False Imagination, Wonder, and Learning from Nature: Student or Judge

Orientation #

He ends the third reading of Physics VI (“maybe I’ll stop there at the end of the third reading”) and says “next time we’ll start in the fourth reading.” A tail fragment at the end returns to Euclid (radii of a circle, the fourth theorem, “all right angles are equal”), cut off mid-sentence. The previous class worked through Aristotle’s argument that magnitude, motion and time are infinitely divisible; the next continues Book VI with Zeno.

The class, in order #

1. False imagination as the main cause of deception (“imagine something that cannot be imagined”) #

Point: Thomas’s “false imagination” is the main cause of deception on the side of our knowing powers, and it has two forms.

• A vs. B: imagining something other than it is vs. trying to imagine something that cannot be imagined at all.
• Soul: the poet and the average man imagine the soul as an air-like substance in the shape of a man. Homer’s souls in Hades, shadows of their former selves, Achilles preferring to be up plowing the ground; Dante in Purgatorio trying to hug a recognized soul and hugging the air. “They’re being deceived… by false imagination.”
• Universal: in the Parmenides young Socrates imagines the universal as a big sail covering the individuals; then only part of “man” is over each head (one gets “animal”, another “rational”). Modern logicians cannot understand universal and substitute class, because a class, a multitude, can be imagined.
• Rule: whenever something cannot be imagined, you try to imagine it; if you follow imagination you are deceived. Thomas’s commentary on the De Trinitate of Boethius has a section (an article) on this: you cannot judge by imagination about angels or God; you cannot “resolve to imagination.” Same in logic, same about the soul: the soul is indivisible, but not like a point, it has no position “here or there.”

2. False imagination even in geometry: the falsigraphus (“smaller than any what? Rectilinear”) #

Point: even in geometry, where things can be imagined and imagination is where you finally resolve, false imagination deceives.

• The Latin falsigraphus, “the falsely drawn.”
• Incommensurability: men imagined any two lines have the ratio of a number to a number; the diagonal to the side of the square does not. A shocking discovery that forced rethinking geometry until Euclid’s Book V, where ratios and proportions exist that are not expressed in numbers.
• His favourite: Book III, the line at right angles to a radius at the circumference touches the circle only at that point. Untutored, one imagines a straight line could be drawn between circle and tangent, because “above that point there’s space” and space is infinitely divisible. The horn angle between curve and tangent is smaller than any rectilinear angle, though a rectilinear angle can be made as small as you like “like a scissors closing up.”
• Story: after college his old teacher, the curate, told him “go out and buy Euclid” with no reason given; he found it nothing like high-school geometry. His politician friend Roy Monroe sneered at his studying geometry until shown this theorem; then the mocking stopped and he was “full of wonder.”
• Aside: Killebrew, razzed as “full of brew,” hitting the ball out of the park, and Babe Ruth pointing to where he would hit it: all the mocking stops at once.

3. Wonder is aroused especially by what is contrary to expectation (“contrary to what you expect”) #

Point: Thomas, explaining the mathematical example of wonder at the end of Aristotle’s proem to wisdom in the Metaphysics (the incommensurability), notes that though we can wonder about any cause we don’t know, we especially wonder at an effect contrary to what we expect.

• Razor falling to the floor: you don’t wonder, though you don’t know why it falls; if it went up, you’d wonder, not just from ignorance but because it is contrary to expectation.
• Einstein makes the same point (autobiographical sketch in the Harper Torchbooks Einstein: Philosopher-Scientist, essays by scientists with Einstein’s reply): two kinds of wonder; the magnet his father brought home moved bodies without contact, contrary to his expectation. People don’t wonder at what happens all the time.
• Newton knew he did not know why the stone falls (his editor tried to hide it); Einstein in England admired Newton “for knowing what he didn’t know, like you admire Socrates.”
• Euclid II.5, expanded: a rectangle with less perimeter can contain more area, contrary to what the average man thinks (“more fence, more land”). Ancient crooked geometers sold land by perimeter; estimating an island’s area by how long it takes to sail round it (indentations). Thales: if philosophers wanted to make money they could, as the geometer could in buying and selling land.

4. The fifth postulate, and whether a line can be bisected (“you can’t imagine an infinite line”) #

Point: geometry’s postulates and proofs are shaped by what can be resolved to imagination.

