Metaphysics Book III, Part 2: Which Comes First, Ability or Act? Mathematical Things, and the Start of Book IV (Knowledge of Being as Being)

Orientation #

He is finishing the list of doubts of Book III (the last two of the six he has been counting), then hands out readings from Book IV, which he announces are the ones preceding “the great turnaround.” He says the class will resume “next Thursday” with how Aristotle reasons that wisdom is the knowledge of being as being. The previous class went through the second group of six doubts of Book III.

The class, in order #

1. Is the first beginning in potency or in act? (“which came first, the chicken or the egg”) #

The point: the fundamental question of wisdom, hidden in a nursery puzzle.

• Materialists (ancient first philosophers, today’s “evolutionary humanists,” the Marxists’ “dialectical materialism” — materialism = matter is the beginning, dialectical = struggle of opposites in matter) all make the first cause what is most in potency, since matter is able to become all things. He notes Marx dedicated one of his major works to Darwin.
• The Platonists insist on the forms instead.
• The chicken/egg knot both ways: the chicken lays the egg (act first), yet chickens come from eggs (ability first).
• Forward reference: Book IX has three parts — ability; act; the order of act and ability. Order means before and after, and before and after (from the Categories) has many senses; Aristotle will run through those senses to expose the mistake.
• The mistake is the second kind outside the words from the Sophistical Refutations: simply vs. in some way (secundum quid). He says it is the mistake everyone makes daily whenever they think they should do what they shouldn’t: “every time you go wrong, you’re making this kind of mistake.”
• Example: the Meno. Meno’s sophism — if you know what you’re looking for you needn’t look; if you don’t know it, you can’t look for it. Socrates replies and makes the same mistake. He wonders aloud whether Plato knew what he was illustrating. Most men are materialists because of this mistake.

2. Do things come to be only by motion? (“whether otherwise than by motion”) #

The point: this question is really asking whether there is creation.

• If everything comes to be by transformation of matter (carpenter takes wood from the tree, cuts and smooths it into a table), then matter is eternal, and natural philosophy — the study of changing things — would be the whole.
• Consequence for the soul: it would have come to be by the parents’ transformation of matter, hence tied to the body, and understanding would be a material process in the brain.
• Counter-sign: if I understand continuous things in an uncontinuous way — the definition of square is not continuous though the square is — understanding is not continuous, not a body. (He says there are many other such arguments.) Then the soul did not come to be by transformation of matter; matter was only prepared as a suitable receptacle.
• Then not everything comes to be by motion; and then matter may be a beginning but not the first — the first may be one that can create, not merely transform.
• Aside: his teacher Kasurik, the best of six or seven philosophers at the College of Saint Thomas, said “compared to Aristotle I’ve got the brain of an angleworm.” These are real questions, not moderns’ much ado about nothing — the student asking “how do I know if I exist?” answered by “Who’s asking?”

3. How the six divide, and Hegel’s universal as ability (“the first four are about the one and the many”) #

The point: the first four doubts concern one and many; the last two ability and act; and universality is a disguised form of putting ability first.

• The more universal stands to the less as ability to act: knowing the cat is an animal is not yet actually knowing what a cat is; adding the difference makes it more actual. So Hegel, evolving everything out of the most universal, makes what is able to be everything the beginning of everything.
• Story: at a philosophical association his friend’s paper defended the distinction of nature and art (given in Physics II); an objector said the philosopher can’t distinguish them, “because in being there is no distinction between nature and art.” Reply: “that’s the being that Hegel says passes over into non-being.”
• The giraffe: “the giraffe is something” is true yet tells you nothing — so vague and indeterminate; that is why Hegel can slide being into non-being.
• Locke’s general idea of triangle: are the three sides equal or unequal, at right angles or not? He ends with “all and none.” Berkeley quotes this in the Principles and concludes there are no general ideas. Compare Anaxagoras’ matter, where everything is in it but nothing distinct or cut off.
• His answer: the three lines are equal and unequal in ability, neither in act; the species-making difference actualizes what was there only in ability. Hence Porphyry (and Aristotle before him, not Plato): genus taken from matter, difference from form — and adding the difference gives eidos, a species/form (cf. English “forms of government”). Wood is chair, table and door as triangle is scalene, isosceles, equilateral.
• Why materialism is so common: as you go forward in natural philosophy you go toward matter; even our English word “ground” for cause shows we begin there — but that is not where to end.
• Positive use: Aristotle in the Eudemian Ethics takes what everybody says confusedly and makes it distinct; Newman on Aristotle in the essay on the idea of a university. A movement from ability to act in the mind.

4. Are numbers, lines, figures and points substances? (“res extensa”) #

The point: identifying substance with quantity is the ancient Pythagorean-Platonist error, renewed by Descartes.

