Demonstration and Dialectic: Form and Matter of the Syllogism, Probable Opinions, Propter Quid and Quia, the Four Questions, and Why Definition Needs Genus and Difference

Orientation #

He refers back to “last time” twice: the ice-cream-cone analogy for form and matter, and the question whether God is a philosopher (custom of speaking); he also asks whether “we talked last time” about how Aristotle defines probable opinions (not resolved by the context block). Verified sources place the handout “Contradiction and the Growth of Reason”, p. 22 (about ten minutes read) and DHB Vol. III, p. 983 in this episode; the handout most likely underlies the stretch on light as waves and particles (inferred). The previous class treated the divine attributes and the dictum de omni/de nullo in syllogistic; the next continues into the Topics and the four tools of the dialectician.

The class, in order #

1. Form and matter of a syllogism (“adding, subtracting, multiplying, or dividing correctly”) #

Point: demonstration and dialectic differ in the matter, not the form, of the syllogism.

• Analogy (a “mono-duxio” [ed.: manuductio], his word, garbled): to get the right result you must (a) multiply correctly, which you can do even with the wrong numbers, and (b) have the right numbers. Ice cream cones for 19 grandchildren on the beach: multiplying the number of people by the cost is one thing; being sure of the cost and the number is another.
• Proportion: “does something follow necessarily from these premises?” ↔ multiplying correctly (form); “are these propositions true, necessary, or probable?” ↔ having the right numbers (matter).
• Hence the difference between demonstration and dialectic “would be in the matter.” Using letters A, B, C abstracts from the matter so the two are not mixed up. (Aside: this “drives my wife crazy”; men understand better, women love better.)

2. The demonstrator’s premises are necessarily true (“all right angles are equal”) #

Point: the demonstrator sees his premises as necessary, either because self-evident or because shown through what is self-evident.

• Self-evident: axioms and postulates of geometry (all right angles equal; the whole more than the part; quantities equal to the same are equal to each other).
• Worked theorem: two straight lines intersect; opposite angles are equal. Argument as given:
  1. A straight line meeting a straight line makes angles equal to two right angles (from what a right angle is: equal angles made by straight meeting straight; if it meets obliquely, the parts still sum to two right angles).
  2. So x + b = two right angles, and a + x = two right angles.
  3. Axiom: things equal to the same are equal; so x + b = a + x.
  4. Equals subtracted from equals leave equals; therefore b = a.
• Conclusion: demonstrated from statements that are either obvious or shown through obvious ones by “real syllogisms.”

3. Is modern science reasoned-out knowledge? (“a hypothesis in science is freely imagined”) #

Point: what he calls science (Euclid’s Elements: “reasoned-out knowledge of things,” including the thinking-out of distinctions, definitions and statements before conclusions) is not obviously what modern science is.

• Einstein, 1905, three Nobel-worthy papers; yet Einstein says the hypothesis in science is “freely imagined” — not self-evident, not reasoned out. Great discoveries made by young men in their twenties and thirties, when imagination is freer; Heisenberg explains his theories better as he ages but no longer discovers.
• Testing a hypothesis by predictions is not a syllogism proving it: “If my hypothesis is correct, there will be an eclipse at ten”; the eclipse comes; that does not prove the hypothesis. The class agrees: no.
• Huygens (wave) vs. Newton (particles): an experiment shows light behaving as a wave, so Newton was “proven” wrong; then the photoelectric effect (Einstein, 1905) follows if light is particles (more intensity gives more electrons at the same speed, not faster ones, like individual collisions), not if it is a wave. How can it be both? Heisenberg: Einstein knew there was at least an apparent contradiction here, yet could only explain the effect by that hypothesis. Bohr applied the quantum to the atom.
• Student: is there an interface between reasoned-out knowledge and flashes of intuition? He: those familiar with these things get some insight into what they are like — left largely open (“not get too much into that right now”).

4. Prior Analytics is about form; custom of speaking (“they syllogize in the same way”) #

Point: the Prior Analytics, written in letters, asks only whether something follows necessarily; demonstrator and dialectician syllogize in the same way, as two people multiply in the same way though one has the right numbers.

