Why Wisdom Defends the Axioms and the 'Great Turnaround' in the Order of Wisdom (Book IV, Reading 5; Overview of Book V)

Orientation #

He begins from the previous reading, where the philosopher showed that the wise man considers being as being, and (in a part not read) that being and one are convertible. This fifth reading shows that wisdom considers the axioms. At the end he has the Book Five handout passed out for what follows. The next class takes up Book Five itself, beginning with the senses of “beginning.”

The class, in order #

1. Why the axioms must be considered at all (“Why not just use them”) #

Recap of a question already dealt with. Since the axioms are the statements known through themselves by all men, why not simply use them?

• Because Sophists, ancient and modern, deny an axiom and even give a reason for denying it — a reason most people cannot untie, so that people begin to think they do not know what they do know. From Physics II: if, as Socrates showed, a man can think he knows what he does not know, the reverse is possible too. And if you think you do not know the axioms, you think you know nothing: a universal skeptic.
• Second reason: many of these objections rest on mixing up the senses of the words in the axioms. Aristotle discovered that the very words in the axioms are all equivocal — but equivocal by reason, there is a connection among the meanings. Distinguishing them both unties objections and gives a more distinct knowledge of the axioms than everyone has; and since the axioms are the beginnings of all our knowledge of statements, a distinct knowledge of them lets you build better.

2. Why the defense belongs to the wise man (“they pertain to being as being”) #

The axioms pertain to being as being, so the man who considers being as being and the one as one considers them. Clearest in the most fundamental axioms, those about being and non-being, of which he gives two:

1. something cannot both be and not be, in the same sense of being, at the same time;
2. something must either be or not be, in the same sense.

• Example: “To be or not to be, that is the question” — it is a question precisely because you cannot both be and not be, and must be one or the other. Contrast “to eat or to drink, that is the question”: not a question, you can and had better do both.
• Reading of the text: the investigation of the axioms belongs to one science, that of the philosopher (he notes Aristotle now calls the wise man simply the philosopher, by antonomasia), because they belong to all beings and not to one kind privately. Other sciences use them as beings, but only so far as their genus extends.
• Example: the mathematician says an odd number cannot be an even number — taking the impossibility of being and not being into his own domain.

3. The naturalists’ exception (“they thought it was first philosophy”) #

No one demonstrating by art tries to show the axioms true — not the geometer, not the arithmetician; Euclid takes them for granted. But some of the naturalists reasonably did touch on them, because they thought what they were doing was first philosophy.

• As Metaphysics VI says, if only material substances existed, natural philosophy would be wisdom. For roughly two hundred years the Greeks identified the two; with Anaxagoras, Plato and Aristotle came evidence of something that could be without matter.
• Physics IV: the common Greek opinion was that whatever is must be somewhere — “if you go on Main Street today you find that the common opinion too.” But to be contained in a place is a property of bodies, not of being as being.
• He notes the parallel division of the naturalists’ opinions in the second reading of Physics I: they talked about being the same way, since they identified natural things with all things.

4. Axioms are not proved (“there is nothing before them”) #

You do not try to prove the axioms: nothing is before them, and they are known through themselves, through their parts. Those who attempt it do so through want of training in the Analytics, where it is settled what can and cannot be proved. Should you try to prove the whole is greater than its parts?

• The same holds in lesser degree of the private beginnings of a science: all right angles are equal; Euclid’s fifth postulate. His brother Mark studied the historical attempts to prove the fifth postulate and showed (a) the proofs are not good, they are circular, and (b) the fact that they assume the very thing they are proving without realizing it is a sign that it is really obvious.
• The same with the principle of contradiction: men deny it because something they study seems to involve a contradiction — so they deny it because something contradicts it, accepting it in the attempt to overthrow it. “They’re saying it isn’t so because it is so.”
• Parallel in ethics: a man who says you should live by your emotions, if he argues about it, concedes that reason has the right to decide how you should live. (Aside: “Maybe he’s planning on arguing from his emotions.”)

5. The great turnaround, stated (“If you understand the great turnaround”) #

He puts three and three on the board. What we learn wisdom is about, in order: (1) the first causes (proemium); (2) being as being, and the one and the many (beginning of Book IV); (3) the axioms (this fifth reading).

