Metaphysics Book 6, Part 2: Natural Philosophy, Mathematics and First Philosophy; Introducing Accidental Being

Orientation #

He is continuing the division of the sciences in Book Six of the books of wisdom, taking up the subdivision of the looking (theoretical) sciences. He ends by announcing that next Thursday they will start with the second reading, on accidental being and being as true. The previous class distinguished wisdom from the other sciences and separated the looking sciences from the doing and making ones.

The class, in order #

1. Natural philosophy: defined with matter and change (“things that have matter and that change”) #

Natural philosophy is about things that have matter and change, and defines them with matter or change. To distinguish teeth from tongue, or bones from muscles, you must bring in, at least in general, the kind of material each is made of; and because they are material they are subject to change — of place, of quality, even growth. Nature itself is defined by change: motion is in the definition of nature. You leave out this flesh and these bones (individual matter), but keep sensible matter in general.

2. Mathematics: about things with matter, but defined without it (“can be defined without matter or change”) #

Mathematics is the odd science: its things have matter and change, but can be defined without either.

• Spheres: rubber ball, marble, steel ball, snowball, Earth, Sun — all have matter and change (the snowball melts, the ball bounces). But the shape of a sphere is understood without rubber, glass, snow, steel.
• Euclid’s solid geometry reaches the sphere long after the circle, and helps imagination by rotating a circle about its diameter — pure imagination, no matter.
• Because no matter, no reference to motion: a lead balloon goes down, a helium balloon up, but a geometrical sphere neither. A rubber ball bounces, a glass ball shatters, a steel ball sticks or goes through — the geometrical sphere is neither brittle, heavy nor elastic, so none of this can be said of it.
• Cubes: wooden block, plastic paperweight, ice cube. The ice cube has a melting point, the plastic cube too; the geometrical cube has no freezing or boiling point. Math is thus more removed from matter than natural philosophy: not only individual but sensible matter is left out. What remains is sometimes called intelligible or imaginable matter — extension — not matter in the original sensible sense.

Asides: Proclus the Neoplatonist: mathematics purificat oculum mentis, it purifies the eye of the mind, freeing one to some extent from the material world. Hence the Pythagoreans in Italy were almost a religious order about it; and at the University of Paris one had to know at least the first book of Euclid before admission to theology.

3. Thales, and 200 years of two philosophies (“the first philosopher is usually considered to be Thales”) #

For 200 years the Greeks pursued only these two kinds of looking philosophy. Thales of Miletus: water is the beginning of all things, especially living things; also first to prove a geometrical theorem. Two attributed to him: (a) the angle inscribed in a semicircle from any point other than the endpoints of the diameter is always right (proof in Elements III); (b) the diameter divides the circle into equal parts — which Euclid states without proving. His manifestation: since all points on the circumference are equidistant from the center, flip one half over the other; if they do not coincide, the radii are unequal and it is not a circle. Compare Euclid I.4, seen the same imaginative way.

4. Anaxagoras to Aristotle: the discovery of immaterial things (“a sober man among drunk men”) #

The third looking philosophy becomes possible only when immaterial things are known.

1. Anaxagoras (a young Socrates’ contemporary; Aristotle calls him a sober man among drunk men; fragment DK 12) concluded there is a greater mind than ours behind natural order, and gave a good reason why that mind cannot be mixed with matter.
2. Socrates, Plato, Aristotle see that human reason is not material.
3. From motion: motion depends on a mover; the movers we know are moved movers; a moved mover moves not by itself but by another; before what is by another is what is by itself; so there is an unmoved mover.
4. An unmoved mover is not a body, since no body moves another without itself being moved — he cannot move the bottle with his briefcase without the briefcase moving.
5. And if the soul can exist without the body (Phaedo; better in On the Soul III), understanding is not in the body. So there are things not depending on matter for existence, and knowable: hence a third looking philosophy — first philosophy, wisdom, sometimes metaphysics, i.e. meta ta phusika, “after the books in natural philosophy,” as Andronicus of Rhodes correctly saw in ordering the fourteen books; modern anthologies still print the natural books first.

5. Order within wisdom: from the communia toward the separated (“things that can be in matter but need not be”) #

A distinction he calls important: (a) things that can be in matter but need not be — the communia: being, substance, act and ability; (b) things that cannot be in matter — the separated substances (angels) and God. Once immaterial substances are known, substance is seen not to require matter. Wisdom moves from (a) to (b), because (a) is more known to us who begin from material things. Monsignor Deian’s word: the order of wisdom is “towards the immaterial.” Book Nine shows this beautifully: act and ability first as found in material, moving things; then a wholly universal consideration reaching the immaterial; then the order between act and ability — the beginning of the reasoning at the end of Book Twelve that God is pure act.

6. Crisscrossed divisions that yield three, not four (“you crisscross these and you get four”) #

Sometimes two divisions by opposites crisscross into four members, sometimes only three.