• The naturalists’ earth, air, fire, water have size and shape — something more than numbers and figures.
• Descartes identifies material substance with extension, res extensa. But what a dog or cat is is not its size; if substance were size, every change of size were a change of substance — “Descartes never grew up,” not just mentally but physically.
• Theological footnote: in the Eucharist the substance of bread and wine is changed while the quantity and the sensible qualities following it remain; if substance were quantity, transubstantiation is contradicted.
• The order of reasons he insists on: Aristotle’s account of substance and quantity is not true because it harmonizes with the Eucharist — that harmony is a sign to him as a Catholic; it harmonizes because it is true. Parallel: “Mozart’s music is the best” — I don’t say it because I like it most; I like it most because it is best. Likewise Aristotle’s philosophy is not true because useful in theology; it is useful because true. Hegel, Spinoza, Descartes are harmful there because false.
• Aside on distinctions: commentators lump married priesthood with abortion and contraception, or capital punishment with abortion; the Church could never approve abortion, which is really murder, whereas a married priesthood is a question of suitability. “Aristotle says somewhere most men aren’t good at making distinctions.”
• Modern parallel: Schrödinger, who perfected wave mechanics and showed its equivalence with Heisenberg’s, wrote that the modern atom consists of no stuff at all, comparing it to Plato’s geometrical elements in the Timaeus. There is no matter in mathematics; the Soviets, enforcing orthodoxy from Moscow, were troubled that matter seemed to disappear. “How can there be equations out there?”

5. Separated or only in sensible things? (“Plato… got tanked up in Pythagoreanism”) #

The point: the last doubt — whether the mathematical substances are separate (Platonists) or only in sensible things (Pythagoreans, and in a way Descartes).

• Plato left Athens after Socrates’ death, went to the Greek cities in Italy, studied with the Pythagoreans. His name means broad, and he is broad: Socrates; Heraclitus through his teacher Cratylus (hence the Cratylus); Parmenides and Melissus (hence the Parmenides); the Pythagoreans (the Timaeus, some of the Phaedo). Reading Plato you are not reading one man — as Leo XIII quotes Cajetan that Thomas so venerates the Fathers that he seems to have inherited the mind of them all; as Euclid’s construction of the Elements acknowledges earlier mathematicians; as Mozart studied every master thoroughly.
• These questions catch everyone: Atomists, materialists, Descartes, Hegel all come down on one side or another, though Aristotle could not know the later ones.
• Aristotle’s closing remark: it is not only hard to find the truth about all these, it is not even easy “to doubt well” about them — Thomas glosses this as attaining well to the reasons for doubting, seeing that there is a real question. Compare the end of Book II: you cannot acquire episteme and the tropos, the way of reasoned-out knowledge, at once, and neither is easy.
• He notes he is skipping the rest of Book III, where Aristotle argues both sides and ties the knots — like the learned dispute over how many knots Shakespeare unties in one scene of Cymbeline (some say twenty-five).

6. Prooemium and play: Book III ties, IV–XIV untie (“the great turnaround”) #

The point: the structure of the Metaphysics is that of a play.

• Almost every work of Aristotle divides as Romeo and Juliet does, into prologue and play. Aristotle’s opening is what the Greek commentators call a prooemium — etymologically, paving the way. (Vatican II’s Dei Verbum has a prooemium in the official Latin; translations wrongly render it “introduction.”)
• The chief part of the prooemium is the skopos, a concrete Greek word for the target. Aristotle uses it in Nicomachean Ethics I of knowing the end of life: like a man with a bow. Sherwood Forest story: hard to hit the balloon at a distance even aiming — but not aiming, forget it.
• The plot is the soul of the play (Poetics), and a good plot ties and unties a knot. Shakespeare’s explicit use of the word in Twelfth Night: “O time, thou must untangle this, not I; it is too hard a knot for me to untie” — the disguised girl loving her master, sent to Olivia, who falls in love with her.
• Hence Book III ties the knots (Aristotle himself compares it to tying knots, as in the first reading), Books IV–XIV untie them; and hence another reason why the philomythos, lover of plots, is in some way a philosopher. Detective stories are said to be popular with high IQs.
• He promises the great turnaround will show almost the whole order within wisdom, and why it cannot be otherwise: “Aristotle is going exactly in the right order… proceeding orderly, easily, without error.”
• Handout distribution and a pun: asked about the loaves/Loes, “now you’re confusing theology and philosophy — multiplication of the loaves.”

7. The first sentence of Book IV, and its double question (“There is a reasoned-out knowledge… of being as being”) #

The point: the opening line contains two things to be shown, and the fifth reading likewise.

• Translation: “There is a reasoned-out knowledge [episteme] — or reasoned-out understanding — which looks at being as being, and what belongs to this through itself.”
• First thing: that such a knowledge exists (confirmed especially in Book IX on act and ability). Second: that this knowledge is wisdom.
• Parallel double question in the fifth reading, about the axioms: (a) is it necessary to consider the axioms by reason, or may one simply use them since all men know them? Reasons it is necessary: people deny them and give sophistical reasons others can’t solve; the axioms are expressed in equivocal words. (b) Does that consideration belong to the wise man rather than everyone, since everyone uses them? Should the man above everything “get down in the basement” to what all reasoned-out knowledge ultimately rests on?

