Motion and Indivisible Points: Aristotle's Physics, the Three Senses of "Before," and a Digression on Mill

Orientation #

He opens mid-thought, saying he “does the same thing with the word before” (the three senses of before from the Categories), then continues reading the argument from where the class left off. Near the end he says next time they will “start here with the third reading, or with the second reading again,” and that he will hand out copies paraphrasing the Latin and Greek. The previous class read the opening of Physics VI (continuous, touching, next; a line not composed of points) and the next opens on the philosophy of the continuous as foundational across philosophy.

The class, in order #

1. Three senses of “before” applied to motion (“before in time, before in the what motion”) #

Point: the same triad Aristotle gives in the Categories orders the argument: before in time, before in the motion that takes time, before in the magnitude over which the motion goes; so what holds of the magnitude carries over to the motion.

2. Reading: if the magnitude is of indivisibles, the motion is of indivisibles (“as if the magnitude ABC were composed”) #

Point: he reads the text: if magnitude ABC is composed of indivisibles A, B, C, then the motion DEF over it, by which O is moved, has each part indivisible; O has moved on A by the motion D, on B by E, on C by F.

• Premise he draws from the text: motion being present, something necessarily moves; something moved, motion is present. So “to be moved” would be from indivisibles too.
• Key premise: a thing moved from one place to another cannot at once move and have moved to where it is moved. His reading of the text’s example: one who walks to Thebes cannot at once be walking and have walked to Thebes.
• Applied to A: O is moved on partless A while D is present; so if O “has come” later than “it comes”, A is divisible (“when it came, it neither rested nor had come, but was between”). If instead the walker goes and has gone at once, he “will have walked and moved to where he moves.”
• Conclusion (his reading of the text): if the whole ABC has been traversed by motion DF, and in partless A the thing is “not moved but has moved”, then “motion will not be from motions but from having been moved.”

3. What “having been moved” (momentum) means (“momentum is to motion what the now is to time”) #

Point: the Latin renders the indivisible of motion as momentum; momentum is to motion what the now is to time and the point to the line.

• His question to the class: can you distinguish my moving to A from my having moved to A? Answer reached: only if A is continuous, since one is divisible. If A is indivisible I cannot be moving into A before I have moved into A—“so I have moved without moving.” Same for the next indivisible B.
• Example: coming into this room before having come into it—possible because part of me is in the room and part outside; but one cannot be “coming into a point” before having come into it. So in every part of the magnitude “I’m not moving, but I have moved.”
• Translation note he gives: he does not render momentum as “momentum” because in English it now means something in physics that is not this meaning; he renders it “having been moved.”

4. Reading: walked without walking; rest that moves (“something will have moved without moving”) #

Point: the next paragraph draws the absurdities: something will have gone through A without going through it, will have walked without ever walking; and since everything must move or be at rest and it rests in each of A, B, C, something continuously resting is at the same time moved—it moves over the whole ABC and rests in each part, hence in the whole.

• He notes an article by T. J. Kasuri [name unclear in recording] called “Motionless motion”: a motion composed of having-moveds with no motion but rest—“really a kind of a contradiction.”
• Example, rooms vs. points: moving from this room to the next, I am partly in each; if instead they were points, I could not be partly in a point (it has no parts), so I would be wholly in this one, then wholly in the next. When did I move? Not while wholly in this room, not while wholly in that. That is how it would be if the line were composed of points and motion correspondingly of indivisibles.
• Student: “like a movie”—no motion, just frames. He agrees: “that’s kind of the way the moderns envision these things.”

5. Instantaneous velocity and the inertial “state” as fictions (“isn’t this a fiction”) #

Point: modern physics speaks of motion in the indivisible, but there is no motion there; this is a fiction, though sometimes a useful one.

• Schrödinger, who “perfected the mathematics of wave mechanics,” after quantum theory thought again about instantaneous velocity; his remark (as Berquist reports it): “it should have struck us” that something is fictional there. Newtonian physics tries to unite motion in a circle with motion in a straight line by speaking of motion at the point where the line touches the circle—but velocity implies motion and there is no motion in a point or instant.
• Law of inertia: scientists, even Catholic ones, deny “whatever is in motion is moved by another,” thinking of a body “in a state of motion.” But a state is a standing; so they conceive what is in motion as if not in motion. Argument: (1) they call speeding up or slowing down “change” and say it depends on something else; (2) so when they conceive change as change they agree with Aristotle; (3) uniform motion in a straight line, “which remains the same,” is treated as not a change—a fiction. Is that a reason to deny that what is in motion depends on a mover? No.
• Parallel fictions: “by health you are healthy,” “by blindness you are blind”—as if blindness were a form like the clay’s shape, though it is the non-being of something; reason “takes what is not and speaks of it as if it were something.” Aristotle’s metaphorical sense: “my car is totaled,” “a complete wreck,” “completely empty”—a lack spoken of as complete. “You don’t realize how much fiction is involved there.” The question is why a given fiction is useful, while realizing it is a fiction.

6. “Fictional sharpness” in history (“fictional sharpness”) #

Point: the same useful fiction appears in dating historical periods.

• McNeill’s The Rise of the West (a gift from his thesis director; “from a secular point of view the best world history we have”) uses the phrase “fictional sharpness” for all dating of periods: the industrial revolution 1760–1820, the age of the automobile, the modern world beginning 1500. Old things live on beside new (horse and buggy gave way gradually to cars—when did one age end?). Somewhat arbitrary, “but maybe it’s better to call it fictional.” A historian must divide into periods or it is “all a blur, all continuous”—“in a way it’s something like the continuous.” Can the historian avoid these fictions? No; so they are useful.
• Aside: he will prepare copies with paraphrase of the Latin and Greek for next time.

