Substance, Accident and Dialectical Probability: Resolving the Apparent Contradiction in Physics I

Orientation #

He picks up at “the bottom paragraph on page four, reading eleven,” and recalls that “last time” he emphasized the first argument for a third thing because it has more necessity and because it illustrates the role of contradiction in developing knowledge (prev. lecture). No announcement of next time. The previous class treated contradiction as a spur to discovery in science and theology; the next continues Physics I on whether the principles are two or three.

The class, in order #

1. Recall of substance and accident (“recall it from logic a bit”) #

The second and third arguments for a third thing rest on the substance/accident distinction, so he restates it.

• Substance: a thing that exists not in another subject. Aristotle’s first example is always a man; second an animal (a dog), because the unity of a man or dog is clearer than that of a plant. A rock: you might think it a substance, but perhaps it is several substances fused together.
• Accident (in this sense): a thing that exists in another subject and cannot exist apart from it. Health of a man or dog: you can put the man in one room and the dog in another (and the cat elsewhere at night), but not the man in one room and his health in the next; likewise his shape, his knowledge (“I have to take my knowledge with me when I go home”).
• Etymology: “substance” from substare, to stand under — well named, since it is the first subject underlying the accidents. English “understanding” has the same etymology, and not by chance: the senses know only accidents; reason/understanding knows substance. Greek: ousia, which lacks the same sense.
• Second basis of the arguments: contraries are accidents, and substance is more fundamental than accidents.

2. The second and third arguments for a third thing (“no substance is what? Contrary”) #

Point: if contrary accidents are beginnings, the substance underlying them must be a beginning even more so. Second argument (bottom of p. 4):

1. The beginnings are contraries (from reading ten; “everybody’s saying that”).
2. No substance is contrary to another (man, dog, horse, plant have no contrary); contraries are accidents like health/sickness, virtue/vice.
3. But a beginning ought not be said of any subject, else there would be a beginning of the beginning; the subject is a beginning and is before what is said of it (healthy, colored). Conclusion: the underlying substance must be a beginning as much as, or more than, the contraries. Third argument (top of p. 5): how would substance come from what is not substance? If everything comes from the contraries and contraries are accidents, the body would come from health or sickness, the butter from hardness or softness — “doesn’t seem to make any sense.” Nothing is non-substance except accidents; how could accidents be the origin of substance?

3. Aristotle concludes three, and the predecessors saw it (“some third thing underlie”) #

Point: if changes are between contraries and the three arguments hold, some third thing must underlie — water, fire, or something in between; the in-between is more reasonable because it is more unlimited in respect of qualities. Fire, earth, air, water are “twined together with contrarieties” (hot/cold, dry/wet), so those making the underlying thing other than these do not act unreasonably; among the others, air is best (least sensible differences), then water, worse fire. Next paragraph: all the predecessors shaped this one thing by contraries — beside density and rareness they had something made dense or rare (water, air, mother earth), and by “the more and less.”

4. Plato vs. the natural philosophers: where the multiplicity lies (“Christmas cookies”) #

Distinction: Plato puts the contraries (excess and defect) on the side of matter; the natural philosophers see unity on the side of matter and the contraries as two opposite forms it can assume.

• Plato, a logician and metaphysician, thinks of forms separated from matter, which matter partakes of; so multiplicity is on the side of matter. Christmas cookies: one Christmas-tree shape, stamped into this piece of dough, this, this — you run out of dough; many cookies because many separate pieces of matter receive one form. Window panes, many glasses of the same shape: multiplicity from the matter. This is the viewpoint of the extrinsic cause, the maker.
• From the viewpoint of matter and its transformation: one lump of clay can be molded into sphere, cube, cylinder, pyramid — matter one, forms many. His body healthy one day, sick the next, healthy again.
• Student: “that must be an interesting world, everything absolutely unique — only one sphere.” Reply: many pieces of matter partake of the one form; what a man is is one, individual men who share that nature are many. “There’s some truth in that way of speaking too,” but the natural philosopher’s viewpoint, as in the definition of nature, is that of the matter being changed.
• Why Plato came at it “from the outside”: shaken by his teacher Cratylus (everything is changing; how understand what always changes?), near despair, he needed something unchanging; Socrates’ definitions of the universal seemed to give true, unchanging knowledge. Add the “central question” (seen in an earlier reading): Plato thought truth requires that the way you know be the way things are; since we define man without Socrates, Plato, you or me, man must exist apart from us — the world of forms (“ideas” is a false English rendering of eidos, form).
• Parallel: Pythagoras came into natural philosophy from mathematics and spoke of ratios; natural philosophers and modern scientists tend to start as materialists, since matter is what stands out in change — the natural place to begin.