• Warning against equivocation in “wisdom is about”: only being as being (or substance) is the subject; the first causes are the end or goal. This is why first philosophy is less wisdom than theology — theology has God as its subject, first philosophy does not.
• Every part of philosophy is about a subject and seeks the causes of that subject. But “wisdom is about the axioms” is unique to wisdom. From Ethics VI, where Aristotle distinguishes natural understanding (nous) from episteme and then wisdom from both: wisdom is the head of all understanding, embracing both, knowing the cause of the causes and also knowing what natural understanding knows, more distinctly and able to defend it. “Everybody has natural understanding, but they can’t defend it” — his students cannot answer sophistical objections against the whole being greater than the part; they are convinced, until he tries to show them they shouldn’t be.
• The order of treatment reverses this: the rest of Book IV defends the axioms of being and non-being; Books V–X consider being as being and the one and the many; the last books determine the truth about the first causes. (He says “in books seven through fourteen” while calling them the last four books — the numbering as he leaves it is inconsistent.)
• Summa Contra Gentiles II: God is the last thing considered in philosophy, the first in theology — the reverse orders. Theology’s order imitates God’s knowledge, who knows all things by knowing Himself.
• So: you learn wisdom is about A, then B, then C; then he takes up C, then B, then A. “That seems kind of screwy at first sight.”

6. The reason for both orders (“from what is more known to us”) #

A student proposes: because the axioms are the causes of our knowing the other things. He presses for the one underlying reason.

• The second order is easy: the axioms are the statements most known of all; the first causes are least known to us; being as being lies in between, less known than the axioms, more known than the first causes, just as effects are usually more known than causes. The rule is the inborn road: from what is more known to us toward what is less known.
• The paradox: what is most known to us (the axioms) is least known to be what wisdom is about; what is least known to us (the first causes) is most known to be what wisdom is about. And this is the same rule: the first order too goes from what is more known to us to what is less.
• Why it is not really paradoxical: we look to the wise man as knowing more than the rest of us. Asking freshmen whether wisdom comes at the beginning, the middle, or the end of our knowledge, they say the end. So the last thing you would think wisdom is about is what everybody knows. One might doubt whether the first causes can be known, but no one doubts that a man who knew them would be wise.
• Why “being as being” also sounds unlike wisdom: we think the more advanced knowledge is the more particular. Example: asked what he has been given to drink, “something, not nothing” is very general; “a glass of water” is more advanced; “a dry red wine” more still; and the man who can say “Napa Valley Cabernet Sauvignon” goes beyond the man who says only “dry red wine.”
• The tree: the tree is above all other plants, and its roots go below all the others — and the two are connected, and botanists would say height and root system are proportional. So the wise man rises above everyone in knowing the first causes and goes deepest of all back to the beginnings.

7. Not merely common sense (“glorified common sense”) #

A student offers the phrase “glorified common sense” for the defense of the axioms. He accepts it only so far: some of these arguments are very difficult.

• De Koninck’s article in Laval théologique et philosophique, in French, on the paradox of becoming — paradoxion, from being to not being. Hegel in the 19th century argued that in becoming the same thing both is and is not; that is solved by Aristotle in Physics VI, but it is very difficult. The article shows the difficulty felt all through the Middle Ages over the Eucharist; Thomas could solve such difficulties because he knew Aristotle.
• The easier case, solved in Physics I, eleventh reading: Heraclitus says day and night are the same because day becomes night, and hard becomes soft — one contrary comes to be the other.
• Zeno’s paradoxes: you cannot walk out the door, since you must first walk half the way, and half of the half, and so on forever, since the continuous is divisible forever; and Achilles never catches the tortoise given a head start, since he must first reach where it was, by which time it has moved on. Aristotle unties these in the eight books of Natural Hearing; most people cannot. Hence in the rest of Book IV he shows where these doubts arise — many from motion and change — and how they are solved.

8. The three considerations are continuous (“the end of one is the beginning of the next”) #

Not only is the order right; the parts are “continuous,” imitating Euclid’s continuous proportion.

