Metaphysics III, Reading 1: Tying and Untying the Knots — Doubting Well and How Discoveries Are Made

Orientation #

He looks back to Book II, especially its first reading (difficulty of knowing) and its fifth reading (which he says settles the division and order of the questions of Book III) — the fifth reading was the previous class’s matter (prev. lecture). He says the class will stop at 4:30 and begin the second reading next, “but think about this first reading.” The neighbouring classes treat the fifth reading of Book II and, afterwards, the role of contradiction in coming to know.

The class, in order #

1. Proemium and treatise (“the prologue and the play”) #

Every work of Aristotle, like Romeo and Juliet, divides first into a short proemium and the main work: the prologue is brief but situates you with respect to the play. The Latin of the proemium is sometimes mistranslated “introduction”; it is not an introduction but a proemium, followed by the treatise, “the drawing out.”

2. The lover of plots is something of a philosopher (“the philomythos is something of a philosopher”) #

In the proemium Aristotle compared the philomythos to the philosopher because both are full of wonder — the child wide-eyed as daddy reads what happens to Red Riding Hood, the philosopher wondering more universally and deeply. But mythos means first myth, then story, then precisely plot; so “the lover of plots is, in a way, a philosopher,” since wisdom consists in seeing a knot and untying it.

3. Books III–XIV as a plot (“the tying of the knots and the untying”) #

Aristotle sometimes divides plot in three (he praises Homer for teaching the Greeks beginning, middle, end), sometimes in two: the tying of the knot(s) and the untying.

• Book III ties all the main knots of wisdom: it raises the main questions, about twenty-three, all disputed questions, with reasons on both sides, so that the mind is tied in a knot.
• Books IV–XIV untie them. (He first says “three through fourteen,” then corrects: “four rather, through fourteen.”)
• In a play more time goes to tying than untying; here, less time is spent untying than tying.
• Aside: Aristotle says the young or imperfect poet is better at tying knots than untying them — “and that’s even more true in philosophy.” Most philosophers can tie themselves and others into knots but cannot untie them; what we admire in Aristotle and Thomas is that they can.

4. Footnote: where do the rest of Book I and Book II fit? (“Shakespeare will take the plot over”) #

An objection he puts to himself: the comparison leaves out the rest of Book I and Book II. Answer by a further likeness. Editors note that Shakespeare’s plots usually have an antecedent by someone else, which he takes over, improves, and makes a masterpiece of; read the original and you see the other man had marred the plot and the characters, folded up and without piquancy, suddenly blossom.

• So the rest of Book I: Aristotle criticises earlier thinkers, who were not the first to look for the first causes but marred the job.
• So Book II: as Shakespeare in Hamlet gives his own view of what fiction should be and how it should proceed, Aristotle there says how one should proceed.
• Aside: his brother Richard, a leading actor in high school, tried writing stories and owned books like “101 plots used and abused.”

5. Why discovery is the theme now (“how discoveries are made”) #

Point: the first reading of Book III is most of all about how discoveries are made, and this ties back to the end of Book I.

1. From the proemium you know wisdom is the most divine, best, most desirable knowledge — so you really want it.
2. There are two ways to get what you don’t know: learn it from someone who already knows it (more convenient), or discover it yourself.
3. The rest of Book I recalls and examines the predecessors, and shows they have not adequately, let alone fully, reached the first cause or causes — not even an adequate knowledge of the kinds of causes.
4. Therefore you must to some extent discover these things yourself — hence: how are discoveries made? He notes what Aristotle says about discovery was taken over by Augustine and Thomas in the Middle Ages, and by some great 20th-century physicists.

6. Book II is not an intruder (“some people thought that Book Two was just interpolated”) #

Against those who think Book II was inserted by chance between I and III:

• The fifth reading of Book II explains the division and order of the questions of Book III: questions about what wisdom is about come first, because they are needed for how one should proceed; then questions about the things themselves.
• The first reading of Book II, on the difficulty of knowing — whether from the thing or from the weakness of our mind — illuminates this reading. Natural philosophy is harder than geometry because of the things; wisdom is harder than geometry because of the weakness of our mind.

