK 5 — “all things are neither more nor less” — is, he says to students, the basis of all modern physical science. If ever more than now, something came from nothing; if ever less, something became nothing. The sciences express the world in equations — the word itself says equality. The algebra example: writing 2(x + y) as 2x + y is marked wrong because a y has become nothing; going the other way, from 2x + y to 2(x + y), a y has come out of nothing. All you may do is mix and separate — x + x + y + y — never let anything go out of or come into existence.

10. The way to a greater mind (“like effects have like causes”) #

Point: how Anaxagoras reasonably arrives at a greater mind — and why our own mind is the starting point for knowing it. Three premises:

1. The order in the parts of artificial things and in the parts of animals and plants is alike — the chair, the briefcase, the car are well arranged, and so are the animal’s teeth; a dentist making false teeth puts the biting teeth in front and the chewing teeth behind, not for looks, but as nature did.
2. The cause of the order in artificial things is known: the human mind; the cause in animals and plants is unknown.
3. Like effects have like causes. Conclusion: the cause of order in plants and animals is something like the human mind, and since it is responsible for much greater order, a greater mind. Text support: near the end of DK 12, “every mind is similar, both the greater and the lesser”; also the earlier fragment, “in everything there is a part of everything except mind, and there are also other things in which there is mind.”

11. First statement: mind is unlimited (“unlimited in its ability”) #

Point: in what sense “unlimited” is said of mind. Not unlimited as a multitude, nor as going on forever in continuous quantity like Anaximenes’ air — for he will later call mind the thinnest of all. Rather unlimited in its ability to know and consequently to make. Evidence from our own mind: outwardly, there seems no end to what we can learn as long as we live; man always makes something new or an old thing in a new way (the automobile, the airplane, the computer — his son-in-law: don’t bother turning the computer off, it will be outdated before it wears out); and language, by which a man keeps signifying something new. Inwardly and best: the mind knows the universal, which contains an infinity — as said in the proemium to wisdom, the wise man in some way knows all things; the mathematician, knowing odd and even, states that no odd number is even, a statement about infinitely many things, and can descend from the confused universal to three, five, seven, nine forever. Hence Aristotle in the De Anima, after the senses and reason: the soul is in some way all things. He notes: this sense of “unlimited” differs from air’s going on forever, and is closer to the sense in which God is unlimited.

12. Second statement: mind is self-ruling (“what part of philosophy is a sign of this?”) #

Point: the three main parts of philosophy arrange themselves around “mind is self-ruling.”

• Directly: logic — logic is the art that directs reason itself; that there is such a thing as logic is a sign that mind is to some extent self-ruling. (Reason as Shakespeare’s “ability for large discourse, looking before and after”; to rule is to order, and one must know order.)
• Behind it: to rule something you must know it, so mind could not rule itself unless it knew itself; being unlimited in its ability to know, it knows itself. He adds in brackets: mind is self-knowing — whose sign is the De Anima, especially Book III (and the philosophy of nature generally, of which the philosophy of soul is a part).
• Ahead of it: ethics — reason ruling will and emotion. Are you fit to rule others if you cannot rule yourself? The frightened commanding officer whose fear is heard in his voice is not fit to lead; the parent who cannot control his anger or his drink is not fit to be a parent. And mind alone knows itself — the eye does not know what an eye is, nor the hand, nor the lung — so mind alone can rule itself, and so is the only part fit to rule the rest: the basic thing in ethics, that we live by reason. Aside: the legislators his friend saw coming into the state house session drunk at night. Qualification: said of God, “self-ruling” has a different meaning — an affirmative way of saying something negative, that God is not ruled by another; he need not be directed to an end, being the end of all things, and is the source of all other rule.

