Metaphysics III, Second Reading: Which Causes Wisdom Studies, the Axioms, and Whether the Way We Know Must Be the Way Things Are

Orientation #

He is continuing through Book III of wisdom [ed.: the Metaphysics], having done the first reading earlier (“this is from the last time”). He divides the second reading into nine questions and says the third reading will have fourteen; today he treats only the first two, plus the two “stuck-in” questions about immaterial substances, and ends saying “we’ll come back to these questions here in this second reading.” Handouts on the word “beginning” and on “the first statement and king of statements” belong to this hour.

The class, in order #

1. Why the second reading differs from the third (“you can’t at the same time learn reasoned-out knowledge and the way”) #

• Thomas takes the division from the end of Book II: you cannot at once learn reasoned-out knowledge and the way of reasoned-out knowledge, and neither is easy.
• Since the way must fit what the knowledge is about, questions about what wisdom is about come first (second reading); questions about the things themselves come second (third reading).
• The same split is the split between what we know and how we know. Aside: reading Matthew 10 (the sending of the twelve), he noticed Christ says two things — how you are to speak and what you are to say (Greek pōs, Latin quomodo; then quid).
• Custom shapes both. In the fifth reading of Book II Aristotle notes men accustomed to mathematics want to proceed mathematically everywhere — the Pythagoreans, and the moderns with their mathematical and symbolic logic. Thomas in the Summa contra Gentiles says men think God’s existence obvious from childhood custom. His students say water is H₂O with no doubt and cannot describe one experiment for it.

2. First question: which causes does wisdom consider? (“whether it belongs to one or many forms of reasoned out knowledge”) #

• The four causes from the first book of Natural Philosophy, on the wooden table: wood (matter), the shape (form), the carpenter (mover), something to put papers or lunch on (end).
• The difficulty: each science seems to take one or two. The natural philosophers talk of matter, and with Empedocles and Anaxagoras also the mover (moderns: mass and force). The geometer takes form; the moral philosopher takes end.
• So no one science seems to treat all causes — yet which one then belongs to the wise man?
• Student: wouldn’t metaphysics have a strong claim to all the causes? — His reply: if everything were material, matter would be cause of everything and wisdom would just be natural philosophy; but in natural philosophy Aristotle proved an unmoved mover, and in the De anima the soul immortal. So the question whether there are immaterial substances bears on this one: if there are, matter is only a particular cause, cause of material things.
• Likewise geometry uses form only in a limited way, and ethics the particular end of man, not the end of everything.
• The disagreement is real: the Platonists and Pythagoreans reduced all to numbers, making form the only cause. Schrödinger — who perfected the mathematics of wave mechanics, Heisenberg publishing quantum mechanics the same year with different mathematics, Schrödinger then showing the two formalisms equivalent — said the modern atom consists of no stuff at all, and compared this to the Timaeus, where the four elements are geometrical figures with no matter. Aside: the Moscow communists looked at modern science strangely, since it seemed to deny there is any matter.

3. Second question stated: only beginnings of substance, or also the first statements? (“or also the beginnings of which all demonstrate”) #

• Substance = the fundamental things. But does wisdom also consider the beginnings from which all demonstrate, e.g. that the same cannot be affirmed and denied at once?
• The first beginning stated of things: something cannot both be and not be — “more precisely, at the same time, the same way.” Sometimes two are given: it is impossible to be and not be; you must either be or not be. Illustrated by “To be or not to be, that is the question” — it is a question because you can’t both be and not be, and because you must be one or the other. “To breathe or to eat” is no question: you can and had better do both.
• Stated with the help of logic: you cannot affirm and deny the same of the same at the same time. Other axioms: the whole is larger than one of its parts; nothing is before itself; nothing is the beginning of itself. Euclid gives some at the beginning of the Elements: the whole larger than a part; equals added to equals give equals; quantities equal to the same are equal to each other (if he is your height and he is your height, what about you two?).
• Boethius: such statements are known through themselves, unproven, and known by everybody.
• He divides the question in two: (a) is it necessary to consider the axioms at all? (b) to whom does that consideration belong?