• Euclid: 4 is to 6 as 6 is to 9 is continuous, the end of one ratio being the beginning of the next; 2 is to 3 as 4 is to 6 is proportional but not continuous, since 3 is not 4. So he calls syllogisms continuous when the conclusion of one is a premise in the next. Example: Euclid II.14, finding the side of a square equal to a given oblong, uses the Pythagorean theorem (end of Book I) and the theorem about cutting a line into equal and unequal segments. Definitions could be called continuous likewise — quadrilateral and square.
• The upper three: from wisdom being about the cause of all things he reasons to wisdom being about what is said of all. Example: the science about the king speaks of what is said of more than the science about the general — the general’s science speaks of the soldier, the king’s of the citizen. So the proemium’s conclusion is the premise for Book IV; Book IV’s conclusion (wisdom is about being as being) is the premise for showing it is about the axioms, since the axioms are about being as being.
• Example of tightness: between Mexico and the United States, and between the United States and Canada, there is no country in between.
• Aside on six days: Euclid taught Augustine and Thomas that six is the first perfect number — measured by 1, 2, 3, not by 4 or 5, and 1+2+3=6, with nothing between one, two and three; the next perfect number is 28. So six symbolizes the perfection of what God has made, and need not mean six ordinary days.
• The lower three are continuous the same way: the axioms, though not conclusions, are premises for reasoning out an understanding of being as being; and that understanding gives the premises for reasoning out what the first cause is. He stresses Book Nine, on act and ability, and in fact its third part, as giving the premise for knowing that God, rather than matter, is the beginning of things.

9. What the turnaround does not explain (“It doesn’t explain why the third book is there”) #

This accounts for the proemium and Books IV to the end, not for the rest of Book I, nor Book II, nor Book III.

• Book III (dialectic) comes first for a reason given at the beginning: dialectic before determining the truth.
• The rest of Book I: to find out whether wisdom can be learned from one’s predecessors or must be discovered oneself, with their help.
• Book II starts from the same premise (wisdom is about the first causes) but goes in a different direction: that consideration of truth belongs most of all to the wise man, in two steps — (1) it belongs more to looking than to practical knowledge, since truth is the end of the one and not of the other, and the practical man’s truth is often contingent; (2) among the looking sciences, the cause is more true than the effect, by the rule that when the same belongs to two things, but to one because of the other, it belongs more to the cause; therefore the first cause is most true. “As a thing is in being, so is it in truth.” As a Catholic he adds: God to Moses, “I am who am,” and Christ saying “I am,” and “I am truth itself.”
• He calls these in his article the secondary things wisdom is about: how man stands toward knowing truth, how the road to truth should be determined. Parallel: geometry is primarily about lines, angles, plane and solid figures, but it belongs to geometry secondarily to know how geometry proceeds, for the sake of those.

10. Book Five and Thomas’s division (“names pertaining to causes, subject, properties”) #

The handout is passed out. Thomas, in his exposition (he notes Thomas commented only the first twelve books, which gets to God), places Book V as the first book of the consideration of being as being and the one and the many.

• Reason: Book IV taught that being is equivocal. Could there be one science of what is said equivocally? Not if equivocal by chance. Example: “bat” — the baseball bat and the flying mouse (as the German name has it); no reason to treat them in one science. And a man named Fox and the animal. But the words about being are equivocal by reason, so Book V distinguishes and orders their meanings as a preliminary.
• His own addition, “not contradicting Thomas”: Book V is also in a way the end of the defense of the axioms, since these words are the words in the axioms too, useful for a distinct knowledge of them and against the commonest attack, equivocation (he mentions equivocating on two senses of “part”). So again the end of one is the beginning of the other.
• Aside on where wisdom begins: the culmination of the three books on the soul, and of Plato’s Phaedo, is the immortality of the human soul — a sign being that it has an operation not in the body. With that, or with showing the unmoved mover is not a body, you are at the end of natural philosophy and the beginning of wisdom — meta ta physika, after the books of natural philosophy.
• A third use of Book V: all other parts of philosophy use these words. He uses “perfect” in ethics to understand the better, and “nature” when teaching natural philosophy.

11. The three groups and his three chosen words (“the rule of two or three”) #

He asks the class how Book V is divided, invoking his rule of two or three (Matthew in three parts, John in two). Answer: three, because every science has a subject, causes of that subject, and properties.

1. Names of causes: beginning, cause, element, then — “strange as it may seem” — nature, since one meaning of nature is what a thing is, common to all things; then necessary, which seems tied to cause, since something follows necessarily from a complete and unimpeded cause. Order: every cause is a beginning but not every beginning a cause; every element is a cause but not every cause an element. His chosen word: beginning (the first).
2. Names of the subject: one, being, substance, then the parts of one and of being. His chosen word: being — “the most key word.”
3. Names of properties: first and fundamental is perfect; perfect and imperfect belong to the very first divisions of being — substance and accident, act and ability, one perfect and the other imperfect — and this is tied to the good. He compares Thomas in theology showing God is perfect and attaching to it the goodness of God.