• Aside from his own reading of Thomas that day, “question twenty-three” on liberum arbitrium [ed.: locus as he states it; not otherwise identified]: objection — iudicium liberum names an act, so free choice is not a power. Thomas’s reply: the vocabulary would indicate an act, but by the custom of speaking it is understood as the source of the act.
• Same move with “philosopher” (prev. lecture): by the word, God is a lover of wisdom more than anyone, since he alone loves himself adequately; but by the origin of the word (Pythagoras: “don’t call me wise, God alone is wise; call me a lover of wisdom”) it names a man who knows he is not wise as God is, yet pursues wisdom. Names signify by custom, so custom must be respected.

5. The dialectical syllogism and probable opinion (“because of the quantity or the quality of men”) #

Point: a dialectical syllogism is a syllogism from probable opinions; an opinion is probable because of the quantity or the quality of those thinking it.

• Quantity: the opinion of all or most men (sugar is sweet).
• Quality: the opinion of all, most, or the most famous in a given art or science, when speaking about what pertains to that art or science (most doctors: smoking is bad for health; Einstein, the most famous scientist, on hypotheses — at a philosophical conference he was told “that’s just Einstein’s opinion,” but you must take it seriously).
• Thomas’s disputed questions quote Augustine, Anselm, Damascene — famous in theology — not as necessarily true but as to be taken seriously.
• Opera: Mozart, famous for operas, says the words must be the obedient servant of the music; Wagner says words are the masculine element, music the female. Both famous; “Mozart is more probable in my mind.” (Aside: Mozart operas at West Point for the bicentennial, City Opera of New York.)
• Geometry: Euclid, the most famous book of geometry for thousands of years; Pythagoras, about the only theorem in geometry named after a man — what they say is probable.
• Student asks what “mathematician” means: one fond of learning, a synonym for Philomathes; Plato says a philosopher must be a Philomathes, but “philosopher” is more precise about the ultimate goal, wisdom (his granddaughter Sophia: knowledge of God).
• Result: from probable premises the conclusion follows necessarily but is only probable (“it ain’t necessarily so”); from necessary premises in syllogistic form the conclusion is necessarily true. “That’s the big difference between them. They differ in their matter.”

6. Two kinds of demonstration (“propter quid” and “quia”) #

Point: Aristotle distinguishes demonstration propter quid (Greek dioti) from demonstration quia.

• Propter quid, as he defines it: a syllogism making us know the cause, and that of which it is the cause, and that it cannot be otherwise — three elements. The angle theorem: the straightness and intersection of the lines is the cause of the angles’ equality; you know the cause before the effect and reason from cause to effect with necessity.
• Quia: “that it is so,” reasoning from effect to cause. The five ways of the Summa Theologiae are of this kind: the first way goes from motion (effect) to the first, unmoved mover (cause). Its premises must still be seen as necessary: everything in motion is moved by another; there cannot be moved movers ad infinitum — both in the proof, proven more fully in the Summa Contra Gentiles, whose first two arguments are from motion.
• Aside: motion is the most proportionate starting point for us, since knowledge begins with the senses (“things in motion catch the eye”).
• Student asks the spelling: q-u-i-a.

7. The four questions in two pairs (“Is this that? Why is this that?”) #

Point: the philosopher’s four great questions come in two proportional pairs, each with a first and a second question.

• Pair one: does it exist? then what is it? If existence is obvious, start with the second: in Physics III (“Natural Hearing”) Aristotle does not ask whether motion exists.
• Soul: a man in the street admits he has a body but is not sure of a soul (“never saw one”), so first show it exists — give the word a meaning, “source of life in a living body,” otherwise you ask “does X exist?”; living bodies exist and are alive from something within; so the soul exists, in plants and animals as in man; then ask what it is. People begin instead from a confused religious notion (something spiritual going to heaven or hell), whose existence is not obvious.
• Pair two: is this that? then why is this that? A student thinks the interior angles of a triangle are two right angles — is that so? then why? Is light both wave and particle — why? Do trees grow — why? “Is he dead? Why?” “Is Seric going to Russia? Why?” You do not ask why unless you think this is that. Not so much who, where, when.