4. Must the axioms be considered? (“why bother… just use it”) #

• Objection: everybody knows them — a man who says he doesn’t know the whole is more than the part will scream if given part of his dinner, part of the car he bought, part of his salary. You don’t prove the obvious; you use the obvious to prove what is not obvious.
• Against: men do deny the axioms in words and give reasons most people cannot answer. His own stock argument: man is an animal (his mother objected; “an animal that has reason”), so animal is a part of man and not the whole; but animal includes besides man dog, cat, horse, elephant — so the part is more than the whole. His students are convinced, “and therefore they think they don’t know what they do know.” Bertrand Russell gave a harder argument that the part equals the whole; his teacher Charles De Koninck showed its defect. Zeno argued you cannot walk out the door.
• Since someone must answer such objections, it is necessary to consider the axioms.

5. The objections rest on equivocation (“mixing up different senses of whole and part”) #

• Animal is part of the definition of man: a composed whole, put together from its parts (animal plus reason). Animal said of man, dog, horse is a universal whole, said of its parts. This distinction is one of the fundamental ones of the fifth book of wisdom.
• So “more” shifts too: the composed whole is put together from more than any one part; the universal whole is said of more than any one part (animal is said of more than dog, quadrilateral said of more than square). Man is more than animal (put together from more); animal is more than man (said of more).
• The words of the axioms are therefore equivocal — not purely, there is a related and connected meaning. Hence “particular” comes from part, and the Greek for general, katholou, from holos, whole — whence “catholic.”
• Most men have only a confused knowledge of the axioms; distinguishing the senses gives a distinct knowledge, and is especially needed to meet the common objections.
• “Nothing is before itself”: today is before tomorrow, yesterday before today; if A before B and B before C then A before C. Chaucer came before Shakespeare, but the critics put Shakespeare before Chaucer — so Chaucer is before Chaucer. Student: needs a qualification. — Yes: before in time vs. before in excellence.
• “Nothing is a beginning of itself” (Physics I), where there is always a distinction between the beginning and that of which it is beginning. Objection: the foundation is the beginning of the house and also a part of it (so too the keel of the ship, Aristotle’s example). Answer: in that sense of beginning the distinction is between the fundamental part and the whole; take an extrinsic beginning — your father is your beginning and no part of you — and the distinction is sharper. The distinction differs with the sense of “beginning.”

6. Whose business is it? (“why should it belong to him more than anybody else”) #

• Difficulty: everybody uses the axioms; and since the question is put in terms of affirming and denying, it looks like the logician’s job — or the geometer’s, since Euclid states the axioms.
• Student: Euclid only posits them, never discusses them, only uses them. He agrees Euclid is one of the few who tries even to state them.
• Aristotle gives the reason why it belongs to the wise man in the fourth book. Aside: even Aristotle and Thomas hardly enumerate axioms — the ones about being and non-being, and “the whole is more than the part,” and that is about it; “I don’t think they could ever enumerate them all.”
• Thomas, following Averroes: as in natural philosophy and ethics, dialectical disputation precedes determining the truth; but there the dialectic is particular (a little about place at the start of Book IV, then the truth about place), while here a whole book is dialectic about all the main problems of wisdom. This shows an affinity of logic with wisdom — Plato in the Republic identifies dialectic with wisdom.

7. The remaining questions, and the two that don’t belong (“it is also necessary to investigate whether only sensible or material substances exist”) #

• The first two questions concerned causes or beginnings. The rest concern things, divided by substance and accident: substance is what exists not in another as in a subject (man, dog); accident exists only in another (health, shape, knowledge, virtue of the man). Of the remaining questions, the first four or five are about substance, the last three about accidents. (He hesitates between “first five” and “first four”; he leaves the count loose.)
• The exception: two questions here are about the things themselves — whether only material substances exist or also others, which the philosophers call separated substances (“angels” is a name from Scripture, from their task of carrying messages); and, if there are such, whether there is one kind or many.
• They are stuck in here because they bear on what wisdom is about: if there are immaterial substances, is there one knowledge of both material and immaterial substances, or two — and which is wisdom? In the dialectic proper (not read in this course) these are pulled out as a separate part.
• Anaxagoras posits only the greater mind, unmixed with matter; Plato posits the Forms and the mathematical substances.