• The fifth postulate is not about parallels: it says a straight line falling on two lines making angles less than two right angles, those lines meet. Why a postulate about meeting rather than never meeting? Because you can imagine two lines meeting; you cannot imagine an infinite line, “any time you imagine something you make it finite.”
• Euclid was supposed to have written a book on the falsigraphus (mentioned in Heath’s notes). A former student, at Dartmouth graduate school in math, was puzzling over such pretended demonstrations; “makes you kind of fearful.”
• Student exchange: is it obvious every straight line can be bisected? Even numbers can be halved, odd numbers not. It’s easy to prove, but the proof assumes the line is continuous. Aristotle proves in Book VI that the continuous is infinitely divisible; geometry just assumed it. Or does the theorem itself teach us there is always a middle point? “Think about that a bit.”

5. Physics VI, last paragraph of the third reading: one uniformly moving body (“if time is continuous, distance will be also”) #

Point: Aristotle re-argues the mutual divisibility of time and distance from one and the same body moving, as the moderns say, uniformly, rather than from two equally fast bodies as before.

1. Earlier, for clarity, two equally fast bodies: one goes this distance in this time; the equally fast one goes a lesser distance in lesser time, and vice versa.
2. Now one body at the same speed: if it goes this distance in this time, in less time it goes less distance; so if time is divisible forever, so is distance.
3. And vice versa: this distance in this time, less distance in less time. “For there will be the same divisions of time and distance.” Stops at the end of the third reading.

6. Digression on babies and natural signs: the smile (“a smile is much more interesting than a laugh”) #

Point: are a smile and a frown natural signs?

• His youngest son’s birthday and a picture of him (the oldest grandfather) talking to the youngest grandchild; the baby tries to talk back, gets excited, “in a very human way.” Hospital babies without hugging fail to develop even physically.
• A smile is not a simple sign: sign of joy or pleasure, of amusement, of affection or love; a laugh is tied to the laughable, a smile is more ambiguous (speaker seeing someone in the audience smile; the Mona Lisa, which he doesn’t much like).
• Frown at a baby and it whimpers; smile and it smiles back; they catch your eye. So: are they learning to smile like they learn English, or is it natural? He thinks smile and frown are natural signs, unlike white and black (cultures where white means sorrow; a place where the bride wears black). “You’ve got to hold on to every little bit of nature you can… given this crazy modern world.”

7. Why the moderns deny natural understanding (“there are no statements that we naturally know”) #

Point: the denial is self-refuting, and he looks for a cause besides pride.

1. If no statements are naturally known, no statement could be known; so they couldn’t know that there are none.
2. Pride exists in every age; why should the moderns be prouder? Something else must encourage it, possibly operating independently of pride.

• Student: much of it is moral, since listening to nature means hearing moral responsibilities. He agrees.
• One reason (said before): once philosophy is developed and there are many books, you can start anywhere, whereas at the beginning you must start with your senses; so you come to think you could start anywhere.

8. Aside on the Apology exam: the unexamined life (“not worth living for a human being”) #

Point: the most famous statement in Plato, explained and applied.

• Not worth living for a man: examination is by reason; an unexamined life is not based on reason, so not a human life.
• The two parts of Socrates’ main speech: first, he goes around examining people because of the Oracle; second, he examines the Athenians about preferring goods of the body and outside goods to goods of the soul, i.e. about the life they lead.
• Students agree American life is like Athenian life, so based on a mistake; being told that is irritating, especially if you go on living it, “no wonder they put him to death.” The statement is an exhortation to practical philosophy, maybe to an examination of conscience. A student he asked said students lead an unexamined life.

9. Aristotle’s two proportions: reason to the emotions (“like a father is to a son”) #

Point: Aristotle sets up the question by proportions: should reason be to the emotions as master to slave, or as father to son? Answer: father to son.

• Two differences (Greek family): the master rules the slave for the master’s good, the father rules the son for the son’s good; the slave has nothing to say about what he does today, the son has some say and the father allows leeway within reason.
• Conclusion: reason rules the emotions for the good of the emotions, and the emotions have a certain leeway. Hence the fine arts, good music and literature: they appeal to the senses, so the emotions are ruled but “given a little what they like.”
• His experience: children with firm discipline but love are happier; children allowed to run ragged become restless and dissatisfied; likewise reason prevents excesses that are emotionally upsetting, “deranging.” The saints almost say the emotions must sometimes be done violence.