8. Dividing logic: Thomas’s three acts, Albert’s two parts (“the rule of two or three or both”) #

Point: Thomas divides logic by the three acts of reason; Albert into defining and reasoning; both are right, and Albert’s division likely comes from the four questions.

• Thomas (proemia to the Posterior Analytics, “the major proemium,” and the Peri Hermeneias, the only two Organon books he commented on; he did not finish the Peri Hermeneias): first act, understanding what a thing is (square, circle, prime number) — Categories; second act, understanding true or false, statements — Peri Hermeneias; third act, reasoning — all the other books. Albert paraphrased all of them.
• Hugo’s definition of reason (corrected from a student’s version): the ability to understand, reason, and direct itself and others — “plagiarizing Thomas.” Compared with Shakespeare’s: “looks before and after” ↔ directing, since you must see order to direct; “discourse” ↔ reasoning; understanding not named but implied by both. (Aside: “Hugo” originally meant bright mind.)
• Albert (met at Laval through his paraphrase of the Isagoge): logic is needed because we do not know everything (God and angels need no logic); there are two unknowns, the simple (known by definition) and the complex (known by argument); so two parts, the art of defining and the art of reasoning. Oesterle’s Logic: The Art of Defining and Reasoning follows Albert (used by his grandchild and at the College of St. Thomas).
• Who is right? “Albert gives reasons for both” — hence his “rule of two or three or both”:
  • Poetics: Homer, “the poet” by antonomasia, taught the Greeks unity of plot — a course of action with beginning, middle, end (three); elsewhere plot is tying the knots and untying them (two; people count ever more knots Shakespeare unties in a last act). Both.
  • Names said of many: with one meaning, or more than one (chair of a department vs. chairs in the room); later, more than one meaning either by chance (his brother Richard and his student Richard — no reason, “they both like Boston”) or by connection (healthy body, healthy diet, healthy looks). But Thomas sometimes divides into three: exactly the same meaning, entirely different, partly same and partly different — like Shakespeare’s tragedies, comedies, and plays in the middle (forgiveness plays, love-and-friendship plays). Two or three? Both.
• Albert’s art of defining corresponds to the first act; his art of reasoning must absorb the Peri Hermeneias, since reasoning goes from statements to statements — which brings out logic’s usefulness. His guess: Albert was influenced by the four questions — “what is it” concerns a simple unknown (what is the soul; what is a perfect number: a number equal to the sum of what measures it), “why is this that” a composite (why is man’s soul immortal and a dog’s not: the combination soul-immortal).
• Aside: joke about the office secretary named Claire (“say Claire”).

9. A complete definition is a demonstration differing in form (“speech signifying what a thing is”) #

Point: Aristotle’s “fundamental statement” in the Posterior Analytics, that a complete definition is a demonstration by a different form, shown on the board.

• Syllogism:
  1. Minor: a definition is speech signifying what a thing is.
  2. Major: speech signifying what a thing is is speech composed of a genus and differences.
  3. Conclusion: a definition is speech composed of genus and differences.
• The minor states the purpose of a definition (one of the four causes); the reasoning goes from that cause to “kind of the matter,” the speech put together from genus and differences.
• Why the major is true, argued “a little bit dialectically”:
  1. Name and speech are both vocal sound signifying by custom; a name has no parts signifying by themselves, a speech does; a speech (definition, statement) is composed of names.
  2. So a speech signifying what a thing is must contain a name signifying what the thing is.
  3. Objection (“stupid Berquist”): then a man is a man, a square is a square, “a rose is a rose is a rose” (the poet gave up defining), a syllogism is a syllogism — “you didn’t get out of the starting gate.” If you use such a name you say nothing; if you don’t, the speech cannot say what it is. Mary: “Totally.”
  4. Solution: a name that signifies what the thing is, but not distinctly — only in general: “animal” for man, “quadrilateral” for square. The mind knows the confused before the distinct and goes from confused to distinct in order, so a more general name is a stepping stone. That name is the genus (Isagoge): a name said with one meaning of many things differing in kind, signifying what they are — “animal” says what a dog, a cat, a horse is, but only in general.
  5. To complete the knowledge you need a name signifying how it is what it is: the difference (Isagoge; “Porphyry was a very good friend of ours”), the name of what the species has in addition to the genus, what separates species of the same genus.
• Aside: he “was going to give up philosophy” over this insoluble-looking problem until he saw there could be a name closer to his own confusion.