8. The central question of philosophy (“does truth require that the way we know be the way things are?”) #

• He calls it central because it joins the end of philosophy (truth) with the only two things the philosopher ever talks about: the way things are (natural, political, all things) and the way we know (logic, and the road of each science).
• Two possible answers — “they’re looking for something very deep and obscure; I’m looking for yes or no.” Plato answers yes, Aristotle no. Down the history of thought more agree with Plato, often implicitly; “few would agree with crazy Aristotle.”
• Why men lean to Plato: a confused notion of truth as agreement or harmony of the mind with things. If I say you are sitting and you are, I am true; if I say you are standing, false.
• Aristotle’s answer, seen first in particular and then more universally (as Thomas says in the Summa theologiae, in the question on the teacher). In the second book of Natural Hearing [ed.: Physics II]: we can truly know in separation what does not exist in separation. Sugar is white and sweet: the eye knows the whiteness without the sweetness, the tongue the sweetness without the whiteness — incomplete knowledge, but not false. Falsity would come only from saying “this white thing is not sweet.”
• His students know him as a philosopher leaving out that he is a grandfather; the nurse knows the grandfather and not the philosopher. Neither is false; “this philosopher is not a grandfather” would be.
• Cube: I know the shape cube apart from ice cube, sugar cube, wooden cube, plastic cube. Plato, rightly convinced that geometry is true, and answering yes to the question, had to posit a mathematical world besides the sensible one.
• Order as well as separation. I know you before your parents, your parents before your grandparents; in things the order is the reverse. My knowledge may be imperfect — not seeing your parents’ influence — but not false. (Aside: after his businessman father died, people said “that’s just like your father”; he imitated him without realizing it, “a no-nonsense guy.”) Water is known before hydrogen — which is named from water — and hydrogen before proton, though proton means first: what is first in things is last in our knowledge. Sherlock Holmes to Watson: we must reason backwards, from effect to cause. “Our mind goes forward by going backwards.” Falsity comes only from attributing the order of our knowing to things: saying you really came before your parents.
• Socrates saw the role of definitions and convinced Plato that through definition we know the truth. But defining man as an animal that has reason, no individual man is in the definition — we know the universal in separation from singulars. Answering yes, Plato had to make the universals exist separately: the Forms (eidos, form; “ideas” is a bad translation).
• Aside: you remember the past now; the now is in your knowing, and only thinking the past is now is a mistake.

9. The yes-answer after Plato, and Boethius’s change of side (“introduces Aristotle as a true follower”) #

• Ockham (14th c.): no world of forms, no universals — but our knowledge is universal, therefore we know nothing: universal skepticism.
• Marx (19th c.) takes experimental science as the only way of knowing, by custom; and Kant points out that in experimental science we know by making. Answering yes: we know only what we make, and I am beginning and end of what I make — therefore I am God.
• Hegel makes the beginning of everything correspond to the beginning of our thought; the most confused and general thought is the thought of being, which he identifies with the one who says “I am who am” — a terrible confusion leading to pantheism, as with all the German thinkers after him. Spinoza had already said the order of our thoughts and the order of things are the same; Aristotle says they are for the most part contrary.
• Boethius in the Consolation I announces himself a member of the Academy, Plato’s school, and his early treatment of happiness is Platonic. But in Book V, to defend God’s eternal knowledge — no before and after in it, yet the past, present and future of time all present to it and truly known — he must give up Plato and follow Aristotle: Lady Wisdom introduces Aristotle as a true follower, politely (salva reverentia, as when Thomas disagrees with Albert without naming him).
• His example of the non-conformity in human knowing: I know fully what a square is by its definition — an equilateral, right-angled quadrilateral — but the definition is not continuous while the square is. So we know a continuous thing in a non-continuous way; which is also one way of seeing that the reason knowing the universal is not a body.
• Aristotle’s final refutation of Plato, he says, is in the thirteenth and fourteenth books of wisdom.

