Aristotle's Physics I.11: Why Two Contraries Need a Third Thing

Orientation #

He opens by recapping “last time”: Aristotle found the common basis of all the Greek natural philosophers in explaining change by contraries, and began “becoming strong” in it (giving a reason, showing it forced by truth, first contrary, senses vs. reason, same in general and proportionally, one member lacking) (prev. lecture). He says “later on, in the 13th reading,” the importance of lack will be developed, and the fallacy of the accident will return “in the 15th reading.” The previous session discussed modern physics’ talk of matter, energy and order after reading ten; the next develops contradiction as the engine of intellectual progress.

The class, in order #

1. Recap of reading ten and the plan of reading eleven (“these two contraries are not enough”) #

Point: reading eleven takes the major step in becoming strong in the common understanding: contraries are not enough, a third thing is needed.

• Recap: everyone (Greeks; the Chinese I Ching, unbeknownst to Aristotle; Helmholtz as quoted by Einstein, with attraction and repulsion) explains change by contraries. Aristotle, following “the central thinker in human thought, Heraclitus,” becomes strong in this basis: gives a reason where they gave none; notes their thought was “forced on their mind by truth itself” (contrast Einstein’s freely imagined); all take the first contrary, some judging more by senses, some by reason; all say the same in general and proportionally (full : empty :: love : hate :: dense : rare). Agreement in general with disagreement in particular confirms that the general is more known to us.
• One member of each ratio lacks something: the empty plate vs. the full; hate vs. love; cold as privation of heat. Hinted in “better and worse,” which Thomas reads as one contrary good, the other bad (the Pythagorean lists of good and bad contraries).
• Plan: he will show the need for a third thing by three arguments; the first is emphasized because it “exemplifies the role of contradiction in coming to know.”

2. Contradiction as the way the mind goes forward (“untying sometimes a contradiction”) #

Point: since Heraclitus and Aristotle, the mind’s major steps come by untying a contradiction: in our own thinking, apparent in things, or between thinking and things.

• Anaxagoras’s fragment on mind: mind is self-ruling (true, as logic shows) yet the ruler must be separated from the ruled (as in an army). Untying: one mind, not two, rules what it does not know by what it does know, what is less known by what is more known; but one must separate what one knows from what one does not, “no easy thing, as Socrates showed.”
• Socrates and the slave boy (doubling the square): he shows the boy does not know what he thinks he knows by showing him in a contradiction, which helps separate the known from the unknown.

3. The question and its shape: one, infinite, two, three (“whether there are two or three or more beginnings”) #

Point: Aristotle eliminates the extremes, then goes from two to three, then stops.

• Not one: beginnings are contraries, contraries are at least two; very quick.
• Not infinite (“unlimited multitude”): four arguments, stated briefly.
• At least two; but two not enough, “especially by the first argument,” or else contradiction; then three is enough, with a couple of reasons not to go beyond.
• Of the three arguments for a third, the second and third are “to some extent dialectical” (based on predecessors’ opinions); the first “has got more necessity.” Nothing forces more than three: a beautiful example of the principle of fewness (some say “simplicity”): fewer causes are better if they are enough. Einstein says this underlies all natural science from the Greeks on; Newton’s first rule of reasoning in the Principia; also Kepler and Galileo. That three is enough recurs often enough to be worth noting.
• Aside on brevity: Thomas on Ephesians, Greek en oligo (“in few”), Latin brevitas: Paul shows wisdom by touching many great things in few words. In the Metaphysics commentary, Aristotle’s syntomos becomes Latin breve, which Thomas glosses as small in size, great in power. Shakespeare is closer to the Latin (“brevity as the soul of wit”) but also says “fewness and truth” (a passage in the readings he gave).

4. Not unlimited, third argument first: fewness against Anaxagoras (“as Empedocles does”) #

Point: if a limited multitude can explain things coming to be forever, it is better than an infinite one.

1. Things keep coming to be forever (every spring); the source must explain this.
2. Empedocles explains it with a limited multitude (four elements plus love and hate: a cycle of uniting and separating); Anaxagoras with a straight line, mind separating things out of the mixture forever, which requires an infinity of things inside.
3. Fewer are better if enough; six is fewer than infinite. So the limited is better.

• Circle vs. straight road: to run forever on a straight road you must lay an infinite road; a circle lets you run forever on a finite one (superiority of the circle).
• Bag of blocks vs. finished toy: blocks are built, knocked down, rebuilt forever; the toy breaks and must be replaced (“the Empedoclean principle of buying Christmas gifts”); likewise recycling rather than exhausting resources.
• Our mind naturally inclines to fewer: 365 days explained by one sun rather than 365 suns (an extinguished-in-the-ocean sun would need a new one daily); whether the sun circles the earth or the earth turns, neither hypothesis uses more than one sun.
• Twin-brother teaching on Thursdays: absent any reason for two, you assume one teacher; a report of Berquist in the cafeteria at 2:30 while in class would give a reason. Montgomery’s actor-double sent to Africa: the Germans assume one man unless they get reports of him in Algeria and England at once.

