Nature vs. Art, Rhetoric, Experimental Science, and Mathematics vs. Natural Science (Physics II, Readings 2–3)

Orientation #

He opens by saying the class is now “masters” of the “first road in our knowledge” (from the senses into reason) and refers back to “my example there, the tree and the stone” and the definition of nature “we just had … the other day” (prev. lecture). At the recorded break he announces reading three (nature vs. mathematics, touching “the central question of philosophy”) and, after that, the “natural fragments” of the first philosophers before returning to Aristotle. The previous class worked through the definition of nature and the natural/artificial distinction; the next takes up the central question of philosophy raised in reading three. Note: the recording is spliced; a class ending (“we have to stop now”) occurs mid-transcript, followed by a question period and then the start of reading three.

The class, in order #

1. Four reasons the philosopher follows the natural road (“at least four reasons why he follows”) #

The point: the road from senses into reason is the philosopher’s road for four reasons.

1. He is a man, an animal with reason, so the road is natural to him.
2. All our knowledge is over that road, since knowledge is either in the senses or in reason.
3. As lover of wisdom he follows Heraclitus: wisdom is to speak the truth and act in accord with nature, “giving ear thereto”.
4. It is the road to wisdom: Aristotle’s animals with sensation seem wiser than plants, the animal with memory wiser still (the fourth reason is completed later in the recording: “the road is going in the direction of wisdom … he’s a lover of wisdom”).

2. Rhetoric as an offshoot of two orders (“rhetoric … is an offshoot of dialectic”) #

The point: rhetoric, the art of persuasion, is a “mixed thing”, an offshoot (paraphysis) of logic and of ethics/political philosophy.

• Of dialectic/logic, because it argues; of ethics and politics, because you persuade more by the image you project (man of foresight, justice, character, who has your good in mind) and by moving emotions, prejudices and customs, which those sciences study.
• Different constitutions need different rhetoric: Demosthenes mocks an opponent for scrubbing benches as a boy (ill-born, slavish), which would be “lousy rhetoric” in America, where the self-made man is admired. Politicians talk differently to businessmen and to a labour union; Edmund Burke speaks to a not-yet-democratic England.
• Power of the art: Jerome’s vision (“are you a Christian or a Ciceronian?”); Augustine in the Confessions first finding the Bible unworthy beside Cicero’s style.
• Aristotle’s history of the art: it began in the Greek cities of Sicily after the tyrants were expelled and advancement depended on persuading a crowd; a crowd cannot follow an intricate argument, so an educated man often does better than a professor who goes back to first principles (politicians talk economics without giving an economics lecture).

3. Experimental science as offshoot of nature and the mechanical arts (“modern experimental science is a paraphysis”) #

The point: as rhetoric is an offshoot of two orders, modern experimental science is an offshoot of natural science and the mechanical (servile) arts, and this has consequences.

• Sign in the words: “physics” from physis (nature), “mechanics” from the mechanical arts; the oldest part of modern science, mechanics (Galileo, Kepler), is the union of the two, strong from the 17th–18th century.
• Mutual dependence: developments in the arts allow experiments; developments in theory suggest inventions; you need the theory to know what the instruments are telling you. Philosophy of nature, by contrast, is “purely natural knowledge” that only compares with art.
• Kant (second preface to the Critique of Pure Reason) saw that here man knows only what he in some way makes; Marx (Theses on Feuerbach) generalizes it.
• Argument he draws out: (1) if experimental science is the only reliable knowledge of the natural world, we know nature only as transformed by instruments, i.e. only what we have made; (2) mathematics too is made by us and brought in to “reduce to order” (Niels Bohr’s phrase, not “find an order”); (3) so of Thomas’s four orders, the one not made by reason collapses into an order made by man, closing a circle: man, beginning and end of all he makes, becomes beginning and end of all he knows, “he’s God. I am the Alpha and the Omega.”
• “The trouble with modern man is he’s trying to live entirely in a world of his own making”, which is necessarily inferior to him and cannot satisfy him; God resting on the seventh day found satisfaction in himself, not in what he made.
• “Everything we do in this course … is important for more than one reason”: the natural/artificial distinction defines what natural philosophy is about and also shows what experimental science is.

