Can Motion Be Defined? Why Descartes and Locke Say No, and Aristotle's Approach to Definition

Orientation #

He refers back to “last time” for two things: the remark from the start of the Nicomachean Ethics on Aristotle speaking according to prevalent opinion, and the claim that Descartes denies motion can be defined (prev. lecture). He looks forward to “Book Six” for the solution of the paradox of the continuous, and closes with “Aristotle is trying to define motion here,” i.e. the definition is next. Verified source: the class is reading from DHB Vol III, The School of Aristotle, p. 185 (the opening of Physics III). The previous class treated the definition of motion’s setting in Physics III and the senses of “before” and “in”; the next works through the definition of motion as act of what is able to be.

The class, in order #

1. Where motion, the unlimited, place and time fall in the Physics (“following motion intrinsically”) #

Point: Books III–IV are organised by what follows on motion, intrinsically or extrinsically.

• Reason “looks before and after” (Shakespeare), so logic, the science of reason, distinguishes the senses of “before”; Aristotle distinguishes the eight senses of “in” in treating place.
• Those defining the continuous use “the limited”: the continuous is what is divisible without limit.
• Thomas: Book III takes motion and then the unlimited (continuous), which follows motion intrinsically; Book IV takes place and time, which follow it extrinsically — place is “kind of outside of things,” and time is an extrinsic measure, as when every motion down here is measured by the (apparent) motion of the sun around the earth.

2. “Motion is impossible without place and the empty and time” (“atoms and the empty exist”) #

Point: Aristotle here states what he does not hold; he speaks according to common opinion until the time comes to determine the truth.

• Democritus held that atoms and the empty are real and that motion is impossible without the empty. Empedocles denied anything empty, as involving a contradiction. His imagined argument against “empty space”: does it have length, width, depth? Then either something has them (so it is not empty) or nothing has them, which is absurd.
• Aside: Einstein, with fields everywhere (gravitational etc.), seems to deny the empty too; since Faraday the field is taken as real, not a mathematical device — perhaps a return to Aristotle. Early modern scientists (Dalton) followed Democritus on atoms.
• Student: is Aristotle lying, saying what he doesn’t think? Answer: he takes the common notion, which is where you begin. Thomas notes more than once that Aristotle speaks according to his contemporaries’ opinion until it is time to determine the truth, so as not to give them unnecessary impediments.
• Parallel from ethics (mentioned last time): NE I begins “every action, every choice, every art seems to aim at some good,” defines the good as what all want, and lists ends of arts — health for medicine, wealth for the household art. But Politics I argues wealth is only an instrument of the household. Thomas: at NE I he speaks per prevalent opinion; in Politics I he says what the truth is and why.
• So in Book IV he takes place, then the empty, then time, and in taking up the empty refutes the arguments for its existence.

3. Change of place first among changes (“the emission of energy is what, jump-like”) #

Point: change of place is the most evident change and presupposed to the others, yet not the only change.

• Empedocles and Anaxagoras explicitly, and modern science of the 17th–19th centuries by tendency, took change of place as the only change. Aristotle rejected this and showed how other changes are possible.
• Modern turning point: quantum theory. In Bohr’s picture the electron passes between energy levels by emitting energy, and the emission is jump-like; a change of place from orbit to orbit would give continuous motion and continuous emission, contradicting the spectrum studies. So that change can’t be understood as change of place. “Strange, huh?”
• Order of presupposition: to melt butter you take it out of the refrigerator; to freeze it, put it in — change of quality presupposes change of place. Chemical change requires bringing chemicals together in one place, not vice versa. Growth presupposes change of quality and substance: carrots must become flesh, blood, bones, or we’d be “a mini patched fool” in appearance.
• Hence in the four books on the universe [ed.: De Caelo] Aristotle studies change of place first — still going from general to particular: change of place without chemical change but not vice versa; chemical change in non-living and living, growth strictly only in the living.

4. Can there be change of place without place? (“the president and his position”) #

Point: place is distinct from body, and Democritus admitted “nothing” in words to save motion.

• Body vs. place: the place where one body was later holds another — good reason they differ. Analogy: the president and his position; if always the same man held the office you might not distinguish them, but one man succeeds another, so office and man differ.
• Democritus: without the empty everything would be packed tight like sardines in a can, or clothes in a suitcase you sit on to close; nothing could move. He admits the empty is nothing, yet the nothing must be for motion to be — a man admitting, in words at least, a contradiction, desperately holding on to the reality of motion.

5. Aside: the paradox of becoming (“To be or not to be”) #

Point: the hardest apparent contradiction in motion is the one Aristotle solves in Book VI; Hegel, unable to solve it, admits contradiction in change. Reference: his teacher De Koninck’s French article in Laval théologique et philosophique, “Paradox de devenir par contradiction” (title as heard). The hint of the paradox:

1. Take what is not a sphere becoming a sphere: a time in which it is not, then a time in which it is.
2. No time can lie between: in any in-between time it must either be a sphere or not (Hamlet: “you can’t both be and not be, and you must either be or not be”), so that time belongs to one side or the other.
3. So there is a last instant of not-sphere and a first instant of sphere. Same instant? Then it both is and is not a sphere — Hegel goes along with that. Different instants? Two instants can’t touch any more than two points can without becoming one; between two points there is always a line, between two instants always a time — and we are back at step 2.

