Moving and Having Moved, Becoming and Contradiction, Eucharist and Idealization in Science

Orientation #

He twice refers back to “the seventh reading” (that there is a first, indivisible, when a thing has changed) and to “the earlier reading” (prev. lecture). He says they will “come back” to Hegel’s difficulty, which Aristotle develops in the eighth book, and ends: “next time we’ll look at this eleventh reading.” The previous class treated order vs. distinction and why there is no first instant of motion; the next continues the Physics on motion, rest and the now.

The class, in order #

1. Order in the strict sense vs. symmetry (“the strict proper sense of the word order”) #

Point: a student’s suggestion that double/half shows an “order of relation” leads him to distinguish order (before and after) from symmetry.

• Order vs. symmetry: order in the strict sense is before and after; the word is often broadened to any relation, “a broad or loose use.” Symmetry is different: a cruciform of four dots seen as a whole has no before/after, yet has order in the loose sense.
• Aristotle, 13th book of the Metaphysics (“Wisdom”): the three main forms of the beautiful are order, symmetry, and the limited; so Aristotle himself distinguishes order from symmetry.
• Example of symmetry: the five Platonic works around the Apology (Meno, Euthyphro | Apology | Crito, Phaedo). The Apology is the odd item (a courtroom defence, not a conversation). Quantitative symmetry: Euthyphro and Crito short, Meno and Phaedo long. Symmetry of content: Euthyphro asks what piety is without settling it; Crito shows Socrates’ piety toward Athens (abide by its decisions even if wrong in this case). Meno is an introduction to logic; Phaedo says we need an art about arguments (to his knowledge the first explicit call for logic). Meno gives the recollection argument for immortality; Phaedo recalls it and gives a stronger one. Meno distinguishes right opinion from episteme (knowledge “tied down” by an account of the cause, introducing demonstration); Phaedo has Cebes demand a necessary reason, and Socrates goes back to his experience as a natural philosopher, where one reaches the four kinds of cause. Phaedo’s “one opposite can never be the other” grounds the Meno’s certainty that guessing and knowing differ (whoever says “Socrates, you’re only guessing” already admits the distinction). Meno insists on knowing what virtue is first; Phaedo discusses the soul’s immortality without determining what the soul is, a deficiency the Meno lets you see.
• Same symmetry in A Midsummer Night’s Dream by place: court, peasants’ house, forest, peasants’ house, court.
• Mozart mass: Kyrie and Agnus Dei ask mercy; Gloria and Sanctus/Benedictus praise; the Credo is the odd one, a profession of belief not a prayer.
• Bodily symmetry: arms, legs, eyes, ears of equal length, with no before/after.

2. The limited and the beautiful: knowing when to stop (“the supreme gift of the artist”) #

Point: a student asks how “the limited” relates to the beautiful.

• Holmes, “The Norwood Builder”: the builder fakes his own murder to frame the son of the woman who refused him, hides in a secret compartment, is exposed when Holmes fakes a fire; afterwards Holmes says he was very clever but “lacked the supreme gift of the artist: knowing when to stop.” (He tried to add one more bit of evidence.)
• Chesterton: art and morality are alike, you have to draw the lines.
• Nicomachean Ethics, beginning of book 2: moral virtue compared with art, where too much or too little is bad.
• Critics praise Mozart (“arrives at his goal and never goes beyond it”), Titian, Shakespeare for knowing when to stop; “most people don’t know when to stop, including myself.” Aside: songs nowadays never stop, they fade away.

3. Two more symmetries (“appeals to us because of its what symmetry”) #

• McNeill’s division of world history: Middle Eastern dominance to 500 BC; Eurasian cultural balance 500 BC-1500 AD; rise of the West. Dominance of the East / rise of the West around a balance: symmetrical, unlike “ancient, medieval, modern,” which has none.
• Heisenberg as a young man reading the Timaeus: Plato’s geometrical account of Empedocles’ four elements by the regular solids (end of Euclid’s Elements), which are symmetrical rather than ordered.

4. The reading: what has changed was changing before (“the first will never be taken”) #

Point: he reads the third paragraph of page 12 through the bottom of page 12.