Geometry vs. wisdom and natural philosophy, by guessing. In geometry, for the most part, before the rigorous proof we would all guess the same thing: that in a triangle with two equal sides the base angles are equal (Euclid I.5, inferred), and that an equilateral triangle has three equal angles — nobody guesses otherwise. In natural philosophy, wisdom, ethics and political philosophy, men regularly guess differently before they know, and sometimes never get past their different guesses. That is a sign of the greater difficulty, and of a difficulty of discovery which geometry does not have. (He grants Aristotle does not say this himself; there are a few interesting exceptions in geometry.)

Why the difference: imagination. As Monsignor Dionne taught him, imagination is very important in discovery; mathematics is closest to the imagination, and our agreeing in our guesses is a sign of it. Geometry is in a sense on the surface of things, proportioned to our mind. But as “the great Heraclitus” said, nature loves to hide, and of God we say he is the hidden God; so imagination is quite insufficient, indeed deficient, there — especially in wisdom, also in natural philosophy.

7. The text opened (“necessary for the reasoned-out knowledge sought”) #

“It is necessary” — a strong word — not for all reasoned-out knowledge (geometry is reasoned-out knowledge, indeed our clearest example of syllogistic knowledge), but “for the reasoned-out knowledge sought,” which in this book is wisdom: that we go over first those things about which one should first raise questions. Which things?

1. Those about which earlier thinkers have taken opposite and different positions — clearly a question to be discussed, a quaestio disputata.
2. “Whatever else has been overlooked” — questions his predecessors did not explicitly disagree about, which he has seen. Note he mentions the first sort first. Aside: so many of Thomas’s works are quaestiones disputatae, and each article of the Summa Theologiae is a contraction of one — three or four objections instead of fifteen or twenty, but the same method.

8. First reason: to doubt well (“bene dubitari — to doubt well beforehand”) #

Thomas glosses it: “to attain well to those things which are truly doubtful.” You doubt well when you see a good reason for thinking it is this way and a good reason for thinking it is that way.

• Example, the great fragment on Mind (Anaxagoras): Mind is self-ruling — good sign, there is a science whereby the mind directs itself, namely logic. But Mind cannot be mixed with the material world, because the ruler must be separated from the ruled. Then how can the mind rule itself, not being separated from itself? Both sides have reasons: that is doubting well. [He says “good reasons for thinking the mind can rule itself, and a good reason to think it can rule itself” — the second plainly should be cannot.]
• Separation of ruler and ruled: in the army, those who command and those who obey are separated; his mother was mixed up with the kids all day and got disobeyed, while his father came home and said “you sit in that chair and you don’t move” — if the roles were reversed it would be the reverse.
• Contrast: Descartes says he has sometimes been deceived, so he will doubt everything. Is that doubting well? No — “it’s more an act of the will than an act of reason,” not seeing reasons that it is so and is not so.
• The untying, i.e. the discovery: the mind directs itself in what it does not know by what it does know, and in what is less known by what is more known — which requires separating what you know from what you don’t. As we learn from the life of Socrates, most men have mixed up what they don’t know with what they do, so they lack that separation. Money example: “I’ll buy each of you a coke” — you use the numbers you know (how many men, the price) to reach the number you don’t; likewise adding up your purchases in a store.
• Einstein, The Evolution of Physics: every essential idea in science was born this way, in “dramatic conflict,” from a difficulty which is a contradiction; Einstein’s metaphor is a wall of contradiction blocking progress, which must be broken down before the mind goes forward. Niels Bohr — “in some sense even more influential than Einstein” as a teacher — says the same; so does Heisenberg.
• Theology: the quaestio disputata was the main way in the Middle Ages, and the Fathers explained Scripture so too. Thomas takes over Augustine’s reasons for the Incarnation; he gives ten reasons for God’s becoming man, each built like a little disputation: God can make infinite reparation but did not sin; man sinned but cannot make sufficient reparation — a problem, solved by God becoming man. God should be followed but cannot be seen; man can be seen but is not a perfect model — solved the same way. And Augustine says heretics are necessary for the development of theology: they contradict an article of faith on some reason drawn from philosophy or Scripture, and the untying of that knot is a discovery in theology not had before.
• The knot itself: “it is impossible to untie without considering the knot.” The doubt of the mind shows this about the thing: insofar as it doubts, it undergoes something like those tied up — in both cases it is impossible to go forward. As with tied feet, you must examine the knot, find the loose end, and unravel it.
• Twelfth Night: Viola shipwrecked, disguised as a man, serves the Duke and loves him; the Duke loves a woman who will not give him the time of day and uses Viola as messenger; that woman falls in love with Viola thinking her a man. End of Act II: “O time, thou must untangle this, not I; it is too hard a knot for me to untie.” And in the Nicomachean Ethics Aristotle says time is a good helper in untying these knots — sometimes it takes a long time. He notes this first reason is “kind of a double reason, but the difference here is one reason.”