5. Aristotle’s modesty and the count so far (“fewer are better if they’re enough”) #

Fourth paragraph: “to say the elements are three would seem to have some reason” — modest phrasing. Context recap: he asked how many beginnings; one was eliminated (beginnings are contraries, opposites are two); the unlimited was eliminated by four brief arguments; now three reasons force a third thing. Does anything force more than three? The principle of fewness is not “fewer are better, period” — two is fewer than three, but fewer are better only if they are enough; two was not enough (contradiction without the third thing, plus the substance/accident arguments).

6. Two arguments that three is enough (“one is enough to undergo”) #

1. More than three would have no reason: one subject suffices to undergo; with two contraries and a subject, change is possible. A fourth would mean two contrarieties, each needing its own in-between nature — six things — which is not necessary. Nothing forces more than three, as something forced more than two. Hard butter becomes soft not because hardness becomes softness but because the butter loses hardness and acquires softness.
2. There cannot be many first contrarieties, for substance is one genus of being — the genus underlying all the rest — and in one genus there is only one pair of contraries (the species furthest apart). So the beginnings are in substance, and only one contrariety is needed.

7. The apparent contradiction (“how can he have his cake and eat it”) #

Point: reading before and after, the arguments contradict. Before (second argument against the unlimited, p. 4: one contrariety in one genus, substance one genus) and after (second argument that three is enough) reason from there being contrariety in substance; the middle second and third arguments reason from there being no contrariety in substance, only in accidents. Student exchanges, in order:

• Student: does “one contrariety in one genus” refer to the particular accident? No — substance is one genus, and only one contrariety in it.
• Student: “this is an equivocation.” “No, it’s not an equivocation. It’s a contradiction.” Later: “there can be apparent contradictions even without equivocation.”
• Student: “I don’t understand contrariety in genus.” He re-runs last time’s examples of genera of accidents: color — white and black are the contraries; yellow is nearer white, blue nearer black, but yellow and blue are not as far apart as white and black, so contraries are the species furthest apart, only one pair. Habit — virtue, continence, incontinence, vice: in the virtuous and the vicious man, will and emotions go the same way (toward good, toward bad); in the continent and incontinent there is conflict, the continent holds on (the alcoholic who calls his buddy), the incontinent gives in and regrets it, whereas the vicious man (Don Giovanni seducing someone’s wife) rejoices. Virtue and vice, furthest apart, are the contraries. Drama — tragedy and comedy are the contraries; in between, what the Renaissance called tragi-comedy and the standard Shakespeare edition now calls the romances (his four last plays; “romance” in the Greek or medieval sense, not just a love story): more serious than comedy, not tragic in ending.
• Student: what of a substance genus like animal? He takes the genus substance itself, the absolute universal — material and immaterial, or living and non-living.
• Spectrum image: many points on a line can be equidistant, but only one pair furthest apart; contraries are the points furthest apart.
• “He knows what he’s doing. But we need a teacher — not me, but Thomas.”
• Student suggests per se / per accidens; not taken up.

8. Thomas’s resolution: dialectic and probable opinion (“proceeding dialectically from probable opinions”) #

Point: Aristotle has not yet determined the truth with complete necessity; he reasons from probable opinions. To see what “probable” means, return to contradiction in the logic of the second act.