5. First argument: unlimited causes would be unknowable (“nature does nothing in vain”) #

Point: this too rests on fewness, as Newton states it (“nature affects not the pomp of superfluous causes,” “more is in vain when less will serve”).

1. We have a natural desire to know the causes.
2. Nature does nothing in vain: hunger and thirst are given only because food and drink are possible in principle, even if not always obtained.
3. So knowing the causes must be in some way possible; but it is impossible if they are infinite (a word with an infinity of letters: not even the spelling-bee winner could know it).

• Objection he anticipates: “the unlimited is not possible because it would not be knowable?” Reply: he assumes reason can know the causes, and may, because the desire is natural. Hamlet’s “or strip not the modesty of nature” [ed.: usually "o'erstep not"]: nature is modest, does not do more than necessary.
• First and third arguments go together (fewness, not zeroing in on contrariety); second and fourth assume the beginnings are contraries and draw a difficulty from adding “infinite.”

6. Second argument: one pair of contraries in one genus, substance one genus (“furthest apart in the same genus”) #

Point: if the beginnings are contraries and substance is one genus, there is only one pair, not an infinity.

• Contraries defined: the species or forms furthest apart in the same genus. Colour: white and black, not blue and yellow, not yellow and black. Habit: virtue, continence (chooses good, struggles, does not give in: the alcoholic in AA), incontinence (struggles, gives in, then sadness), vice (passion and will both disordered, no conflict, like Don Giovanni); virtue and vice are the contraries. Thomas in the commentary: on a line many points are equidistant, but only one pair is furthest apart, the two endpoints; so one spectrum has one pair of contraries.
• Substance is one of the ten genera but more fundamental: the others are accidents existing only in substance, so the beginnings of all things are sought in substance. Substance is broader than body (immaterial substances exist), though at first they seem the same to us.
• So there is incompatibility between “principles are contraries” and “principles are infinite.”

7. Fourth argument: not every pair of contraries comes first (“some pairs of contraries are before other ones”) #

Point: infinite contrary principles would make every pair a first beginning, but some pairs cause others.

• Empedocles: hot and cold cause hard and soft, black and white. So only a couple of pairs could be first. “Contraries are principles” plus “principles are infinite” gives infinite pairs among the first beginnings: reduced to the absurd.
• Conclusion he reads: “Hence, it is clear from these things that they are neither one nor unlimited.”

8. From two to three: the apparent contradiction in change (“the same thing would be hard and soft”) #

Point: fewer are better if enough; two is fewer but not enough, or change is a contradiction.

• Aristotle’s “there is some reason for making them not only two” is philosophical modesty (Thomas): there is much, indeed necessary, reason. Text: how could density make rareness something, or rareness density? Love does not bring together hate and make something from it; both act on some third thing.
• The contradiction: we must say day becomes night, the healthy becomes sick, the hard becomes soft (deny it and the healthy are always healthy, the sick always sick). But “becomes” means “comes to be”; if the hard came to be soft, the hard would be soft, so the same thing hard and not hard, soft and not soft: impossible. Hence Parmenides against Heraclitus: only a “two-headed mortal” could think it, one head thinking it is, one that it is not. “Two heads is not better than one”: something monstrous, against what is naturally understood, that a thing cannot both be and not be, which Aristotle calls the natural beginning of all the axioms, the most basic statements.
• Applied: if density made rareness dense, that by which things are rare would be dense; if hardness made softness hard, softness would be hard. So there must be a third thing apart from hardness and softness that is made hard or soft; otherwise change involves a contradiction.

9. As such vs. by what happens: the butter (“it’s not the hard as such that becomes soft”) #

Point: the third thing, e.g. butter, is what becomes soft as such; “hard” belongs to it by happening.

• To be butter is not the same as to be hard, nor as to be soft; so butter as such becomes soft, the hard only by what happens to it. Distinction as such vs. accidental: “you can’t do philosophy without seeing that distinction.”
• Carpenter who plays the violin: not what carpenters as carpenters do; mother should answer the child with what carpenters as such do, or he is confused by the million things a carpenter may happen to be. “The musician built my house” is true only in some way, since musician happens to the cause as such.
• The good: Aristotle at the start of the Nicomachean Ethics (touched in the Meno) concludes by induction that the good is what all want. Objection: people want what is bad. Reply: the good as such is wanted; the bad is wanted as apparently good. The last drink is wanted to continue the good time, not to get sick; delicious poison is drunk as delicious, not as poison. A definition by effect, but convertible with the good.
• Sophistical Refutations: thirteen fallacies, six from language (first, equivocation, the most common), seven outside (first, the accident, which “deceives even the wise,” even Plato); to return in the 15th reading.
• So “the hard becomes soft” is true only accidentally, false as such; the butter as such becomes soft, “not the hard at all.”

10. The third thing as subject and ability; confused to distinct (“a real distinction between the butter and the hardness”) #

Point: the third thing is the subject underlying, introducing potency or ability; and the step from two to three is also a step from confused to distinct knowledge of the contraries.