His words #

• reasoned-out knowledge — knowledge through reasons, as against its way or road [ed.: scientia / demonstrative science].
• wisdom — the science of this course, whose books are cited by “book” and “reading” [ed.: Metaphysics; lectio].
• beginnings — principles and causes; also the first statements.
• known through themselves — Boethius’s term for unproven statements known to all [ed.: per se nota, axioms].
• composed whole — a whole put together from its parts (the definition of man).
• universal whole — a whole said of its parts (animal said of man, dog, horse).
• set of — said of, predicated of (ASR spelling of “said of” throughout).
• separated substances — the philosopher’s name for immaterial substances; “angels” is from Scripture.
• Natural Hearing — [ed.: Aristotle’s Physics].
• Perkus / Perkins — ASR for his own name [ed.: Berquist].

Texts #

Read in class

• Aristotle, Metaphysics III, second reading: first question (whether one or many sciences consider the causes); second question (beginnings of substance or also the beginnings of demonstration); the paragraph “whether only sensible or material substances exist, or others besides these.”
• Aquinas, Commentary on the Metaphysics V, lect. 2, on the senses of “beginning” (inferred, from the handout matched to this hour; he treats foundation of house, keel of ship, father).
• Matthew 10 (how you are to speak, what you are to say).

Mentioned

• Aristotle, Metaphysics II, end, and its fifth reading (custom); Metaphysics IV (why the wise man treats the axioms); Metaphysics XIII–XIV.
• Aristotle, Physics I (nothing is a beginning of itself; four causes); Physics II (knowing in separation); Physics IV, beginning (dialectic about place); De anima.
• Aquinas, Summa contra Gentiles, beginning; Summa theologiae, question on the teacher; Averroes on Book III.
• Euclid, Elements, axioms. Plato, Timaeus, Republic. Boethius, Consolation of Philosophy I and V. Shakespeare, Hamlet (“To be or not to be”). Schrödinger, Heisenberg, Russell, De Koninck, Ockham, Kant, Marx, Hegel, Spinoza, Conan Doyle.

His questions #

• Which causes does wisdom consider, when natural philosophy takes matter and mover, geometry form, ethics end? Left open here as a difficulty; it turns on whether there are immaterial substances, which would make matter only a particular cause.
• Does wisdom consider only the beginnings of substance, or also the first statements on which all demonstrate? He argues it must consider them; Aristotle gives the reason in Book IV.
• Is it necessary to consider the axioms at all, when everybody knows them? Yes: men deny them in words with reasons most cannot answer, and our knowledge of them is only confused until the senses are distinguished.
• Is the part ever greater than the whole (animal, part of man, said of more than man)? No: the objection equivocates on composed whole and universal whole, and on “more.”
• Can Chaucer be before Chaucer, since Shakespeare is put before Chaucer? No: before in time and before in excellence are different senses.
• Is the foundation a beginning of itself, being both beginning and part of the house? No: the distinction there is between the fundamental part and the whole, unlike an extrinsic beginning such as your father.
• Why should considering the axioms belong to the wise man rather than the logician or the geometer? Left open today, with the note of an affinity between logic and wisdom (a whole dialectical book, Plato identifying dialectic with wisdom).
• Does truth require that the way we know be the way things are? No — Aristotle’s answer; we truly know in separation, and in reverse order, what does not exist so; falsity comes only from attributing our way and order to things.
• Is the eye false in knowing the whiteness of sugar without its sweetness? No — incomplete, not false.
• Is our mind false in knowing water before hydrogen, or you before your parents? No: our mind goes forward by going backwards.