9. Second and third reasons (“like those who do not know where they ought to go”) #

Two sides of one coin: if you do not see the difficulty, you do not know where to go; and you do not know when you are right. Aristotle: those investigating without first considering the difficulties are like men who do not know where they ought to go, and in addition do not know whether the thing sought has been found — for the goal is not clear to such a man, but it is to the one who has raised the difficulties first.

• Meno’s objection: Socrates does not know what virtue is, nor does Meno; how can you investigate what you don’t know, and how would you know if you found it? (Like being told “go and get one” — by chance you might get it, but you would not know you had found what was wanted.) Answer: you can in a way know what you are looking for — you are looking for the solution to this problem, this knot; and when you untie it you know you have arrived.

10. Heisenberg on asking the right question (“more than halfway to the truth”) #

In the Gifford Lectures, in the lecture on the history of quantum theory, Heisenberg says the physicists began to make progress when they asked the right questions, and that to ask the right question is often to go more than halfway to the truth.

• Diagram he uses with students: a line from ignorance to knowledge representing the time and effort; most people put the question at the first percent, or at most somewhere in the first half; Heisenberg puts it past the halfway mark.
• His own experience: more time and effort goes in before asking the right question than after. Doing his doctoral thesis at Laval, on a problem he had carried since he was an undergraduate and neither he nor his professor could answer, he suddenly asked the right question and was at the answer at once — “after nine years” — and went to put the question to Professor Dionne, who said “Duane, I know where you’re going.”
• Meno’s slave boy: Socrates draws the doubling of the square out of the boy’s own volunteered answers, and infers he knew geometry already. Berquist doubts the assessment: asked first how to double a square, the boy says double the side — so he not only did not know, he was mistaken. What is true is that Socrates asks all the right questions. What Socrates really shows is that the boy can recognise his mistake, and come to know what he does not know, out of what he does know; the questions make him put together for the first time things he already knew.
• Corollary: learning from another should imitate discovery. You may cut out the dead ends, but the essential steps go the way the discovery was actually made. We learn badly because we get knowledge second, third, fourth hand and do not know how the discovery was made; go back to the man who made it.
• Why he brought Heisenberg in here: Heisenberg says those right questions had practically all to do with the strange apparent contradictions between the experiments. Mapped onto Aristotle’s second and third reasons: every investigation goes in the direction of the questions asked (as you feel on the witness stand), so to ask the right question is to go in the right direction; and the physicists knew they had arrived because the contradictions began to disappear. So the third reason already touches not only discovery but the judgment that what you discovered is true.

11. Fourth reason: the lawsuit (“like that of two parties in a lawsuit”) #

“Moreover, the one who has heard all the reasons of those disagreeing, like that of two parties in a lawsuit, is necessarily better prepared to judge.” On a jury, having heard the man arguing guilt and the man arguing innocence, you judge better than having heard one side only. The difference: in court the matter is a contingent individual affair, in philosophy a universal thing, and eventually necessary. These are the four reasons for examining the reasons pro and con in the great questions of philosophy.