His words #

• form vs. matter of a syllogism: whether something follows necessarily vs. whether the premises are necessary or probable
• “mono-duxio” [ed.: manuductio, garbled]: his leading-by-the-hand analogy from arithmetic
• reasoned-out knowledge: his rendering of science, including thinking out distinctions, definitions and statements [ed.: scientia]
• Natural Hearing [ed.: Physics]
• liberum arbitrium; iudicium liberum: free choice, “free judgment,” understood by custom as the source of the act
• probable opinion: held by all or most men, or by all, most or the most famous in an art or science speaking of what pertains to it
• Philomathes: lover of learning, what “mathematician” means
• demonstration propter quid (dioti): syllogism making us know the cause, that of which it is the cause, and that it cannot be otherwise
• demonstration quia: “that it is so,” from effect to cause
• the four questions: does it exist / what is it; is this that / why is this that
• simple unknown vs. complex unknown: known by definition vs. by argument (Albert)
• the rule of two or three or both
• antonomasia: Homer “the poet”
• equivocal by chance vs. by connection [ed.: pure equivocation vs. analogy]
• name vs. speech: vocal sound signifying by custom, without vs. with parts signifying by themselves
• genus: name said with one meaning of many differing in kind, signifying what they are in general
• difference: name of what the species has in addition to the genus, what separates species of the same genus
• Hugo’s definition of reason: ability to understand, reason, and direct itself and others

Texts #

Read in class

• Aristotle, Posterior Analytics: definition of demonstration propter quid; “a complete definition is a demonstration by a different form” (no chapter given)
• Thomas Aquinas, Summa Theologiae, first way (from motion)
• handout: “Contradiction and the Growth of Reason”, p. 22 (verified; probably the wave/particle passage, inferred)
• DHB Vol. III, The School of Aristotle, p. 983 (verified)

Mentioned

• Aristotle, Prior Analytics (form, letters)
• Aristotle, Physics III (“Natural Hearing”), on motion
• Aristotle, Poetics (plot: beginning, middle, end; tying and untying knots)
• Aristotle, Categories; Peri Hermeneias
• Porphyry, Isagoge (genus, difference); Albert’s paraphrase of it
• Thomas Aquinas, proemia to the Posterior Analytics and Peri Hermeneias; “question twenty-three” on liberum arbitrium (as stated)
• Thomas Aquinas, Summa Contra Gentiles, first two arguments from motion
• Euclid, Elements; the Pythagorean theorem
• Oesterle, Logic: The Art of Defining and Reasoning
• Shakespeare on reason (“looks before and after,” “discourse”); Hugo’s definition of reason
• Plato on the philosopher as Philomathes

His questions #

• What’s the difference between a demonstration and a dialectical syllogism — different forms? No; they differ in matter, as multiplying correctly differs from having the right numbers.
• Does an accurate prediction (the eclipse at ten) prove the hypothesis correct? No, it does not prove it.
• Is God a philosopher? By the word, yes, more than anyone; by the custom and origin of the word (Pythagoras), no.
• Is the proof of God’s existence in the Summa a demonstration propter quid? No — from effect to cause, demonstration quia (motion to the first mover).
• Does the soul exist? Yes: the source of life within living bodies, which exist, in plants and animals and man.
• Who is correct, Thomas or Albert, in dividing logic? Both; the rule of two or three or both.
• Should a plot be divided into beginning, middle, end, or into tying and untying knots? Both.
• If a definition needs a name signifying what the thing is, must we say “a man is a man”? No: use a name signifying what it is only in general (genus), then add the difference.
• Is there an interface between reasoned-out knowledge and flashes of intuition? Left open (“not get too much into that right now”).