1. Everything that has changed from A to B has changed in time: not in the now in which it is in A (it would be at once in A and B); if in another now, there is a time between, “for nows are not next to each other.”
2. All time is divisible; in the half it will have changed, and in the half of that, always; so it was changing before.
3. Clearer in magnitude: if CD were indivisible, partless would be next to partless, shown impossible “in our study of the continuous”; so what is between is a magnitude divisible without limit, and it changes in these before.
4. “The same demonstration” in non-continuous changes (contraries, contradiction) by taking the time in which it changed. Conclusion: what has changed changes, the changing has changed; to have changed is before (Greek proteron, the same word as in the Categories) changing and changing before having changed, “and the first will never be taken.” His gloss: there is no first distance moved, no first time in which it has moved (any time you give, in part of it a lesser distance was moved), no first time in which it is moving (moving for an hour is moving for half an hour, a quarter…). “Strange reality.”

5. Students press: nows, and the door (“is there a first when the door is open”) #

• Student: time is “that which is between two nows”? Yes; before any time there is a now, and before any now there is time; no first.
• Student: the door from not-open to open: is there a first when it is open? Yes, as in the seventh reading, a first when it has completed the motion, and that is indivisible; but no first in which it is in motion (opening is divisible forever: half the door passes the beam, a quarter before that…). Completion vs. the process: the boundary case is the door just past the beam. He defers Hegel’s difficulty (developed in the eighth book).

6. The cause: partless not next to partless; acquiring abilities by doing (“the partless is not next to the partless”) #

• Cause of the whole result: the indivisible is not next to the indivisible; division is unlimited, as in a line increasing and decreasing. Euclid defines a point as that which has no parts.
• Aristotle refers back to this in the ninth book of the Metaphysics and raises it in the Ethics: one becomes courageous by doing courageous acts, moderate by moderate acts, just by just acts; objection: then you must already be courageous; likewise you acquire piano-playing by playing, but playing presupposes the ability, so you would have the ability before you had it.
• His answer (1): you are able before acquiring the ability “in a different way”: with great concentration, effort, mistakes, instability; after the habit, with ease and stability. Courage and moderation likewise: the man who must phone his buddy to resist the urge to drink does not yet have the virtue. So not the same ability before and after.
• His answer (2), the Physics parallel: after playing a year the kid has “something of a habit” and continues to build it, as “I have moved a certain distance, and I’m moving further, and I have moved another distance.”

7. Finishing the reading: things not simple; ceasing to be (“not always, however, what comes to be”) #

Point: reads on: it is not always what comes to be, but sometimes another thing, “as the foundation of the house,” in things not simple; likewise in corrupting; “right away there exists something unlimited” in coming to be and ceasing to be, always having ceased before ceasing and ceasing before having ceased; “there will not be a first in which it will be.” No discussion beyond the reading.

8. Zeno’s contradiction in becoming, and the Eucharist (“no last now in which it is bread and wine”) #

Point: the change between contradictories (not-sphere to sphere) seems to force a now in which it both is and is not a sphere.

1. The time in which it is not a sphere is limited, so has an end; the time in which it is a sphere has a beginning.
2. Nothing between being and not being a sphere, so no time between the two times.
3. If the last now of not-sphere and first now of sphere differed, there would be a time between; so they are the same now.
4. Zeno: in that now it is and is not a sphere; a contradiction in becoming (Hegel’s position). Impossible. Solution (student prompted: “that now really isn’t time”; he corrects that there is a now in time, the end of a limited time): there is a first now in which it is a sphere but no last now in which it is not a sphere; as Aristotle said earlier, when the time of becoming is completed, in that now it has become. “This is the way Aristotle solves this problem and then what Hegel has.”

• Theology: on the altar there is a time of bread and wine, then of the body and blood; no time between; so the last instant of bread and wine would be the first instant of the body and blood, “and now you have heresy, just for one moment” (coexistence, often condemned). The theologians could not solve it; Thomas solves it as Aristotle does: no last instant of bread and wine, a first instant of the body and blood. “A beautiful example of how philosophy is useful… in theology.”
• Objection: is it arbitrary? Why not the reverse (a last now of the old, no first now of the new), which also avoids contradiction? Reply: from the seventh reading, a thing that has changed is in that to which it has changed, and it first has changed in an indivisible; changing from this to that is leaving this behind; so when the change is completed in the now, the from-which is left behind and the now belongs to the to-which. Only “it can’t be the same now” is forced by the axiom of non-contradiction; which now exists follows from what was shown. Same for the Eucharist.
• De Koninck’s article, in French, “Paradoxes du Devenir,” on this and the theologians’ problems; someone named [Renal/Reynolds? unclear] remarks about Hegel. He thinks this is harder to solve than Heraclitus’ contradiction.

