Seeing Likeness and Proportion, Then Q&A on Places and Comedy

Orientation #

He opens with “now the fourth tool”, continuing the four tools of Topics I; the third tool (seeing differences) and the second (senses of a word) are referred back to as already treated (prev. lecture). At the close he says next time will be “a little bit more about the material logic… sophistry”, then some natural philosophy, and that when he starts natural philosophy he gives a syllogistic argument as a challenge. The previous class covered the dialectician’s two arguments and the first two tools; the next treats equivocation, “as such” vs. accidentally, and simpliciter vs. secundum quid.

The class, in order #

1. The fourth tool: seeing a likeness, i.e. a proportion (“the ability to see a what proportion”) #

The fourth tool, the ability to see a likeness, is the opposite side of the third, but the mind is exercised differently by each.

• Difference vs. likeness: the mind is exercised in seeing differences between things close together (hard to tell apart), but in seeing likeness between things far apart. Dog and cat, same genus: too easy, does not exercise the mind.
• Hence the likeness that exercises the mind is proportional likeness: “this is to that as that is to that”.

2. A logical example: defining and reasoning in the Meno (“come to know what you don’t know through what you do know”) #

The likeness between defining and reasoning is his worked example of a proportion between things far apart.

1. The Meno introduces the art of defining (first part) and the art of reasoning (third part); the middle part is about what is common to both: in each you come to know what you don’t know through what you do know.
2. Definitions cannot regress forever: Euclid defines square by quadrilateral, quadrilateral by rectilinear plane figure, then plane figure, then figure; if every part of every definition had to be defined first, you could never define anything.
3. Analogously, if every premise of every syllogism needed proof, you could never begin to syllogize (“prove that before you use it”).
4. Therefore, as the highest genera (the ten categories) are to defining, so axioms, statements known through themselves, are to reasoning.

• Third instance of the same proportion: words. If every word had to be explained by other words you could not begin to use a dictionary; a baby comes into the world knowing no words, not even “mama” or “daddy”, so the first words are not learned from other words, and the first statements we reason from were not reasoned to.
• Aside: his brother Richard said “daddy” first, brother Mark “mama”; his mother said he seemed to say both at once, “so I was the diplomat of the family”.

3. What the fourth tool is useful for (“useful for if then or hypothetical syllogisms”) #

Aristotle gives three uses.

• Definitions: seeing likeness lets you find the genus.
• Induction: you need like things to induce; induction is the dialectician’s other argument (besides the dialectical syllogism).
• Hypothetical (if-then) syllogisms, “most interesting”: with four terms you cannot make a regular three-term syllogism, so you reason from one ratio more known to us to another. If reasoning begins with statements not reasoned to but known, then defining begins with things not defined but known. If nothing is known without defining, nothing is known, not even the statement just made (“you ain’t got nothing to say”); likewise if no statement were known without reasoning.
• Asides: John Duffy, his brother’s friend, told a professor “this is the stupidest exam I’ve ever seen”, tore it up and walked out; Molière’s comedy about the perfectly honest man: “nothing gets you in more trouble than to be perfectly honest”.

4. Why the tool of difference comes before the tool of likeness (“likeness is the cause of what deception”) #

He asks why Aristotle orders difference before likeness and gives two reasons, the first hedged.

• Objection to the easy answer (“perception finds difference easier”): “perhaps, not sure”; people often see a likeness without the difference, and that is why they are deceived. Plato warns that likeness causes deception: if good did not resemble bad, or true false, nobody would mix them up.
• 2:3 as 4:6, then “2 is even, 3 odd, so 4 is odd, 6 even”: overextending a likeness beyond the respect in which the ratios are alike.
• Modern science: water waves, sound waves, light waves — an analogy, but propagated differently; one may assume more likeness than there is.
• “Gross example”: calling homosexual unions marriages — two people, a likeness, seen without the great difference.
• Second reason: seeing a difference is closer to distinguishing the senses of a word (second tool), which is itself close to probable statements (first tool), since all are expressed in words; so the order also follows nearness of the tools.

5. Proportion everywhere: science, ethics, art (“most physical theories are discovered by seeing proportion”) #

He shows how much cannot be understood without seeing a proportion.

• Senior seminar he once gave on the fourth tool: each student hunted proportions in one part of philosophy (logic, ethics, natural philosophy, the book on the soul); “amazing how many”.
• Pierre Duhem (physicist in thermodynamics, historian and philosopher of science, still republished): seeing a proportion is the most important thing in discovering a physical theory. Einstein, The Evolution of Physics: de Broglie developed wave mechanics from proportions.
• Inverse square law of gravity (double the distance, one fourth; triple, one ninth): discovered by Newton and contemporaries from a proportion to light, which spreads evenly and falls off as the square (Faraday’s popular demonstrations); light itself is proportioned to Euclid’s geometry of proportions. “Science is to see” a hidden likeness under differences, not a superficial one. Einstein’s fourth dimension: knowing it would be like a two-dimensional creature discovering its world is three-dimensional.
• Republic: Book I shows the just soul better off than the unjust in itself; to “blow it up” Socrates uses the proportion of three parts of the soul (reason, irascible, concupiscible) to three parts of the city (rulers, army, common citizens). Simpler Platonic proportion: reason is to the emotions as a man to a horse he keeps remounting until it is tamed.
• Aristotle: should reason rule the emotions as a master rules a slave (for the master’s good, “to hell with the slave”) or as a father rules a son (for the son’s good)? He concludes as father to son: the emotions themselves are better off ruled, otherwise “jagged and ragged”.
• Thomas calls vices of the concupiscible appetite (forms of intemperance) childish vices: the uncorrected child grows unruly until the state must step in; children given discipline as a father, not a master, gives it are happier — so too a classroom with a teacher who can control it. Disordered sense appetite is like working at McDonald’s or a pizza place with everyone yelling for their order: enslaved to your emotions.
• Moral virtue as a mean: Aristotle’s proportion to art, easier to see. Too much pepper in the soup (family joke about his father), too little salt, steak over- or under-cooked, a nose too long (Cyrano) or too short. Mozart “always talking about the golden mean” (hedged: “not understood fully”).