10. Kant’s two proportions: reason to nature (“as a student is to his teacher”) #

Point: Kant asks whether reason should learn from nature as a student from a teacher or as a judge/lawyer from a witness, and chooses the second; Berquist says both are true, in order.

• Student: sits and listens to whatever the teacher has to say, doesn’t decide what will be said. Witness: speaks only in reply to the questions the judge or lawyer sees fit to put.
• Kant: the second only; he is caught up in the success of experimental science (Galileo, the inclined plane, three or four famous experiments), where an experiment answers a definite question put to nature as to a witness.
• Schrödinger (perfected wave mechanics, showed its equivalence with Heisenberg’s quantum mechanics; the Schrödinger equation), in the Dover collection Science, Theory, Man, essay “Is Science a Fashion of the Times?”: we perform only the experiments our ideas make interesting; other questions would have produced a different science. Not explicitly about Kant, but a reflection of it.
• A trial lawyer’s book: question a witness at random and he may harm your case; go in with a plan; every courtroom investigation takes the direction of the questions asked (congressional hearings).
• His answer: first listen to nature as a student, see how far you get; later, in particular study, the second way. The eight books of “Natural Hearing” (the actual title, not Physics) may mean listening to nature as to a teacher. Heraclitus [transcript: “Pericleitus”]: wisdom is to speak the truth and to act according to nature, giving ear thereto; the ear is the sense of learning from another, the sense of the student.
• Objection he raises: how listen to everything nature says? Reply: not in particular (every insect, every plant) but in general; that is the philosophy of nature, general knowledge of the natural world from common experience.
• Student asks whether the reason/emotion proportions were Kant’s: no, Aristotle’s; and unlike him here, Aristotle does not say sometimes one, sometimes the other. There is “a lot more truth in the first,” all the principles are there, though there is something in both.

11. Is experimental science known through what we naturally know? (“the hypothesis is the soul of experimental science”) #

Point: philosophy depends completely on the natural, resolving what we don’t naturally know to what we do; experimental science does not.

1. Great scientists rarely experiment at random; a hypothesis suggests the question, and the experiment tests it (though unexpected things sometimes happen in the experiment).
2. Per Einstein, the hypothesis is freely imagined, with no justification from what we already know; its whole justification is what you can predict from it, especially things never observed. Dirac worked out Heisenberg’s theories mathematically and a positive electron came out; months or years later the positron showed up.
3. So water being H2O is true, but not known or proven through what we naturally understand.
4. Even confirmed, the hypothesis remains a “tested guess” (Einstein). Elementary logic: “if A then B; B; therefore A” does not follow; confirmation is not a syllogism.
5. Newtonian physics: planets not where they should be, but too successful to jettison, so they guessed unknown planets, trained telescopes and found “the last planet.” Then Einstein’s different hypothesis predicted all Newton did and more; then it became crystal clear you never know these things are so.
6. More and more precise predictions raise probability: an eclipse at 5:04 is hard to call chance; sociology’s predictions are too vague to mean much.

• A man accustomed to a method where all ideas are hypotheses thinks, by custom, all ideas are like that. Claude Bernard, father of modern physiology (doubt intrinsic to his method): the scientist has ideas, deduces, tests; the philosopher never tests; the theologian just has ideas. Naive views because the only method he knows is the scientific one.
• Warren Murray’s joke: scientists make hypothetical statements about the ancients without reading them, so they don’t use their own method. His kidding: Plato, Aristotle and Thomas thought there was a maximum speed in the universe; no one else did until Einstein. “To err is human.”

12. Tail: Euclid’s axioms and the movement of the mind (“all right angles are what equal”) #

Point: fragment after “next time we’ll start in the fourth reading,” resuming Euclid. If one part fell below the other, that contradicts all radii being equal, hence the definition of circle, so they coincide; Euclid does not make this a theorem, but there is some movement of the mind from definitions to conclusion, more so in the fourth theorem and in the equality of the two halves of a circle by the diameter. Likewise the postulate that all right angles are equal is unproved, but you go through a process, laying one line on another and seeing them coincide. Recording ends mid-sentence.