9. Heraclitus: does the healthy become sick? (“day becomes night by accident”) #

1. Deny that the healthy become sick and the healthy would always be healthy, against experience; likewise the sick (“abandon all hope”).
2. “Becomes” means “comes to be”; if the healthy come to be sick, the healthy are sick; then something is healthy and not healthy at once. Either one opposite becomes the other (contradiction: day is night) or nothing changes (Parmenides: change an illusion). Confirming usage: become a Christian by baptism and you are a Christian; become a geometer, a monk, and you are one. Also love “turns into” hate (poets like to represent it), the hard becomes soft, the wet dries. Answer: day becomes night by accident (“subtle”). As the cook played the piano: not as cook but because cook happens to belong to the pianist; the pianist cooked, not through the art of piano. So not the hard as such that becomes soft but that to which hard happens, the butter. Terms: “as such,” per se (“through itself”), “as cook.”

• Why the sphere case is harder: it seems to make sense that the limited time of not-sphere has an end, and the end of any period is a now, so you imagine a last now of not-sphere; either same or different, and either way trouble (a time between must be one or the other and gets absorbed into one side; two nows are never contiguous, like two points).
• Calculus analogy: square inscribed in a circle, arcs bisected, polygon with ever more sides approaching the circle; the moderns “imagine falsely” that a polygon with infinite sides equals the circle (a straight line coinciding with a curve, contradiction). The circle is a limit never reached; thinking the circle as the limit of these polygons unites circle and polygon in one thought, “a faint imitation” of angels knowing two kinds by one idea, whereas we need different ideas. So too: shrinking the period of not-sphere approaches the first now of sphere but never reaches it; “kind of like an extrinsic limit.”
• Student: no last now simply because the continuous forbids a last now touching the first? He agrees and applies it: is there a last now in which I am alive? No; a first now when I am dead, the completion of the change, indivisible. Aside: some truth in the Epicurean argument that you never experience death (never dead while alive), though they did not see it this way; a pun on Hegel, alive or dead “mentally.”
• Student: Hegel’s error is conceiving the now as time. He agrees, but the problem comes from positing both a last and a first now; the now occupies no time, yet “you could be something in that now.”
• Student: does the absence of a last now come from the definition of becoming? Not necessarily, since it holds for ceasing to be too; the argument is: having changed from A to B you are in B not A, first completed in an indivisible, and changing from A is leaving A behind, the same reality; conversely when I first cease to be, I am not, in an indivisible.
• Aside: scripture on the damned descending in puncto, a point; a student adds the judgment is perhaps not in time.
• Student summarises: admit a last now of the term from-which and you must either identify it with the first now of the to-which (contradiction) or have a time between (in which you must be one or the other); so no time between being alive and being dead.
• Student: is this the moderns’ reasoning that a straight line eventually equals the curve? Yes; likewise instantaneous velocity (velocity at a point, but no motion at a point); after quantum theory they said it was a fiction, “but a useful fiction,” a strange thing.

10. Idealization in science (“nothing is more misleading than a clear, distinct idea”) #

Point: modern science is built on idealizations that depart from reality.

• McNeill calls his dates a “fictitious sharpness”: a pure continuum of history would be unintelligible, so you make things sharper than they are.
• Einstein, The Evolution of Physics, on inertia: no body in our experience is free of exterior forces; we oil the wheels and smooth the road, it goes further, and imagine it going on forever, “in our imagination now.” Tragedy and comedy are likewise idealizations of an aspect of life.
• Heisenberg criticises Aristotle’s critique of the Pythagoreans: “we have to force the facts” (the very thing the philosopher does not do). Lab numbers never fit the equations; “acceptable margin of error”: due to instruments or to false theories? (More precise instruments sometimes force modified theories.) Bohr’s remark [transcript: “Boris”] that the logical analysts make science impossible by demanding perfect fit. A planet treated as a point moving on a line.
• Heisenberg, Gifford lectures: concepts of natural (ordinary) language, vaguely defined, have greater stability in the growth of knowledge than the precise terms of science, because those are based on idealization, a departure from reality.
• De Broglie, book on the quantum: “nothing is more misleading than a clear, distinct idea,” contrary to Descartes [ed.: name not spoken].

11. Complementarity: comedy and tragedy (“kill your opponent’s seriousness with jesting”) #

Point: Bohr’s complementarity applied to tragedy and comedy: bring one aspect of life into focus and the other disappears.