13. Third statement: mind is mixed with nothing (“the ruler must not be mixed up with the ruled”) #

Point: the reason given in the fragment — and the everyday evidence for its hidden premise. The text: if mind were not by itself but mixed with something, it would have a share of all things, since there is a part of everything in everything; and “the things mixed with it would hinder it, so that it would rule over nothing like it does being alone by itself.” Since the greater mind is responsible for the distinction and order of things, especially the parts of animals and plants, it could not rule the world so well if mixed with it. Aristotle refers back to this in the De Anima with a similar argument for our mind’s immateriality. The underlying premise: the ruler must be separate from the ruled. Evidence from what is better known to us:

• The army (student: “anti-fraternization laws”): saluting first, insignia, the commissioned officers’ club closed to the non-commissioned — separation even socially. After the Bolshevik Revolution everyone called everyone comrade and discipline broke down, so the old separation had to be restored.
• The judge: we demand that he be impartial — literally not a part of; a friendship or financial interest disqualifies him; a trial can be transferred out of a community whose opinion is already against the accused.
• Industry: at Minnesota Mining a man promoted to a higher echelon is expected to associate there and not be buddy-buddy with former friends in the lunchroom; an employee told him you can tell a man’s rank by the degree of separation — a desk among desks, a partitioned desk, an office, an inner office with an outer office and a secretary screening visitors, the top floor.
• The Church: a man made bishop must cut off buddy-buddiness with the priests he was close to, so he can rule more objectively.
• The family: parents must not be just one of the kids, the mother joining her teenage daughter’s party loses respect and distance. His father, away all day, had a command over him his mother, mixed up with the children all day, did not — “sit in that chair and don’t get out until I tell you”; and a stranger freezes a child more than his own parents, as when the policeman coming into his aunt Helen’s ice cream store for a Coke said they might put him in jail for a day and the boy spinning the stools at once behaved. Conclusion: if the greater mind rules over animals and plants, arranging their parts, it must not be mixed up with them — it must be separated from matter. The class breaks off as he begins “Now, at this point, there is an apparent —” [recording ends mid-sentence].

His words #

• Natural Hearing — his rendering of the title of Aristotle’s Physics (“the so-called Physics”).
• ability — [ed.: potency]; what Aristotle sees Anaxagoras groping at in “all things were together.”
• the continuous — what is divisible forever; in the Categories, that whose parts meet at a common limit.
• discrete quantity — number, whose parts meet nowhere.
• composed — glossed by him: the Latin for “put together from.”
• false imagination — imagining what is there in ability as actually there; “when you imagine something, you make it actual in your imagination” (Weizsäcker).
• pros ti / ad aliquid — relation, “towards another.”
• seeds of all things — Anaxagoras’ name for the infinitely small pieces.
• greater mind / lesser mind — Anaxagoras’ distinction; “every mind is similar.”
• impartial — “literally not a part of.”

Texts #

Read in class

• Anaxagoras, DK 1, DK 3, DK 5, DK 16, DK 17, DK 12 (handout pp. 7-9; verified handout “Natural Fragments of the First Philosophers,” p. 33)
• Aristotle, Physics I, on Anaxagoras’ argument (with Aquinas’s commentary, lectio 9 — verified handout note)

Mentioned

• Aristotle, Physics VI (the continuous, divisibility, impossibility of a line from points)
• Aristotle, Categories (quantity; relation)
• Aristotle, De Anima, esp. Book III (soul is in some way all things; mind’s immateriality)
• Euclid, definitions of point and line (inferred)
• John 1:1 (“the Word was pros God”); Augustine, Boethius, Thomas on relative distinction of persons
• Genesis, “dust thou art” (inferred locus)
• Shakespeare, on reason as “large discourse, looking before and after”
• Empedocles; Anaximenes and Anaximander on the infinite

His questions #

• What would be the objection to saying you cut a line and end up with nothing? — You cut a thing into what it is made of; the line would be made of nothing.
• Is it possible that a straight line be put together from points? — No: points can touch only by coinciding, and coinciding points have no more length than one, which is none.
• Does a point have any parts? — No; Euclid defines it as that which has no parts.
• Do points really exist? — Yes, as the end of a line that does not go on forever; but they exist as accidents exist, not as substances.
• How do you know you won’t eventually come to a greatest number? — Number arises from the division of the continuous, which is divisible forever, so numbers increase forever.
• In what sense is the mind said to be unlimited? — In its ability to know, and so to make; shown best by its knowing the universal.
• What part of philosophy is a sign of the truth that mind is self-ruling? — Logic, the art that directs reason itself.
• What part of philosophy is a sign that mind is self-knowing? — The De Anima, especially Book III.
• Are you fit to rule others if you can’t rule yourself? — No; hence reason alone, which alone knows itself, is fit to rule the rest of man.
• Is there evidence that the ruler must be separated from the ruled? — Yes: army, judge, company echelons, bishop, parents, the stranger’s authority over a child.