• Contradictory statements: same subject and predicate, one affirmative, one negative (Socrates is / is not a man; every man is wise / some man is not; no man is wise / some man is); both cannot be true, both cannot be false, whether or not you know which. “President George Bush is standing now / is not standing now”: one true, one false, we don’t know which. “Berquist is standing now / is not”: you know which, hence you know the other is false.
• Demonstration: the demonstrator takes the half of the contradiction that is obvious or proven, discards the other, and proceeds. Geometry: an obtuse angle is greater than an acute; all right angles are equal; every whole is more than one of its parts — knowing each, you know its opposite is false.
• Dialectic: the dialectical premise asks which side seems so. If you see a side as probable but not necessary, the contradictory cannot be in no way probable; if nothing were said for it, it would be clearly false and the other side certain.
• Aristotle’s definition of a probable opinion: opinions of all men, or most, or of all or most in an art or science, or of the most famous. Most men say sense pleasure is the best thing in life; moral philosophers say no — some probability on both sides. Most scientists sometimes disagree with the greatest.
• A probable statement needs some part of the truth, not “the truth, the whole truth and nothing but the truth.” The best thing in life will be something pleasant; the hedonist mistakes lower for higher pleasures.

9. The distinction Thomas draws (“contrary differences, but not contrary species”) #

Distinction: in substance there are contrary differences but not contrary species; in accidents both.

• Accident: virtue and vice are contrary species of habit, and their differences (good/bad habit, reasonable/unreasonable) are contrary too.
• Substance: man and stone, man and beast do not seem contrary as virtue and vice do; yet living/non-living, rational/irrational seem contrary — contrary differences, not contrary species. So each side has part of the truth: contrariety is usually defined by species (hence “no contrariety in substance”), but by differences there is contrariety in substance. Both probable, neither demonstrative.

10. Why the first argument is necessary: love, hate, and the heart (“could love itself become hate”) #

Point: unlike the second and third, the first middle argument has necessity: without a third thing, change is impossible.

• We say love turns to hate; but love itself cannot become hate — contradiction. If there is a heart, not the same as love or hate, capable of both, it can lose love and acquire hate, or vice versa (hating food when young, loving it later; disliking someone, then liking them). Does disliking become liking? No. Unless there is a real distinction between my heart and its love, my heart could never cease to love; between my heart and its hate, I could never stop hating.
• Application: when St John says God is love, he speaks properly; there is no distinction in God between Himself and His love, so it is impossible for God to hate — hate said of God in Scripture is metaphorical. From this argument comes the premise that what changes is composed of subject and contrary; syllogized in Summa q.3 (God not composed), and later in the question on God and change (God unchanging because not composed).
• Prior Analytics: dialectician and demonstrator syllogize formally alike, but one can reason from contradictory statements to contradictory conclusions.

11. Socrates on virtue teachable: reasoning from part of the truth (“directed to the good by right opinion”) #

Point: Socrates finds a premise not necessarily true — that what directs us to the good is knowledge — and notes right opinion also directs us (dialogue not named; inferred: Meno).

• Fork in the road to Boston and Providence: the man who knows the right fork takes it; the man who merely thinks it right, and is right, also arrives.
• Hunches: MacArthur at Inchon, opposed by Washington, the army chief of staff and top admiral; told “you’re on your own”; asked his next officer, then read the Bible; had a withdrawal plan (“all will be lost except my reputation”). Nixon in South America ordering the driver to turn off before a planted bomb; Saddam’s foiled plot against the elder Bush; Kennedy’s open car — the wrong guess. Hunches can be correct but are not knowing; military men have a “sixth sense.”
• So “what directs us to the good is knowledge” is not baseless — it is the safest way — but not the whole truth. Virtue can and cannot be taught cannot both be true; the Protagoras solves it differently: no one teacher of Greek, as of piano or French or calculus — mother, father, uncles, teachers all taught a little justice; you cannot point to whom your parents chose to teach you justice.