His words #

• false imagination; Thomas’s phrase, the main cause of deception on the side of our knowing powers; either imagining a thing otherwise than it is, or trying to imagine what cannot be imagined
• resolve to imagination; the way you finally judge in geometry, not possible for soul, angels, God, logic
• class vs. universal; modern logicians substitute the imaginable multitude for the universal
• falsigraphus; “the falsely drawn,” a false geometrical demonstration
• horn angle; angle between circle and tangent, smaller than any rectilinear angle
• rectilineal angle; angle between straight lines
• wonder; especially at an effect contrary to what we expect
• fifth postulate; about lines meeting, not (he insists) a “parallel postulate”
• natural sign; e.g. smile, frown, as opposed to conventional (white/black)
• natural understanding; statements we naturally know, on which philosophy completely depends
• Natural Hearing [ed.: Physics]; the actual title of the eight books, i.e. listening to nature as a student
• philosophy of nature; general knowledge of the natural world based on common experience
• hypothesis; “the soul of experimental science,” freely imagined (Einstein), a tested guess
• confirmation; not a syllogism (“if A, B; B; therefore A” does not follow)

Texts #

Read in class

• Aristotle, Physics VI, last paragraph of the third reading (one body: “if time is continuous, distance will be also… the same divisions of time and distance”)
• Heraclitus fragment (transcript “Pericleitus”): wisdom is to speak the truth and act according to nature, giving ear thereto

Mentioned

• Thomas Aquinas on the Physics (false imagination; wonder at what is contrary to expectation) (inferred as the commentary)
• Aristotle, Metaphysics, proem (“premium to wisdom”), mathematical example of wonder
• Thomas Aquinas, commentary on Boethius’s De Trinitate, article on not judging by imagination
• Homer, Odyssey (souls in Hades, Achilles); Dante, Purgatorio (hugging a soul)
• Plato, Parmenides (universal as a sail); Plato, Apology (unexamined life; two parts of the speech)
• Euclid, Elements: Book V; Book III tangent theorem; II.5; fifth postulate; fourth theorem; all right angles equal; Heath’s notes on the lost falsigraphus book
• Aristotle on reason and emotions, master/slave vs. father/son (work not named)
• Kant, student/teacher vs. judge/witness, Galileo’s inclined plane (work not named)
• Einstein: Philosopher-Scientist (Harper Torchbooks), autobiographical sketch (magnet); Einstein on Newton
• Schrödinger, “Is Science a Fashion of the Times?”, in Science, Theory, Man (Dover)
• a trial lawyer’s book on questioning witnesses
• Claude Bernard on scientist, philosopher, theologian
• Dirac and the positron; Newton and the discovery of a new planet

His questions #

• Why do we especially wonder about an effect contrary to what we expect? Because wonder is not only at an unknown cause (the razor falling) but at what runs against expectation (the razor going up); Einstein’s magnet, Newton’s stone.
• Why is the fifth postulate about lines meeting rather than never meeting? Because meeting can be imagined and resolved to imagination; an infinite line cannot, imagination makes everything finite.
• Is it obvious that every straight line can be bisected? Easy to prove, but it assumes the continuous; Aristotle proves infinite divisibility in Book VI; left open whether the theorem itself teaches there is always a middle point.
• Are a smile and a frown natural signs, or learned like English? He thinks natural, unlike white and black; a smile can signify joy, amusement or love.
• Can someone know that there are no statements we naturally know? No; then no statement could be known, including that one.
• Why do the moderns deny natural understanding, if pride is in every age? Something else encourages it: a student says the moral responsibilities nature imposes; he adds that with philosophy developed you think you can start anywhere.
• Should reason be to the emotions as master to slave or as father to son? Father to son: ruled for the good of the emotions, and with some leeway (hence the fine arts).
• Should reason learn from nature as student from teacher or as judge from witness? Kant says judge only; he says first as a student (philosophy of nature, in general), later as a judge (experimental science, in particular).
• Is “water is H2O” known through what we naturally know? No; the hypothesis is freely imagined, justified only by prediction, and confirmation is not a syllogism; it remains a tested guess.