• Butter is able to be hard and to be soft, not both at once; while actually one it is able to be the other; becoming the other, it ceases to be the former.
• Unless there is a real distinction in the hard between hardness and what hardness is in, no change is possible: if all in the hard were hardness, hardness itself would become softness.
• Day and night: light does not become darkness (darkness is the lack of light; how can light be the lack of light?); the air is able to be illuminated or dark, never both; “the dark is never illuminated.” Wet and dry: dryness is that by which the dry is dry, so it cannot be wet; the cloth is the third thing, able to be either, “the wet is never dry.”
• Heraclitus was not stupid: he mocks Hesiod for not knowing day and night are one, and says sleeping and waking are the same while telling us not to act and speak like those asleep. He says one is the other because one becomes the other: pointing out the apparent contradiction in how we all speak, though the average person could not defend the sense.
• Back to the first reading: we know confusedly before distinctly, e.g. the name before the definition. “Hard” names without distinguishing hardness from what it is in; something must be in the hard besides hardness, in the day besides light, in the wet besides wetness.
• Two ways of stating the step: (a) from two to a third thing; (b) from confused to distinct knowledge of the real distinction in the hard between hardness and its subject. The untying of the apparent contradiction in all change is the discovery of a third thing besides the contraries (especially taken abstractly, hardness and softness) and of the composite nature of the contraries between which there is change: the contrary in the strict sense plus the subject in which it exists without being the same. The recording ends here; the second and third arguments for a third thing and the reasons three suffice are not reached.

His words #

• “becoming strong” in the common basis: Aristotle’s work on the predecessors’ explanation by contraries (Heraclitus’s advice).
• beginnings: his word for principles/causes [ed.: archai / principia].
• “unlimited multitude”: his rendering, in preference to Latin, for infinite [ed.: infinitum].
• principle of fewness (“fewness and truth,” from Shakespeare): fewer causes are better if they are enough; others call it simplicity.
• contraries: the species or forms furthest apart in the same genus (white/black; virtue/vice; the two endpoints of a line).
• substance: the fundamental genus; the other nine are accidents existing only in it; broader than body.
• axiom: “the natural beginning of all the axioms,” that something cannot both be and not be.
• as such vs. by what happens: as hard vs. as butter; carpenter as carpenter [ed.: per se / per accidens].
• fallacy of the accident: the first fallacy outside language; deceives even the wise.
• third thing / subject underlying: the butter, air, cloth in which contraries exist without being the same.
• ability: his rendering [ed.: potency]: able to be either contrary, not both at once.
• confused vs. distinct knowledge: the name “hard” before the distinction of hardness from its subject.
• untying: resolving an apparent contradiction (Anaxagoras on mind; Heraclitus on change).

Texts #

Read in class

• Aristotle, Physics I, reading eleven (Aquinas commentary, lectio 11; handout “Whether the beginnings are two, three or more”, p. 1): the opening question; the four arguments against unlimited beginnings; “neither one nor unlimited”; the first argument for a third thing (density/rareness, love/hate).
• Handout “The First Statement and King of Statements”, p. 3 (verified source; the Parmenides “two-headed mortal” and the axiom passage, inferred).

Mentioned

• Aristotle, Physics I, first reading (confused before distinct; name before definition).
• Heraclitus, fragments (sleeping and waking; Hesiod on day and night); Anaxagoras, fragment on mind; Parmenides.
• Plato, Meno (slave boy; the good).
• Aristotle, Nicomachean Ethics, beginning (the good is what all want); Sophistical Refutations (thirteen fallacies).
• Thomas Aquinas, commentary on Ephesians (en oligo / brevitas); commentary on the Metaphysics (breve, syntomos).
• Newton, Principia, first rule of reasoning; Einstein on Helmholtz and on simplicity; Kepler, Galileo.
• Shakespeare, Hamlet (“modesty of nature”); “fewness and truth”; “brevity is the soul of wit.”
• The I Ching; the Pythagorean lists of contraries; Empedocles (elements, love and hate; hot/cold causing hard/soft); Anaxagoras (mixture and mind).

His questions #

• Last time, all the Greek natural philosophers tried to explain change by what? Contraries; the same in general and proportionally.
• How long must a straight road be to run on forever, and what is the advantage of a circle? Infinite; a circle lets you run forever on a finite road.
• How do you know I don’t have a twin brother who teaches on Thursdays? In the absence of a reason for two, you assume one.
• What is wrong with saying the unlimited is not possible because it would not be knowable? Nothing, once we grant that knowing the causes is possible, since the desire is natural and nature does nothing in vain.
• In the genus of colour, which are the contraries? White and black, the furthest apart; only one pair per genus.
• If the hard came to be soft, what follows? The same thing hard and not hard, soft and not soft: impossible, so a third thing is needed.
• Would you say carpenters play violins? Not as carpenters; accidental to the carpenter.
• How can “the good is what all want” be a good definition if people want the bad? The good as such is wanted; the bad is wanted as apparently good (the last drink, delicious poison).
• Does darkness become light, or dryness become wet? No; the air, the cloth, is the third thing able to be either, not both at once.
• Was Heraclitus really so stupid as not to know day from night? No; he was pointing out the apparent contradiction in our speaking of change.