12. Why dialectic comes first (“we tend to see a part of the truth”) #

Point: Thomas notes Aristotle is not stupidly contradicting himself but reasoning dialectically, and a probable statement needs an element of truth; the second road of knowledge runs from reasonable guesses toward reasoned-out knowledge, so dialectic precedes demonstration.

• Empedocles’ fragment: men live briefly and, having seen a part of life, boast of having seen the whole — pride exaggerating knowledge, but also that we see a part before the whole.
• Bohr’s essays (three volumes, Atomic Physics and Human Knowledge; the respectful Einstein account mentioned the other day): no one Nobel winner saw the whole of quantum theory — Planck 1900, Einstein 1905, Bohr 1913, Heisenberg, de Broglie, Pauli.
• Two armies clashing, Greeks and Trojans: weak men fall on both sides, the strong emerge; stop the fight and make one army of the survivors — Hector and Achilles together. Dialectic brings out a part of the truth at a time; in Plato’s 36 dialogues no one shows the whole truth.
• Student notes Aristotle’s own phrasing (“no substance is contrary” vs. “one contrariety in one genus”) already hints that a genus can be substance while differences are in it — he agrees. Ends: “notice Aristotle’s kind of hesitation here at the end, bottom of page five” — not developed.

His words #

• substance: what exists not in another subject; from “to stand under,” first subject of accidents; same etymology as “understanding”; Greek ousia
• accident: what exists in another subject and cannot exist apart from it
• beginning: his rendering throughout [ed.: principle]
• reading: his term for the lectio/section of Physics I
• excess and defect: Plato’s contraries, placed on the side of matter
• ideas: “falsely translated”; eidos means form
• central question: whether the way you know things is the way they are
• principle of fewness: fewer are better if they are enough
• probable opinion: opinions of all, most, those in an art or science, or the most famous; needs some part of the truth
• dialectical premise: asking which side seems so
• second act (of the mind): where contradiction belongs
• contrary differences vs. contrary species: Thomas’s distinction
• second road of knowledge: from reasonable guesses to reasoned-out knowledge
• romance: serious play ending happily, between tragedy and comedy

Texts #

Read in class

• Aristotle, Physics I, reading eleven (handout pp. 4–5; Aquinas In Physic. I lect. 11, verified): second and third arguments for a third thing; conclusion; predecessors; “three is enough” arguments; Aristotle’s hesitation at the bottom of p. 5 Mentioned
• Physics I reading ten (beginnings are contraries); arguments against the unlimited (p. 4)
• Thomas’s commentary on lectio 11 (dialectical procedure; contrary differences/species)
• Aristotle, Prior Analytics (dialectician and demonstrator)
• Plato, Protagoras; a Socratic dialogue on whether virtue can be taught (inferred: Meno); Plato’s 36 dialogues
• 1 John, “God is love”; Summa Theologiae I q.3 and the question on God’s immutability
• Empedocles fragment; Bohr, Atomic Physics and Human Knowledge
• Shakespeare’s late plays as “romances”; Don Giovanni

His questions #

• Is a rock a substance? Maybe several substances fused together — left open.
• How could substance come to be from what is not substance? It can’t; accidents cannot be the origin of substance, so a third thing is needed.
• Does anything force us to say there are more than three? No; one subject is enough to undergo, and substance as one genus has one contrariety.
• Is the principle of fewness simply “fewer are better”? No — fewer are better if they are enough; two was not enough.
• Can Aristotle have his cake and eat it — contrariety and no contrariety in substance? Yes, dialectically: contrary differences but not contrary species in substance; both statements probable.
• Is it an equivocation? No, an apparent contradiction; such can occur without equivocation.
• If one half of a contradiction is probable, can the other be in no way probable? No; otherwise it would be manifestly false and the first side certain.
• Could love itself become hate? Could God hate? No; change needs a heart distinct from its love; in God no such distinction, so “hate” is metaphorical.
• Does the man who merely thinks the fork leads to Boston get there? Yes, as much as the one who knows — right opinion also directs to the good.
• Who did your parents choose to teach you justice? No one; everyone around you taught a little (Protagoras).