• Theological weight: under the accidents of bread and wine there is first bread and wine, later the body and blood of our Lord, with no time between; so the last instant of bread seems the first instant of the body — the heresy revived by “Ulfrid or somebody” [ed.: name unclear], bread coexisting with the body, with the further problem of how the body gets there without transubstantiation. An originally philosophical problem solved in Physics VI; Hegel seems unaware it was solved.
• Contradiction is impossible, as Parmenides first recognised; Heraclitus’s one-opposite-becoming-the-other was relatively easier. Ulysses in Shakespeare: “things in motion sooner catch the eye than what not stirs” — motion grabs the senses, so we cling to its reality, then fall into seeming contradictions.
• Heisenberg: quantum theory began with strange apparent contradictions between experiments; the mind goes forward not by accepting contradiction but by finding a solution, and the untying is itself a discovery. In Thomas’s Sentences the body of the article is called the solutio, the untying. C.S. Lewis: a problem is a knot; find the loose end. Sherlock Holmes “can make neither head nor tail of it” when he can’t find the loose end.

6. Two reasons for treating place and time; nothing can be imagined without them (“Whatever exists must be somewhere”) #

Point: place, empty, time and the continuous are taken up because connected with motion (which is in the definition of nature) and because common to all natural things — general before particular.

• The Greek common opinion: whatever exists is somewhere; if not somewhere, it doesn’t exist. Being in a place is really a property of bodies; the opinion identifies what is with bodies.
• Our imagination can’t transcend the continuous, or time (at least in the second act of reason). So the soul is imagined as a continuous air-like thing shaped like a man — Homer, and even Dante recognising souls in purgatory by shape. Dr. Kasurik’s joke: “How do I recognise your soul?” — by how screwed-up a man’s approach to a problem is. His cousin Donald could not get his mother to see that God in his divine nature has no body.
• Hence study of immaterial things belongs to the latter part of life and of studies. Logic helps theology: Albert the Great — the first thing logic considers is the universal, which can’t be imagined. Young Socrates in the Parmenides imagines the universal as a sail over everybody — resolving to imagination; modern logicians want a class because a class can be imagined. Logic and wisdom resolve to reason; geometry can resolve to imagination — “plain geometry is plain to us in more than one way.”
• Place seemed the first of all things: place can be without the body, not the body without place. Hesiod: first a yawning gap, then broad-bosomed earth and love. You can’t come into the world until there is a place for you. So place is before everything in the second sense of before (this can be without the others, not they without it) — almost divine. Later we realise not all things are in place: the Soviet rocket reporting back “no God up here” — naive, Thomas and Albert would laugh, but it makes a kind of sense.
• Everything likewise seems in time; students find eternity, God not in time, very hard.
• “The consideration of the particular is after that of the common,” as in the first reading. Aside: he heard Paul VI say general before particular is the common rule of all learning.
• Motion first after nature (Book II) because motion, not place or time, is in the definition of nature.

7. Can motion be defined? Descartes and Locke say no (“denies that motion can be what defined”) #

Point: the moderns who speak of defining motion deny it can be done; the others neglect it.

• Aristotle grants some things are known without definition; in the ninth book of wisdom [ed.: Metaphysics IX] he says this of act. He knew where defining stops; Descartes and Locke put motion there.
• Descartes: confusion of certitude with the clear and distinct — sure motion exists, so he must know clearly what it is, as “I think therefore I am” would require clearly knowing what thinking is; but Descartes is not clear on those.
• Locke: simple vs. composed ideas; composed ideas are defined by simple ones, simple ones can’t be; motion is simple. Reply: motion is in fact divisible forever, but that doesn’t help define it — divide a straight line forever and you get only straight lines; you can’t define a line by the parts got by dividing.
• The real question: is there some multiplicity in what motion is that can found the diversity of parts in a definition?

8. Can the point be defined? Then so can motion (“the point is the limit of a line”) #

Point: even the indivisible point has a multiplicity for definition, being something of another; so does motion.

• Against the student who denies points exist: bodies exist, and finite ones (your body, the table, a sphere). The end of a body is a surface — length and width, no depth (any depth and you haven’t reached the end). It can’t be cut off like a nut from a bolt; it is not a body or substance, it seems like an accident, yet it is. The surface ends: its end has length without width, a line. The line ends: its end, with no length, width or depth, is a point. Euclid: a point is that which has no parts (but has position).
• A definition is a speech of many names, each meaning something by itself, hence more distinct than a name: “square is an equilateral and right-angled quadrilateral.” The point’s nature is to be the limit of a line: limit and line are two meanings — multiplicity. Line is limit of surface, surface limit of body. Compare health defined as a good condition of the body.
• Motion is something of another: Galileo studied free fall, “naturally accelerated motion” — but is it the falling that falls? Stock examples: bowling — is it the rolling that rolls down the lane? Is it the walking that goes for a walk? The ball out of the ballpark — it is the ball that goes out, and if the motion goes out, it is because the motion is in the ball.