• Four: human beings by male/female and good/bad — good men, bad men, good women, bad women.
• Three: the parts of a plot in the Poetic Art. Homer, the supreme poet, taught the Greeks that a good plot is not a story about one man (all sorts of unconnected things happen to one man) but has beginning, middle, end. Aristotle defines these by before/not-before and after/not-after: beginning = before something, not after; end = after something, not before; middle = both. The fourth box — neither before nor after anything — is no real possibility, since such a part would have no connection and so could not be a part of the whole.

Aside after the break: the story of the man who recorded lectures secretly in his briefcase and on the second day pressed the wrong button, so yesterday’s lecture played out of the briefcase; the French students were too shy to ask permission, and he preferred not to know.

7. Thomas’s four boxes for the looking sciences, and why one is empty (“it’s a very subtle thing”) #

Crisscross: about things that do (or do not) depend on matter for existence × defined with (or without) matter.

1. Depends on matter, defined with matter — natural philosophy.
2. Does not depend on matter, defined without matter — wisdom/first philosophy.
3. Depends on matter, defined without matter — mathematics.
4. Does not depend on matter, defined with matter — no such science. Reason: if the thing known has no matter, and the knower (reason) is immaterial, there is no reason on the side of either thing or knower to bring matter into the definition. Whereas box 3 is possible because an immaterial power can know a material thing in an immaterial way. “It’s a very subtle thing.” Thomas comes back to this at the beginning of the commentary on the Physics.

• Parallel in the Trinity: proceed-from / not, and have-one-proceed-from-you / not. Father: no procession from another, but another proceeds from him. Holy Spirit: the reverse. Son: both. The fourth — neither proceeding nor having anyone proceed — is impossible, since there would be no basis to distinguish him; distinction among the persons is only by procession. Part of the reason for the filioque: if the Holy Spirit did not proceed from the Son he would not be distinct from the Son.
• Near-miss example: odd/even × prime/composite gives four boxes, but only one even number is prime — two. (He corrects himself mid-sentence about which number.)

8. Why these three are divided by relation to matter and motion (“the definition of time is timeless”) #

The doing sciences and making sciences were divided in quite different ways; the looking ones are divided by their relation to matter and change, because the mind is immaterial and the whole purpose is to get the thing into the mind, i.e. out of matter in some way. Against Heraclitus’ “all things flow and nothing abides”: you cannot understand what does not stand still, so each science must remove something from motion. Natural philosophy abstracts from individual motion but keeps motion in general, which does not change: the definition of time is timeless (time in concrete flows and waits for no man); the definition of change never changes — the Greeks’ great discovery, that change is between opposites, never changes; even “what is changing is always different” never changes. Mathematics defines without change; wisdom treats things that cannot change.

9. The central question: the way you know need not be the way things are (“Plato thought… Aristotle said no”) #

Plato held that to have truth, the way you know must be the way things are; Aristotle denied it, and most philosophers down through history are mistaken here.

• Boethius’ subtlety: announced in Book I of the Consolation that he is of the Academy, yet at the opening of Book V Lady Wisdom introduces Aristotle as her true follower — just as he takes up God’s eternal knowledge, whence theology’s famous definition of eternity. God knows what is in time without His knowledge being in time.
• Faint human imitation: we know the past now and the future now — yesterday is in my knowledge today — without being false; falsity would be thinking yesterday is today.
• Things existing together can be truly known separately: he is a philosopher and a grandfather; one can be known without the other, and the nurse at the hospital can know him as grandfather knowing nothing of his philosophy. Such knowledge is incomplete, not false. Falsity enters only with “this philosopher is not a grandfather.” Likewise the sphere cannot exist without rubber or steel, but is understood without them.
• Things can be known in reverse order: “I know you before your parents,” though in reality parents came first; we knew water before hydrogen; we generally know effect before cause — Sherlock Holmes to Watson, “we’ve got to reason backwards”; day and night before the earth’s turning on its axis. Falsity would come only if you said the order of knowing is the order of things.
• The rationalists’ mistake: Spinoza — the order in thoughts and the order in things is the same; and the terrible thing Hegel takes from him, identifying the first confused thought of being with the one who said “I am who am.”

10. The conclusion: three looking philosophies, and first philosophy as second only if (“as it is, it’s second philosophy”) #

Wisdom is about what is eternal, immovable and separated from matter. Aristotle concludes there are three looking philosophies: mathematical, natural, and what he calls theological — a word Berquist avoids given our use of “theology.” If first philosophy is called theology, God is its end or goal, but not its subject: its subject is being as being; in revealed theology (sacra theologia) God is both goal and subject. It is the most honorable science because about the most honorable thing. And: if there were no immaterial substances, natural philosophy would be first philosophy and wisdom; as it is, it is second philosophy. For at least two hundred years the Greeks identified wisdom with natural philosophy — reasonably, since if only material and artificial things existed, and artificial depend on natural, whoever knew the first cause of natural things would know the first cause of all. Hence his answer to “you only call wisdom the best knowledge because you like it”: no — we first thought natural philosophy was best, then found something before it.

