Books Two to Four: Truth, Dialectic, Being as Being and the Axioms

Orientation #

He opens by continuing the fourteen questions of Book III (“Now he comes to the two last questions”); the first twelve were treated earlier (prev. lecture). The class reads from his handout The Matter and Order of Wisdom, p. 9 (verified source; also DHB Vol. III p. 458). The previous class went through the twelve questions arranged around Plato’s separated universals; the next treats the “great turnaround” in the order of Books IV–XIV.

The class, in order #

1. The thirteenth and fourteenth questions (“whether numbers and magnitudes and figures and points are substances”) #

Point: the last two questions are divided against the other twelve because they bear on Plato’s other unique position, the mathematical things in between the forms and sensibles.

• Recap: the twelve were about Plato’s universals separated from matter (other positions brought in by their opposition), six of them subjoined on how these things are: four on one and many, two on act and ability.
• Q13: whether numbers, magnitudes, figures, points are substances. Platonists and Pythagoreans say yes; the other Greeks say substances are earth, air, fire, water.
• Q14: if substances, whether separated from sensible things (Plato: a mathematical world besides the forms and the sensible world) or only in the material things (Pythagoreans: the substance of things is mathematical, but only in them — “I got your number”).
• Descartes identifies the substance of material things with their extension (continuous quantity). The man in the street is wiser: what a dog is and the size of a dog are not the same. Student: Descartes and Pythagoreans agree that substance is quantity, differ as continuous vs. discrete? Berquist: perhaps; more importantly they agree the mathematical is in things, against Plato.
• Theological footnote: if substance is extension you cannot understand the Eucharist, where the quantity of the bread remains and the substance changes; you get coexistence and heresy. Notice the before and after: we do not say Descartes is false because it does not fit the Eucharist; it does not fit because it is false.
• Joke: on Descartes’ view “you never grow up” — only a substance with different quantities at different ages grows.

2. Why Plato orders the questions, and the difficulty of doubting well (“difficult to doubt well about them”) #

Point: the fourteen questions are arranged around Plato’s two positions, which shows the respect due him: his opinions most of all speak of a world besides the material one, so he is fit to distinguish and order the questions of wisdom.

• Aristotle’s closing remark: it is hard not only to find the truth here but even to doubt well, to reach the reasons why they are doubtful. Student: of the mathematical questions only? Berquist: of the whole — recall he called the question on the one “most difficult of all” (khalepōtaton).
• Compares Book II, fifth reading: possessing knowledge over a road and knowing what that road is are not the same, and neither is easy.

3. Plato’s argument for the forms: through itself before through another (“the man himself to himself”) #

Point: besides Thomas’s usual diagnosis (Plato thought the way we know must be the way things are, from the certainty of mathematical definitions), Plato’s forms can be reached from a true principle: the through-itself is before the through-another.

1. If something is sweet but not through itself, there is something else which is sweet, by which it partakes sweetness. (Aristotle uses the same: if emotions can be reasonable but not through being emotions, there is something reasonable through itself.)
2. Socrates is not a man through being Socrates — else I would be a man through being Berquist, and everyone would have to be Socrates to be a man.
3. So Socrates is a man through another; behind Socrates and Plato there must be one who is man to himself — the form. Plato’s Greek is almost redundant: “the man himself to himself.”

• Deeper form of step 2: one is a man through what a man is; only what is identical with what a man is would be a man to itself; Socrates is not identical with it (else he would be the only man).
• Aristotle got thinking about kath’ hauto through Plato; it is among the words of Book V and prominent in logic. Brother Mark’s Euclid illustration: I.5 and I.6 turn each other around (two sides equal ↔ two angles equal); I.47 (Pythagorean theorem) and I.48 its converse — showing the property belongs through itself.
• Other uses by Aristotle: statements known through another need statements known through themselves; rational by participation needs rational through itself; the three friendships — the friendship of virtue is more friendship because I love you through yourself (what you are), not through pleasure or usefulness. Illustrated by Hamlet to Horatio: “give me that man that is not passion’s slave” — not the man who pleases or is useful to me. Student: virtue is a habit, a second nature; Berquist: or it perfects what you are.

4. What is wrong with Plato’s argument? (“the thing and what it is are not identical”) #

Point: Plato’s great discovery was that in material individuals (even mathematicals) the thing and what it is are not identical; his error is in the forms.