12. The plan for Book III (“we’ll stop each question and point out some of the difficulties”) #

The great questions of wisdom could be divided in three, but Aristotle first divides them in two: the second reading’s questions are almost all about what wisdom is about (a couple are not, but are involved in those); the third reading’s questions are about the things themselves wisdom is about, mainly about causes. In class they will go through each question, stating it and indicating something of its doubtfulness — why you would think this and why that — but not the whole dialectic of the rest of Book III, which would be a course in itself.

His words #

• proemium — the short first part situating you with respect to the work; “not introduction; it’s a proemium.”
• treatise — the main part, “the drawing out.”
• philomythos — lover of myths; mythos moves from myth to story to plot, so the lover of plots is something of a philosopher.
• tying / untying the knots — the two-part division of a plot, applied to Book III (tying) and Books IV–XIV (untying).
• disputed question / quaestio disputata — a question to which earlier thinkers gave opposite answers; the medieval form of this same procedure.
• bene dubitari, “to doubt well” — Thomas: “to attain well to those things which are truly doubtful”; seeing good reason on each side, as against Descartes’s doubt of the will.
• wall of contradiction [ed.: Einstein’s metaphor] — what blocks scientific progress and must be broken down.
• the right question — Heisenberg: to ask it is often to go more than halfway to the truth.
• nature loves to hide — Heraclitus, on why imagination fails us outside mathematics.

Texts #

Read in class

• Aristotle, Metaphysics III, first reading: “it is necessary for the reasoned-out knowledge sought…”; “to doubt well beforehand is necessary for those who wish to discover”; “impossible to untie without considering the knot”; “like those who do not know where they ought to go”; “like that of two parties in a lawsuit.”
• Thomas’s commentary on that reading, gloss on doubting well.
• Shakespeare, Twelfth Night, end of Act II (Viola’s lines on the knot).
• Anaxagoras, fragment on Mind (recalled from an earlier class; handout “The Royal Fragment,” p. 19 / DHB Vol. I, p. 35).

Mentioned

• Aristotle, Metaphysics I (proemium; critique of predecessors) and II (readings one and five); Poetics (inferred) on plot, Homer, and young poets; Nicomachean Ethics on time as helper.
• Shakespeare, Romeo and Juliet; Hamlet (views on fiction).
• Plato, Meno (Meno’s objection; the slave boy and doubling the square).
• Einstein, The Evolution of Physics; Bohr; Heisenberg, Gifford Lectures.
• Augustine (heretics necessary to theology; reasons for the Incarnation); Thomas, Summa Theologiae (ten reasons for God becoming man; article as contracted disputed question).
• Euclid I.5 and the equilateral triangle (inferred).
• Descartes’s universal doubt.

His questions #

• What are the two parts of Romeo and Juliet? — The prologue and the play; likewise proemium and treatise in Aristotle.
• What are the two parts of a plot? — Tying the knots and untying them; Book III ties, Books IV–XIV untie.
• What is the first reading of Book III most of all about? — How discoveries are made.
• Before the proof, would you guess the base angles of an isosceles triangle are equal? — Yes, and so would everyone; in geometry men do not guess differently, in wisdom and natural philosophy they do.
• Which science is closest to the imagination? — Mathematics; hence our agreement in guessing there.
• What is it to doubt well? — To see a good reason for each side, as in the Anaxagoras fragment; not Descartes’s willed doubt of everything.
• How can you investigate what you do not know, and know when you have found it? (Meno) — You look for the solution to the knot, and when the knot is untied you know you have arrived.
• Where along the road from ignorance to knowledge does asking the right question fall? — Past the halfway point: Heisenberg’s “more than halfway to the truth.”
• What were the right questions in quantum theory? — Practically all of them concerned the strange apparent contradictions between the experiments.
• Why are the reasons on both sides needed? — As with two parties in a lawsuit, having heard both you are necessarily better prepared to judge.