4. Paragraphs four and five: nature, having a nature, being by nature (“has a nature” and “by nature”) #

The point: “natural / by nature / according to nature” is wider than “has a nature”.

• Paragraph four: whatever has such a cause has a nature, and all these are substances; “nature is always a certain subject and in a subject” hints at the two senses of nature, passive (subject, matter) and active (form in the subject), to be met in the first book.
• Paragraph five: the tree and the growth of the tree are both by nature; the tree has a nature, but the growth does not — it is due to the nature of the tree, not to another nature inside the growth. So too the tree’s stopping at the height proper to its kind.
• Consequence: natural philosophy is not only about what has a nature but about both, and “in a way” more about change, since nature loves to hide and is known through what it does.
• Parallel with art: Berquist is not the art of logic, though he has some of it; a syllogism made by the art does not have the art. The medical art, the doctor who has it, and the medical procedure which is by the art but does not have it. Aristotle would say: we said what art is, what it is to have an art, what is by art — “don’t identify these three”.

5. Last paragraph: it is laughable to prove that nature exists (“laughable to try to prove”) #

The point: Aristotle seems to violate the Posterior Analytics order (does it exist? before what is it?, as Summa question 2 on God), but did not ask whether nature exists because it is known of itself.

• Evidence it is obvious: tree and stone with the same sun, rain, soil; the garden with one soil, one fertilizer, one watering, yet broccoli here, lettuce there — due to something within the seeds (the white head was cauliflower seed mixed in, not broccoli turned cauliflower); wood and stone in the same fire, one burns.
• Argument: to prove the obvious you can only use what is less obvious; that belongs to one who cannot separate what is known of itself from what is not.
• Aristotle’s example of the opposite mistake: a man blind from birth syllogizing about colours, reasoning about names while understanding nothing — talking about what he does not know as if he knew it, where the prover of nature talks about what he knows as if he did not.
• Why the opposite example works: if one can mistake a man for a woman (Michael Jackson), one can mistake a woman for a man, since the mistake arises from being unable to tell them apart in some case; Budweiser/Miller likewise. Thinking you know what you don’t is more common (Socrates’ discovery); many thinkers, fleeing it, fall into the reverse, “the characteristic of modern philosophers”.
• Kasurik’s reply to “how do you argue with someone who says material things don’t exist?”: “kick him” — precise, not just jocular, because the senses are closer to things than reason, and touch is the most certain sense. Kant’s “scandal” that the external world has not been proved: the scandal is that they tried. Bishop Berkeley still opens the study door before leaving.
• Both mistakes are fatal to the life of the mind: think you know and you won’t investigate; think you don’t know what you do and you have nothing to know anything by. “See Aristotle’s common sense here.”

6. Break and preview (“next time we’re going to look at reading three”) #

Reading three will distinguish natural from mathematical, raise a difficulty, propose and prove a solution, and touch the central question of philosophy. Then, before returning to Aristotle, the “natural fragments” of the first philosophers: only fragments survive, as quotes in later authors, gathered by German scholars (Diels-Kranz, in Greek in his office; the numbers are only for reference). He has made other collections (ethical, method, natural theology). These are read not as truth but as “reasonable guesses”, introducing the second road, of reason as reason, from reasonable guesses toward reasoned-out knowledge, leading to Aristotle’s logical division of “everything that they say” in the second reading of Book I. Einstein: Greece the cradle of Western science; Heisenberg returns to them; “science is the Greek way of looking at things.”

7. Question: which sense of “in” is in the definition of nature? (“which sense of in is in the definition”) #

The point: it resembles “part in a whole”, but also the sense of form in matter, and this is the sense of part and whole that escapes people most.