7. The fine arts: too high for the beast, too low for the angels (“too high for the beast, and too low for the angels”) #

Point: a remark (from a writer on evaluating music, name unclear in recording—“Austerlitz”/“Owsley”) that the fine arts, music and fiction, are “too high for the beast and too low for the angels”—“most pleasingly proportionate to man.”

• He uses this against Mill. Mill’s ethics is defective, Epicurean/utilitarian: pleasure and pain measure everything. To the objection that this is an ethics for beasts, Mill replies “you are the beast,” since the objector assumes man has no pleasures the beast lacks; those who have experienced both say the distinctively human pleasures are greater; only the experienced can judge (as a woman who has had both a broken leg and childbirth can compare the pains).
• His improvement: three kinds of pleasure—(a) shared with beasts (eating, sleeping), which we have in a more refined way (cooking, wine) but substantially the same category; (b) shared with angels and God (understanding, the sciences), which we have in an inferior way; (c) human in the narrow sense, the fine arts, involving both reason and body/senses/imagination, “the whole man,” hence most proportioned to us.
• Student: with the glorified body we still have these. He: yes; Thomas says explicitly there would be laus vocalis in heaven.
• Sign of the proportion: we can more continuously enjoy literature, music, painting (an opera or museum for two or three hours) than eating (Thanksgiving: an hour exhausts the table and one is uncomfortable) or philosophizing (one tires). Student (Marko): the first beer tastes better than the second, the first swallow better than the rest—his “law of diminishing returns” for sense pleasures; one must be a little hungry, and satiety becomes revolting. Student: in a good novel the body conks out before the imagination.

8. Separated soul, angels, and place (“it’s not going to be in place”) #

Point: my soul separated from my body is not in place—hard to understand because we cannot easily conceive things being distinct without one here and one there.

• Logic example: the species-making “difference” is in Greek diaphora, literally “carried apart”; as Thomas says, put one thing here and one there and they are clearly different; “on the one hand, on the other hand.” But one cannot say Gabriel is here and Michael there.
• Student: like points coinciding? He: not that either—then they would be in the same place; they are neither in different places nor in the same place, “not a place at all.” “You see how hard it is for us to transcend the imagination.”

9. Reasoning in heaven (“there’s no reasoning in there”) #

Point: in the beatific vision there is no reasoning; it is all at once, partaking of eternal life, no before and after. Outside the vision we would still have the ability to reason, though he does not know why we would; in the vision we see not only God but everything else we naturally want to know.

• Aside: a story about carpeting the center of the split-level stairs and the cat at first walking down the bare wood at the sides. The recording ends mid-sentence.

His words #

• “before” (three senses: in time, in motion, in magnitude) — from the Categories.
• “indivisible” / “partless” — of A, B, C, and of the motions D, E, F.
• momentum — Latin for the indivisible of motion, as the now to time and the point to the line; he renders it “having been moved” [ed.: usually left as “moment”].
• “having moved without moving” / “walked without ever walking” — the absurdity of motion from indivisibles.
• “state of motion” — a state is a standing; conceiving motion as if not motion.
• “fiction” / “useful fiction” — reason speaking of what is not as if it were something (blindness, instantaneous velocity, uniform motion as non-change, historical periods).
• “fictional sharpness” — McNeill’s phrase for dating periods.
• “totaled” — Aristotle’s metaphorical sense: a lack spoken of as complete.
• “too high for the beast, too low for the angels” — the fine arts as proportioned to man.
• “law of diminishing returns” — his name for satiety in sense pleasures.
• laus vocalis — vocal praise, which Thomas says will be in heaven.
• diaphora — Greek for difference, “carried apart.”
• “transcend the imagination” — needed for separated soul and angels not in place.

Texts #

Read in class

• Aristotle, Physics VI, opening argument on motion over a magnitude composed of indivisibles (ABC / DEF, walking to Thebes) (inferred: VI.1).

Mentioned

• Aristotle, Categories, the senses of “before” (inferred: ch. 12).
• T. J. Kasuri [unclear], article “Motionless motion.”
• Schrödinger on instantaneous velocity after quantum theory.
• William McNeill, The Rise of the West.
• Mill, on higher and lower pleasures (inferred: Utilitarianism).
• Thomas Aquinas on laus vocalis in heaven; Thomas on difference as placing one thing here, one there (loci not stated).
• Unnamed author “toward an evaluation of music” [name unclear].

His questions #

• Can you make a distinction between my moving to A and my having moved to A? Only if A is continuous; if indivisible, I have moved without moving.
• Can I be moving from A into B before I have moved into B? No—then B would be divisible.
• Can I come into a point before I have come into the point? No; I cannot be partly in a point.
• When did I move from this room to that room, if I was wholly in one then wholly in the other? Never—so motion would be composed of indivisibles, “like a movie.”
• Isn’t instantaneous velocity a fiction? Yes: velocity implies motion, and there is no motion in a point or instant.
• Is the law of inertia a reason to deny that what is in motion depends on a mover? No; when they conceive change as change they agree with Aristotle.
• Can the historian avoid the fictional sharpness of periods? No; so those fictions are useful.
• Where is the separated soul going to be? Not in place at all—neither here nor there, nor coinciding.
• Would we still reason in heaven? Not in the vision, which is all at once; outside it we would have the ability.