• Student’s attempt (being through itself rather than man through itself; exemplar cause): “you’re getting too far ahead.”
• Berquist: what is true of immaterial substances — thing and what-it-is are the same — Plato applied to the forms. But what a man is involves matter. If the forms are immaterial they do not contain the nature of man; if material they are not universal but back in the synolon. Student: so strictly true of angels. Berquist: yes, more true of them.
• Asides: Albert the Great says to be complete in philosophy you must know Plato as well as Aristotle; Thomas calls them the chief philosophers, sophoi kyriōs; Boethius would agree (Augustine perhaps lacked Aristotle). No modern pair is like them: moderns do not build on each other — Descartes “the Father of Modern Philosophy, but he has no sons” (his joke to his teacher Saint-Jacques).
• Asides: Brother Mark’s parody “Liberalism More Geometrico Demonstrata” (on Spinoza’s title); Smollett’s Euclidean joke that a young man’s mind and discretion “extended, never meet.” Break for confessions/retreat.

5. Book II: how man is toward knowing truth, and why the wise man considers it (“even a large amount of truth becomes easy”) #

Point: Book II’s opening on how man stands toward truth belongs to the wise man because truth belongs most of all to him.

• Easy in three ways: no life misses truth entirely (even a hamburger cook learns they contract in cooking); by the efforts of many even a large amount becomes easy (one theorem each from every TAC graduate; “many hands make light work”); some truth is like the proverbial door no one misses (a whole is more than a part). Then how one man helps another.
• Why the wise man considers it: (1) truth belongs more to looking than to practical knowledge, since it is the end of looking knowledge; the practical man deals with things “not very true” — France friend then enemy of England, the stock market up and down. (2) Among looking sciences, wisdom is about the most true: the cause is more true than the effect, by the famous proposition that when the same belongs to two but to one because of the other, it belongs more to the cause; so first causes are most true; “as things are in being, so they are in truth.”
• Subplot of Book II: to argue this he must show there are first causes, so he shows a first cause within each of the four kinds confirmed in Book I.

6. Tying and untying the knots: why wisdom needs dialectic (“reason guesses before it knows”) #

Point: Books III–XIV divide like a play (Poetics): Book III ties the knots (dialectic, the discovery part of logic), IV–XIV untie them.

• A before and after of reason: it guesses before it knows; even the geometer guesses a theorem before seeking why it must be so.
• Geometry does not need dialectic: men guess alike before demonstrating (I.5; angles of an equilateral triangle), and geometry is the reasoned-out knowledge closest to imagination, which does much of discovering.
• Natural philosophy and wisdom need reasoning pro and con because men think opposite things before they know. Two contrary causes of difficulty (back to Book II’s beginning): in natural philosophy the difficulty is in the things — they hardly exist (time: no past, no future, no now in the strict sense); in wisdom it is in us — the things are above our mind.
• Last part of Book II: do not fix the way of proceeding by custom, though most men do; find the matter of the science and the road that fits it, as tools fit wood or cloth; do not seek the knowledge and its way at once. So Book III’s dialectic includes difficulties about the way of proceeding, which go back to what wisdom is about. Subtle preparation: the division of Book III’s dialectic depends on the last reading of Book II; the need of dialectic at all on its first reading.

7. Book IV: wisdom is about being as being (“science about the king, you talk about the citizen”) #

Point: from being about the first causes Aristotle reasons to being about being as being.

1. The more universal the cause a science considers, the more things its causality extends to, so the more its subject is said of. Example: a science of the king is about the citizen, of the general about the soldier; every soldier is a citizen, not conversely.
2. The science of the most universal causes must be about what is said of all — being.

• Objection: being has many meanings, so how one science? Reply: the meanings connect and go back to substance (size, disposition, relation of substance; coming to be or lack of these). Analogy: political philosophy is about the polis, yet treats government (rules the polis), law (government rules by laws), revolution (change of government) — each further from polis but going back to it, as to substance in wisdom.
• One is more or less the same as being — “don’t go into all that.”

8. Is wisdom also about the axioms? (“to think you don’t know what you do know”) #

Point: the subtle question from Book III — is wisdom about the beginnings of all knowledge too? — requires showing both that the axioms must be considered and that the wise man is the one to do it.