8. What “through itself” means (“kath’ hauto in Greek… per se”) #

The point: from the Posterior Analytics, reasoned-out knowledge is of what belongs to a thing as such; so a science of being must treat what belongs to being as such.

• Geometry: the geometer does not treat the triangle as green, red or blue, though a triangle could be. Why not — because a triangle through being a triangle is not green; however well you understand what a triangle is, you would never see through it that it is green. That you learn by sense.
• What does belong kath’ hauto: the definition (a rectilineal plane figure contained by three lines); the property proved from it, interior angles equal to two right angles (Euclid I.32); and the division into equilateral, isosceles, scalene, which is a division of triangle as such. These may involve different senses of “through itself” — one like a definition, one like a property, one a division. (He says “in the postulates we distinguish these” — likely Posterior Analytics [ed.].)
• Philosopher: to love wisdom belongs to him as such; to be white, gray, Swedish or half Swedish does not. Heidegger: “philosophy speaks Greek” — a compliment to the Greeks, but speaking Greek does not belong to a philosopher as such. Schrödinger: no one has science who has not come into contact with the Greeks, science is the Greek way of looking at things — again a compliment, not what belongs to science as such.
• What belongs to being as such: to be good (seen in Book IX, when bad shows as a kind of non-being, and ability is good as ordered to act, though act is better); and more easily seen, to be one — for every being is simple or composed, and the composed would not be if its parts were not put together. Joke: if someone’s outside taking my car apart I have no car; “we take you apart, you won’t be anywhere.”
• He breaks off: next Thursday, how Aristotle reasons that the wisdom of the prooemium is this reasoned-out knowledge of being as being.

His words #

• ability / act — his standing rendering for potency and actuality [ed.: potency / act].
• reasoned-out knowledge (or understanding) — his translation of episteme.
• the second kind of mistake outside the words — the fallacy of “simply and in some way” [ed.: secundum quid].
• to doubt well — Thomas’s phrase: to attain well to the reasons for doubting.
• tropos — the way of reasoned-out knowledge, distinct from the knowledge itself.
• prooemium — from the Greek commentators; etymologically, paving the way; not “introduction.”
• skopos — the target aimed at; the chief part of the prooemium.
• philomythos — lover of plots, in some way a philosopher.
• mythos / lysis — the tying and the untying of the knot.
• eidos — species/form, got by adding the difference to the genus.
• kath’ hauto / per se / through itself / as such — what belongs to a thing through being what it is.
• the great turnaround — his name (capitalized in the syllabus) for the coming point in Book IV that reveals the order within wisdom.
• res extensa — Descartes’ identification of material substance with extension.

Texts #

Read in class

• Aristotle, Metaphysics III — the last two doubts (potency or act; by motion or otherwise) and the doubts on numbers, lines, figures, points and their separation; his closing remark that it is not easy even to doubt well.
• Aristotle, Metaphysics IV, first sentence (first reading of the handout); the fifth reading on the axioms, described not read.
• Euclid, Elements I.32 (inferred) — interior angles equal to two right angles; and the definition of triangle.

Mentioned

• Aristotle: Metaphysics II (end), IX (three parts), Categories (before and after), Sophistical Refutations, Posterior Analytics, Physics II, Nicomachean Ethics I, Poetics, Eudemian Ethics.
• Plato: Meno, Cratylus, Parmenides, Timaeus, Phaedo.
• Locke, Essay; Berkeley, Principles; Porphyry; Anaxagoras; Descartes; Hegel; Marx; Spinoza; Heidegger; Schrödinger’s essays; Newman on the idea of a university; Leo XIII quoting Cajetan on Thomas; Vatican II, Dei Verbum prooemium; Shakespeare, Romeo and Juliet, Twelfth Night, Cymbeline.

His questions #

• Which came first, the chicken or the egg — ability or act? Aristotle will distinguish senses of before and after in Book IX; the class does not yet settle it — left open here, but it decides whether the first cause is matter or pure act.
• Do things come to be otherwise than by motion? If understanding is not bodily, the soul did not come to be by transformation of matter — so not everything comes to be by motion, and there may be a beginning that creates.
• Are the three lines of the general triangle equal or unequal? Equal and unequal in ability, neither in act; the difference actualizes one of them.
• Is Aristotle’s philosophy true because it is in harmony with the Eucharist and useful in theology? No — it is in harmony and useful because it is true; the harmony is only a sign.
• Are numbers, lines, figures and points substances, and are they separate from sensible things? Platonists say separate, Pythagoreans (and in effect Descartes) say only in sensible things; reported as a doubt, left open.
• Why doesn’t the geometer talk about the triangle being green? Because it does not belong to the triangle through being a triangle; you learn it by sense, not by reasoning from what a triangle is.
• Is it necessary to consider the axioms by reason, and does that belong to the wise man? Necessary, because men deny them with sophisms and the words are equivocal; whether it belongs to the wise man is posed and reserved for the fifth reading.
• Is the reasoned-out knowledge of being as being wisdom? Posed; “let’s see how Aristotle brings that out” — taken up next Thursday.