• Aristotle’s proportion: matter is to form as parts to whole; the whole soul in each part of the body is hard because we try to picture the soul.
• Four senses of part and whole (Metaphysics): in reading one Aristotle touches the sensible composed whole (olive oil in salad dressing) and the understandable composed whole (genus and difference in the definition), and the universal whole (general to particular as whole to parts); the one he is after, matter and form, does not appear at the start.
• Metaphysics Book III (the dialectical “third book of wisdom”): Thomas notes three opinions about the beginnings of things corresponding to three kinds of division — Empedocles’ into earth, air, fire, water; by definition, ending in the most universal (square, quadrilateral…); genus into species, ending in the least universal. The answer of Book XII, matter and form / act and ability, does not appear in the dialectic.
• Why: the other kinds of part can be put “one here, one there” (man and dog in separate rooms; the words of a definition separated); but a man and his shape, the letters of “cat” and their order, the rubber of a ball and its shape cannot. Saying the parts of “cat” are the letters and their order “sounds strange”, yet in a sense it is made of those two; tragedy and comedy as parts of drama can be seen on different weeks, Hamlet and The Comedy of Errors.
• Hence primitive people picture the soul as an air-like body of the man’s shape; even Plato has the sailor in the boat, immaterial substance beside material substance. “Very hard for us to get”, yet the key to understanding change and the union of soul and body we were told of as children.

8. Reading three: does mathematics overlap natural science? (“by what the mathematician differs”) #

The point: the reading’s classical division — problem (three paragraphs), solution (fourth), central question (fifth and sixth, skipped for now), proof by reason and sign (last two). Aristotle notes nature has been shown to be said of both matter and form.

• Side one: natural bodies have surfaces, solids, lengths, points, number (five fingers), shape; so mathematics seems a part of natural science.
• Side two: parts of natural science seem to fall under mathematics. Pythagoras’ four sciences — arithmetic, geometry, astronomy, music, later the quadrivium — include astronomy and music, about natural things. Newton’s Principia Mathematica Naturalis Philosophiae: mathematical principles of a natural science; 20th-century physicists call 17th–19th-century physics “Newtonian”.
• Aristotle’s concrete case: is astronomy other than or part of natural science? It would be strange for the natural scientist to know what the sun and moon are but nothing of what happens to them; those speaking about nature also speak of the shape of sun and moon and whether the earth and universe are spherical. Aside: Aristotle held the earth a sphere, one reason being its circular shadow on the moon.

9. The solution: consideration in separation (“in separation from natural bodies”) #

The point: the mathematician treats these things “not in so far as each is the limit of a natural body”, i.e. in separation from natural bodies and from all sensible matter; the natural philosopher only as the number, surface, shape of natural bodies.

• Nor does the mathematician consider what happens to them in matter: the earth flattened at the poles; the tire circular from the side but flattened where it meets the pavement (why a car left for the winter must be propped up). The geometer does not consider that gravity might flatten his circles.
• The solution is “somewhat puzzling to the Platonists” and touches the central question — saved for later.

10. The reason: definitions with and without matter and motion (“no reference to matter and no reference to motion”) #

The point: both are reasoned-out knowledge founded on definitions (as Euclid shows), so Aristotle looks to the definitions.

1. Definitions of sphere or cube contain no reference to matter — no ice cube, wooden block or plastic paperweight; no glass, steel or rubber sphere — and therefore none to motion (Aristotle says sometimes “no matter”, sometimes “no motion”, meaning both, since they go together).
2. Tests: a lead balloon falls, a helium balloon rises — a geometrical sphere neither, being neither heavy nor light; an ice cube has a melting point, a geometrical cube none; rubber ball bounces, glass shatters, steel sticks in the wall, a geometrical sphere none.
3. Nature is defined as beginning and cause of motion and rest; the Greeks identified nature first with matter, later with form and substance; further in, bone and flesh need different kinds of matter. Conclusion: geometry, defining without matter and motion, considers in separation; natural philosophy considers in matter and with motion.

• Standard example: the snub nose (Socrates’) includes flesh and cartilage; the geometer has only the curve. “Socrates’ snub nose lives on.”
• Student: generating a sphere by rotating a circle — motion used equivocally? Yes: not motion of matter, only an act of imagination.