• Cousin Donald and Professor Kasurik topping each other’s funny Navy stories (the sailor who drilled a hole in the hull for his aerial, not realising the ship was not fully loaded); yet “war is…” the tragic aspect, which you cannot hold at the same time.
• Aristotle, Rhetoric, quotes someone’s advice (he forgets who) to kill your opponent’s seriousness with jesting and his jesting with seriousness. Lincoln, called two-faced by Douglas: “If I had another face, would I wear this one?” Reagan on Mondale’s “youth and inexperience,” which finished the age issue. The reverse: squelching a joker with seriousness (the one-upmanship movie: the drunk joke rebuked as mocking a physical ailment), “probably easier to do.”
• Shakespeare, prologue of Henry VIII: “they come no more to make you laugh,” getting you out of one mood for the other. Next time: the eleventh reading.

His words #

• order: in the strict sense, before and after; loosely, any relation.
• symmetry: distinct from order, no before and after; one of Aristotle’s three forms of the beautiful with order and the limited.
• “Wisdom”: his name for the Metaphysics (“the 13th book… of a wisdom”) [ed.: Metaphysics].
• episteme: knowledge in the strict sense, tied down by an account of the cause (Meno).
• proteron: “before,” the same word as in the Categories.
• partless: Euclid’s point, that which has no parts; “the partless is not next to the partless.”
• ability / habit: ability before the habit is with effort and instability, after with ease [ed.: potency/habitus].
• leaving behind: changing from this to that is leaving this behind; grounds the first now belonging to the to-which.
• by accident / as such / “to itself” [ed.: per accidens / per se]: the cook played the piano by accident, not as cook.
• extrinsic limit: the first now of the sphere as approached, never reached, by shrinking periods of not-sphere.
• useful fiction: instantaneous velocity, the infinite-sided polygon.
• fictitious sharpness (McNeill); idealization (Einstein, Heisenberg, de Broglie); complementarity (Bohr).

Texts #

Read in class

• Aristotle, Physics, the reading on pages 12-13 (what has changed was changing before; the first never taken; foundation of the house; ceasing to be). Mentioned
• Aristotle, Physics, “seventh reading” (first indivisible of having changed); “eighth book” (Hegel’s difficulty); “eleventh reading” (next time).
• Aristotle, Metaphysics book 13 (beautiful: order, symmetry, limited); book 9 (abilities acquired by doing).
• Aristotle, Nicomachean Ethics beginning of book 2; Categories (proteron); Rhetoric (jesting and seriousness).
• Plato, Meno, Euthyphro, Apology, Crito, Phaedo; Timaeus.
• Euclid, Elements (definition of point; regular solids at the end).
• Thomas Aquinas on the Eucharist (no last instant of bread and wine), no locus given.
• De Koninck, “Paradoxes du Devenir.”
• Heraclitus; Parmenides; Zeno; Hegel; the Epicureans on death.
• Conan Doyle, “The Norwood Builder”; Chesterton; Shakespeare, A Midsummer Night’s Dream, Henry VIII; Mozart masses; a critic’s book on Venice (Titian).
• McNeill’s three-part world history; Einstein, The Evolution of Physics; Heisenberg, Gifford lectures; de Broglie on the quantum; Bohr on complementarity.
• Scripture on the damned descending in puncto (no locus given).

His questions #

• How is the limited related to the beautiful? Knowing when to stop, the supreme gift of the artist (Holmes on the Norwood builder).
• How much time does it take to move some distance? Where is the first time in which there is moving? None: any time given contains a lesser time in which a lesser distance was moved; no first.
• Is there a first when the door is open? Yes, the indivisible completion; but no first of its opening.
• How can you acquire the ability to play the piano by playing the piano? You are able beforehand in a different way (effort, instability); afterwards with ease; and you build up the habit as you go.
• Can the last now of not-sphere and the first now of sphere be two different nows? No, there would be a time between; so, to avoid contradiction, there is a first now of sphere and no last now of not-sphere.
• Is that arbitrary on Aristotle’s part? No: what has changed is in that to which it changed and has left behind what it was; the completing now belongs to the to-which.
• Does the healthy become sick? Do day and night become each other? Yes, by accident: not the hard as such but the butter becomes soft, as the cook played the piano not as cook.
• Is there a last now in which I will be alive? No; there is a first now in which I am dead.
• Is the margin of error due to our instruments or to the falseness of our theories? Left open; sometimes more precise instruments force theories to be modified.