9. Definitions are hard to grasp; what “understanding” means (“what is said to stand under something”) #

Point: understanding a definition is major work, and definition is the goal beyond examples.

• His own experience: long labour defining comedy (Aristotle’s part on comedy lost; help from Aristotle and the English comic muse) and recognising Shakespeare’s definition of reason.
• Thomas’s method: for Boethius’s definition of eternity, an objection to each part, then explain and defend, then answer; for law in the prima secundae, one article per part (ordering by reason, for the common good, properly promulgated…); likewise moral virtue in NE II. Motion and time are such definitions.
• Colleagues teaching philosophy can’t define reasoning. A student offers: coming to know a statement through other statements already known or accepted — he says he still has to “pull my legs off” [unclear in recording].
• Examples are more real to us because the senses reach them, but you don’t understand fully until you define. Should we define definition? What is understanding? Not perhaps a strict definition, but a more distinct speech is suggested by the etymology: knowing what is said to stand under something. To understand an effect: know its underlying cause, its “ground” (the English word for cause). To understand a word: know the meaning or thing under it — Thomas’s impositio nominis, the placing of a name upon a thing, the Greeks’ label. Ford in Merry Wives of Windsor will not “stand under” the name cuckold, worse than devil. To understand a methodos: know its subject (what lies under) and its road. Connection between understanding and substance: the senses don’t grasp substance, understanding does.

10. Reasoning before and after defining (“examples are not a definition”) #

Point: one can reason imperfectly about a thing before defining it, perfectly only after.

• Plato’s Meno: Meno wants to know if virtue can be taught; Socrates doesn’t know what virtue is nor anyone who does; Meno gives examples — examples are not a definition; his definition fails to separate good from bad man. Later Socrates reasons that virtue can and cannot be taught — imperfect reasoning that decides nothing.
• The moderns’ almost universal failure to define what they talk about. One can also reason one’s way toward a definition. “So Aristotle is trying to define motion here.”

His words #

• “the eight senses of in” — the senses Aristotle distinguishes in treating place.
• “the unlimited” / “the continuous” — what is divisible without limit; defined through “the limited” [ed.: the infinite].
• “follows motion intrinsically / extrinsically” — Thomas’s division of Books III and IV.
• “the empty” [ed.: the void].
• “the four books on the universe” [ed.: De Caelo].
• “paradox of becoming” — De Koninck’s title as he gives it.
• “solutio, the untying” — the body of the article in Thomas’s Sentences.
• “second sense of before” — what can be without others, not they without it.
• “the ninth book of wisdom” [ed.: Metaphysics IX].
• “simple and composed ideas” — Locke’s distinction.
• “a speech as opposed to a name” — what a definition is.
• “something of another” — the mark of what is definable though simple (point, motion).
• “impositio nominis” — placing of a name upon a thing.
• “methodos” — subject and road; the road said to be under the thing.
• “understanding” — knowing what is said to stand under something.

Texts #

Read in class

• Aristotle, Physics III, opening: why treat the unlimited, place, the empty, time (“motion is impossible without place and the empty and time”; “whatever exists must be somewhere”; “the particular after the common”) — DHB Vol III, The School of Aristotle, p. 185 (verified). Mentioned
• Thomas’s commentary on Physics III–IV (intrinsic/extrinsic).
• Aristotle, Physics IV (place, empty, time); Physics VI (the continuous).
• Nicomachean Ethics I opening and Thomas’s comment; Politics I; NE II (definition of moral virtue).
• Aristotle, Metaphysics IX on act (inferred).
• De Koninck, article on the paradox of becoming, Laval théologique et philosophique.
• Thomas, Summa, on Boethius’s definition of eternity; prima secundae on law; Sentences (solutio).
• Plato, Parmenides (the sail); Meno.
• Euclid, definition of point; Hesiod (yawning gap); Homer, Dante (souls); Shakespeare: Hamlet, Troilus (Ulysses), Merry Wives of Windsor; C.S. Lewis; Descartes, Locke, Galileo, Bohr, Heisenberg, Einstein, Faraday, Dalton; Albert the Great; Paul VI.

His questions #

• What famous philosopher said that atoms and the empty exist? Democritus.
• Is Aristotle lying when he says motion is impossible without the empty? (student) No; he speaks according to common opinion until it is time to determine the truth.
• Can you have change of place without place? Would you distinguish a body and its place? Yes, they differ: another body later occupies the same place.
• Is there any time between the time it is not a sphere and the time it is? No; any middle time would belong to one side or the other. Whether last and first instant coincide — left open for Book VI.
• Can you imagine the universal? No; logic resolves to reason, not imagination.
• Divide a straight line forever; what do you get? A lot of straight lines — so division doesn’t define.
• What is the end of a body? Does the surface have depth? A surface; no, or you haven’t reached the end.
• Is it the rolling that rolls, the walking that walks, the motion that leaves the ballpark? No; the ball, with motion in it.
• What is reasoning? Student: coming to know a statement through statements already known; not resolved.
• What does it mean to understand an effect? a word? a methodos? To know its underlying cause; its meaning; its subject and road.