11. The sign: mathematics has to be applied (“you wouldn’t have to apply it”) #

The point: in the “middle sciences” (medieval name for mathematical sciences of nature) something is taken from mathematics and applied to nature; having to apply it is a sign it was separate.

• Envelopes with the stamp built into the paper vs. licking and applying a stamp (his mother preferred the built-in kind, the old glue being poor): if it must be applied, it was not in it. Likewise his hand applied to the desk.
• History makes it clearer, since the mathematics is usually worked out by someone else: Kepler, with Tycho Brahe’s observations, found the ellipse in Greek pure mathematics (Apollonius’ conic sections), which the Greeks never applied to planets (they used circles and epicycles); Einstein used Riemann’s 19th-century geometry; Heisenberg’s quantum ideas reminded Max Born of the “weird” matrix mathematics at Göttingen.
• Still the basic reason is the definitions; the sign is secondary. “Applied mathematics” survives as an expression.
• Student: does application involve idealization, since shapes aren’t exactly mathematical? “It may involve that too”, but that is another thing to consider.

His words #

• first road in our knowledge: from the senses into reason.
• second road: reason as reason, from reasonable guesses toward reasoned-out knowledge.
• Natural Hearing [ed.: Physics].
• offshoot / paraphysis: a science or art growing out of two orders (rhetoric; experimental science).
• mechanical, servile arts: arts that transform exterior matter.
• reduce to order (Bohr’s phrase): mathematics made by us and brought to bear on nature.
• has a nature vs. by nature / according to nature / natural: the latter is more general.
• known to itself: obvious, self-evident.
• act and ability [ed.: act and potency].
• book of wisdom [ed.: Metaphysics]; third book “the dialectical book”.
• essential parts: matter and form as parts of a thing.
• middle sciences: medieval name for mathematical sciences of nature.
• reasoned-out knowledge [ed.: science]: fundamentally based on definitions.

Texts #

Read in class

• Aristotle, Physics II, second reading, paragraphs 4–7 (nature as subject and in a subject; natural vs. has a nature; laughable to prove nature exists; the man blind from birth).
• Aristotle, Physics II, third reading, paragraphs 1–4 and last two (mathematician vs. natural scientist; astronomy; solution; reason from definitions; sign from application). Paragraphs 5–6 deferred.

Mentioned

• Aristotle, Posterior Analytics (four questions); Rhetoric (history of the art, educated man vs. professor) (inferred); Metaphysics III and XII with Thomas’s commentary (three divisions).
• Thomas Aquinas, Summa Theologiae, question 2 (does God exist).
• Heraclitus on wisdom; Demosthenes’ speeches; Edmund Burke; Augustine, Confessions; Jerome’s vision.
• Kant, Critique of Pure Reason, second preface; Marx, Theses on Feuerbach; Berkeley.
• Newton, Principia; Euclid’s definitions; Apollonius’ Conics; Diels-Kranz.

His questions #

• Why does the philosopher follow the natural road? Four reasons: he is a man; all knowledge is over it; wisdom acts in accord with nature; it is the road to wisdom.
• Is everything that is by nature something that has a nature? No: the growth of the tree is by nature but has no nature; it is due to the tree’s nature.
• Am I the art of logic? Does the syllogism have the art? No to both; I have some of the art, the syllogism is by it.
• Why didn’t Aristotle ask whether nature exists? Because it is known of itself; proving the obvious by the less obvious is laughable.
• Why manifest the mistake by the opposite example? If one can mistake A for B one can mistake B for A; thinking you know what you don’t is more common, thinking you don’t know what you do is the modern mistake.
• How do you argue with someone who says material things don’t exist? Kasurik: kick him; the senses are closer to things than reason.
• Which sense of “in” is in the definition of nature? Like part in whole, but also form in matter — the hardest sense to grasp.
• Is astronomy other than or a part of natural science? Mathematician and natural scientist consider the same things, one in separation, the other as belonging to natural bodies.
• Would a geometrical sphere go up or down if let go? No answer: it is neither heavy nor light; no matter, no motion in the definition.
• Does application to nature involve idealization? It may, but that is another thing to consider — left open.