• Objection: they are known to everyone; why not just use them?
• Why consider: sophists object to the axioms and most cannot answer. Physics II: as Socrates showed men think they know what they don’t, the reverse is possible — thinking you don’t know what you do know — because the mistake comes from being unable to tell two things apart (Budweiser/Miller; taking a man for a woman). A philosopher once told him the principle of contradiction “has taken quite a beating.”
• Answering the objections shows the names in the axioms are equivocal by reason, and some sophisms trade on this. His own sophism: the whole is larger than the part; animal is part of man (man is a rational animal); yet animal includes dog, cat, horse — so a part exceeds its whole? Resolution: composing part of a definition vs. universal whole said of its subject parts. Distinguishing gives distinct knowledge: a composed whole is composed of more than one part; a universal whole is said of more than one.
• If a man thinks he lacks the foundation of all reasoned-out knowledge, “it’s over for him.”
• Why the wise man: the axioms involve being as being (nothing can both be and not be; must either be or not be — Hamlet’s question is a question because of this), and wisdom is about being as being and distinguishes its senses.

His words #

• ability — his rendering of potency [ed.: potency]; “act and ability.”
• before and after — a priority/posteriority relation (Descartes and the Eucharist; reason guesses before it knows).
• looking knowledge — theoretical/speculative knowledge [ed.: speculative]; practical knowledge is for doing.
• reasoned-out knowledge — epistēmē, science.
• through itself / to itself — kath’ hauto, per se; opposed to through another (participation).
• the man himself to himself — Plato’s form of man, rendered from the Greek.
• synolon — the concrete whole of form and matter.
• khalepōtaton — “most difficult of all,” of the question on the one.
• sophoi kyriōs — Thomas’s phrase, Plato and Aristotle as the chief philosophers.
• tying / untying the knots — division of a play (Poetics) applied to Books III / IV–XIV.
• subplot — Book II’s proof that there are first causes in each of the four kinds.
• Natural Hearing — [ed.: Physics].
• equivocal by reason — not by chance; the names in the axioms.
• composed whole vs. universal whole — the two senses of whole in the whole/part sophism.

Texts #

Read in class

• Aristotle, Metaphysics III, the two last questions (mathematicals as substances; separated or in sensibles); closing remark on doubting well.
• Berquist, handout The Matter and Order of Wisdom, p. 9 (verified source).

Mentioned

• Metaphysics II: beginning (how man is toward truth), middle (cause more true than effect; first causes), fifth/last reading (the road; way of proceeding).
• Metaphysics IV, beginning: being as being; one and being; the axioms.
• Metaphysics V: through itself.
• Physics (“Natural Hearing”) II: thinking you don’t know what you do know.
• Poetics: tying and untying the knot.
• Aristotle on three kinds of friendship (Ethics, inferred); Aristotle on revolution (Politics V, inferred); Plato, Laws.
• Euclid, Elements I.5, I.6, I.47, I.48.
• Shakespeare, Hamlet (Horatio speech; “To be or not to be”).
• Spinoza, Ethica More Geometrico Demonstrata; Smollett (a novel on the European tour).
• Albert the Great, Thomas, Boethius on Plato and Aristotle as chief philosophers.

His questions #

• Is what a thing is and its size the same thing? No — the man in the street knows what a dog is and its size differ; Descartes identifies them.
• Is the remark about doubting well universal, or only about the last questions? About the whole of Book III.
• Is Socrates a man through being Socrates? No — else everyone would have to be Socrates to be a man; so man through another, hence Plato’s form.
• Why does Aristotle rank the friendship of virtue above pleasure and usefulness? Because it is through itself: I love you for what you are.
• What’s wrong with Plato’s argument? Thing and what-it-is coincide in immaterial substances, but what a man is involves matter, so the forms cannot be man.
• Why should the wise man consider how man is toward knowing the truth? Because truth belongs most to looking knowledge, and within it to wisdom, which is about the most true first causes.
• Why does wisdom need dialectic when geometry does not? Men think opposite things before knowing, because of difficulties absent in geometry: in things (natural philosophy) or in our mind (wisdom).
• Whose causality extends further, the king’s or the general’s? The king’s, to all citizens; so the science of the most universal cause is about being, said of all.
• Why is it necessary to consider the axioms and not just use them? Because sophists’ objections make men think they don’t know what they do know, and someone must answer.
• Is it always true that the whole is more than the part? Yes, once the composed whole and the universal whole are distinguished.