11. What comes next in Book Six: accidental being (“a Christian geometer”) #

Wisdom having been separated from all other knowledge, Aristotle is now ready to begin the study of being as being, recalling from Book Five the division of the senses of being. Book Six treats briefly two of the four: accidental being and being as true, setting both aside as not the wise man’s main concern; Books VII–VIII treat being according to the figures of predication, chiefly substance; Book IX act and ability. Book Five’s first division: being to itself, kath’ hauto, and being by happening, kata symbebēkos. The most accidental kind is when two things happen to a third.

• “Christian geometer”: being Christian happens to belong to him, being a geometer happens to belong to him, but they do not come together into one thing. There is a way to become a geometer (studying Euclid) and to become a Christian (baptism) — but no geometrical baptism, no way to become a Christian geometer; he was not born one; there is something by which he is a Christian (grace) and something by which he is a geometer, but nothing by which he is a Christian geometer. So a Christian geometer “hardly is.”
• Yet accidental being matters in life: affirmative action — a black woman may be hired as black and as woman, a white man not; a Christian white man wants to marry a Christian white woman, so the black woman does not marry him.
• Hence it belongs to biography and poetry: Othello’s tragedy has something to do with the color of his skin; Romeo and Juliet’s, with the man she loves being the son of her father’s enemy — “Romeo, Romeo, wherefore art thou Romeo?” she cannot figure it out. This shows the universality of Aristotle’s mind: he neglects no kind of being, while seeing which kind chiefly concerns us. The goal in the end is to know the one who said “I am who am”; but we start from accidental being, which hardly is.

His words #

• Looking sciences [ed.: theoretical/speculative sciences] — divided by their relation to matter and change.
• Doing sciences / making sciences [ed.: practical / productive] — divided in quite different ways.
• Intelligible or imaginable matter — the extension dealt with in geometry, not matter in the original sensible sense.
• First philosophy / wisdom / metaphysics — meta ta phusika, “after the books in natural philosophy.”
• The communia — common things like being and substance, which can be in matter but need not be.
• Ability [ed.: potency] — as in “act and ability,” the subject of Book Nine.
• Books of wisdom [ed.: the Metaphysics], fourteen in number.
• Purificat oculum mentis (Proclus) — mathematics purifies the eye of the mind.
• Kath’ hauto — being to itself; kata symbebēkos — being by or through happening, accidental being.
• Sacra theologia — revealed theology, where God is subject as well as goal.

Texts #

Read in class / commented on

• Aristotle, Metaphysics VI — the division of the looking sciences (first page of the reading, last paragraph and bottom of page one; second paragraph and conclusion on page two); handout p. 615 of DHB Vol III — The School of Aristotle (inferred).
• Aristotle, Poetics — beginning, middle, end of a plot.
• Aristotle, Metaphysics V — being kath’ hauto / kata symbebēkos.

Mentioned

• Euclid, Elements I (I.4; the definition of circle and diameter), III (angle in a semicircle), and the solid books (the sphere).
• Aristotle, On the Soul III; Metaphysics IX and XII (end).
• Plato, Phaedo.
• Anaxagoras, fragment DK 12 (inferred).
• Boethius, Consolation of Philosophy I and V.
• Thomas Aquinas, commentary on the Physics, beginning (inferred: proemium).
• Thales; Andronicus of Rhodes; Proclus; the Pythagoreans; Heraclitus; Spinoza; Hegel; Shakespeare, Othello and Romeo and Juliet; Conan Doyle (Holmes and Watson); Homer.

His questions #

• Can the shape of a sphere be defined and understood without rubber, glass, snow, steel? Yes — and so without any reference to change; it can neither bounce nor shatter nor rise nor fall.
• What science is about things that depend on matter for existence but can be defined without matter? Mathematics.
• Is there a fourth science — about things that do not depend on matter, but defined with matter? No: the thing known has no matter and the knower has no matter, so there is no reason to bring matter into the definition.
• Could there be a part of a plot that is neither before anything nor after anything? No — it would have no connection to any other part, so it could not be a part of the whole.
• Could there be a person of the Trinity who neither proceeds from anyone nor has anyone proceed from him? No — there would be no basis to distinguish him, since distinction there is only by procession.
• Is my knowledge false if I know the effect before the cause, or know you before your parents? No — incomplete, not false; falsity comes only if you say the order of knowing is the order of things.
• If there were no immaterial substances, would natural philosophy be wisdom? Yes — it would be first philosophy; as it is, it is second philosophy.
• Is there really such a thing as a Christian geometer? It hardly is: there is nothing by which one is a Christian geometer, and no way of becoming one.