• So one word from each group, the first in the first and third groups and the simplest in the second.
• Aside: at Laval, after his time, a whole course was given on Book V; his own first course there was on Book IV, the defense of the first axioms, compressed into extra weekly meetings because the teacher was leaving for Europe.
• Closing: Aristotle was the first man fully to realize that the words in the axioms are all equivocal by reason, and that these same words name the subject of the science and are used of causes and properties — an enormous task done for us, helping us to understand and defend the axioms, to speak clearly in wisdom, and to some extent in all the sciences.

His words #

• Natural Hearing — his rendering of Aristotle’s Physics, “the so-called Physics.”
• reasoned-out knowledge / reasoned-out understanding — episteme [ed.: science].
• natural understanding — nous, the habit of first principles; wisdom is “the head of all understanding,” embracing it.
• looking knowledge / looking sciences — [ed.: speculative or theoretical].
• ability — [ed.: potency], as in “Book Nine, on act and ability.”
• axioms — “the statements known through themselves by all men,” the beginnings of all our knowledge of statements.
• equivocal by reason vs. equivocal by chance — many meanings with a connection among them vs. mere coincidence of name (“bat”).
• the great turnaround — his own name for the reversal of the two orders.
• continuous (of syllogisms and of definitions) — borrowed from Euclid’s continuous proportion: the conclusion of one is a premise of the next.
• private beginnings — the proper principles of a particular science, as against the common axioms.
• the philosopher — Aristotle’s name for the first philosopher or wise man, “kind of by antonomasia.”
• paradoxion — as he glosses it, “from being to not being,” in De Koninck’s title on the paradox of becoming.
• meta ta physika — “after the books of natural philosophy.”
• the rule of two or three — his rule of thumb that a book divides into two or three parts.
• secondary things wisdom is about — how man stands toward knowing truth, as opposed to the three primary things.

Texts #

Read in class

• Aristotle, Metaphysics IV, fifth reading — the whole passage on whether one science treats the axioms, the naturalists’ exception, and the Analytics.
• Aristotle, Metaphysics V — handout distributed; its division surveyed, not yet read.

Mentioned

• Aristotle, Physics II (thinking one knows what one does not); Physics I, second reading (division of the naturalists’ opinions) and eleventh reading (Heraclitus); Physics IV (place); Physics VI (the paradox of becoming); the eight books generally (Zeno).
• Aristotle, Metaphysics proemium, Books I (rest), II, III, VI, IX (act and ability, third part); Nicomachean Ethics VI; De Anima, three books.
• Thomas Aquinas, Commentary on the Metaphysics (division of Book V; only twelve books commented); Summa Contra Gentiles II; Summa Theologiae on God’s perfection and goodness (inferred).
• Euclid, Elements: axioms, the fifth postulate, I (Pythagorean theorem), II.5 and II.14, perfect numbers.
• Plato, Phaedo; Hegel; Heraclitus; Zeno; Anaxagoras; Socrates.
• Charles De Koninck, article in Laval théologique et philosophique on the paradox of becoming.
• Shakespeare, Hamlet, “to be or not to be.”
• Exodus, “I am who am”; Christ’s “I am” and “I am truth itself.”

His questions #

• Why is it necessary to consider the axioms rather than simply use them? Because sophists deny them with arguments most people cannot untie, and because distinguishing the equivocal words in them gives a more distinct knowledge on which to build.
• Why does the defense of the axioms belong to the wise man? Because the axioms pertain to being as being, which is the subject of his science.
• Should you try to prove that the whole is greater than its parts? No; there is nothing before the axioms, and they are known through their parts.
• In what sense is wisdom “about” the first causes, being as being, and the axioms? Being as being (or substance) is its subject; the first causes are its end; the axioms belong to it as it embraces natural understanding.
• Why is the order of learning what wisdom is about exactly the reverse of the order of treating those things? Both follow the one rule of going from what is more known to us to what is less known.
• Is it still the rule of “more known to us” in the first three, where we learn wisdom is about the first causes before the axioms? Yes — it is more known to us that wisdom is about the first causes than that it is about what everybody already knows.
• Is the defense of the axioms just “glorified common sense”? Only in a way; some of these untyings (Hegel, Zeno, Physics VI) are very difficult.
• How is Book Five divided, and why have I chosen three words from it? Into names of causes, of the subject, and of the properties — hence beginning, being, perfect.
• Could the order be otherwise? No.