6. Proportion in theology and poetry (“The Lord is my shepherd”) #

Proportion is “extremely important” in theology and underlies the most beautiful metaphors.

• Vatican II on the Word of God: as the Word, the Second Person, became flesh, so the Bible, the Word of God, takes on human language; the Council reasons from that proportion.
• “Forgive us our trespasses as we forgive those who trespass against us”, with its parable of the unforgiving servant: a continuous proportion, God is to you who offended Him as you are to the one who offended you; so if you do not forgive, He will not.
• “Father”: God is to us as a father to a son. “The Lord is my shepherd”: as a shepherd to his flock; the same proportion in Homer, Agamemnon “shepherd of the people”.
• Aristotle on metaphors: the most beautiful are based on proportions. Pericles on the young men dead in the war: the spring taken out of the year. Capulet over Juliet: death lies on her like an untimely frost on the sweetest flower of the field.
• Caution: proportion can become “a more necessary argument”, but one must ask in what way the two ratios are alike and not make them alike where they are not.

7. The four tools summed up; Shakespeare’s exhortation (“these are the four tools for the dialectician”) #

Recap of the tools’ order and roles, then the handout’s proportional argument.

• The basic tool: selecting probable opinions. To understand them and avoid equivocation, distinguishing the senses of a word (which also multiplies probable opinions). The last two are useful for definitions, for syllogisms about difference, for induction, and for syllogisms based on proportions.
• Shakespeare’s exhortation (handout, “On Dividing Shakespeare’s Plays”, p. 3, verified source): the chief good of man is to man as the chief good of the beast is to the beast; alternating, the chief good of man is to the chief good of the beast as man is to the beast; so if man’s chief good were no more than the beast’s, man would be no more than the beast; but man is more, therefore his chief good is more.

8. Break-time exchange: next class, and truth possessed vs. sought (“possession of truth is better than the search”) #

Loose talk while stopping at quarter to five.

• Next time: more material logic and sophistry; then natural philosophy rather than love and friendship (he polls the students). He always opens natural philosophy with a syllogistic challenge.
• A student offers one on certitude vs. right opinion: right opinion has hope about it, hope is good, so right opinion seems better than certitude. His reply, citing a modern who said “I’m not an incurable romantic”: knowing the truth is the end of searching, and the end is better than what is for the sake of it; some prefer the search as “more exciting”.
• Asides: Chesterton, “the opposite of employment isn’t unemployment; it’s independence”; “the architecture of New York City is continual destruction” (1928); “something worth doing is worth doing badly”; Gilbert magazine; the two committees that both voted the same way, leaving the academic dean free.

9. Student question: places; the a fortiori and “opposites have opposite causes” (“stock example of a place is the a fortiori”) #

A place is where you look to find a (probable) argument; he explains through examples.

• A fortiori: if a predicate belongs where it is less apt to belong, it belongs where it is more apt. Socrates on the soul: the composed is more apt to be destroyed than the simple, and the soul seems simpler than the body; through the senses the body knows this chair, this dog (corruptible), while through reason the soul knows what a chair or dog is (indestructible), so the soul has more affinity with the indestructible; the soul rules the body as God rules the universe, so is more like the immortal. None of this proves immortality, only that the soul is more apt to survive; but the bones (and Egyptian mummies) do survive death, so a fortiori the soul survives. Other instances: if fornication is bad, adultery is; if stealing is bad, taking a life is worse.
• Student: is the place like a major premise? Answer: in a way you can construct the premise from it (“if the body survives death, then the soul”), but it is a place in that many things fit into it, as a place contains many things; Aristotle uses “place” of the second tool too.
• “Opposites have opposite causes”: his own first thinking on comedy (Aristotle’s part on comedy is lost). Tragedy and comedy are contraries; tragedy purges pity (a form of sadness, as Shakespeare’s prologue to Romeo and Juliet singles out the two) and fear; so comedy purges the contraries, joy and boldness/confidence. Some probability there. Correction once he learned from Thomas the four principal passions (joy, hope, fear, sadness): hope, not boldness, is the opposite of fear, and comedy is more concerned with joy and hope — comedy purges melancholy and despair; comedies end in marriage (joy plus “happy ever after”, hope), tragedies in death. A Latin editor of Terence (whom Thomas quotes): for Terence “the greatest of these is hope”. The chief forms of fiction should concern the chief passions. The four passions also in John of St. Thomas, in the opening of Gaudium et spes (“joys, hopes, fears, sadness”), in St. John of the Cross: rectify those four and you rectify the rest.
• Asides: 1929 Wall Street jumpers, hopes in the wrong place; the present stock-market fall. Shakespeare’s King John, the prince leaping from the battlement: “Heaven take my soul, and England keep my bones” — bones, not flesh, being the immortal part of the body; Ezekiel’s bones; the martyrs’ bones in glass cases in the old Quebec seminary, “a little distracting”.

10. Places for the second tool: the opposite, the combination (“does the word to see have more than one meaning”) #

Concrete “where to look” for equivocation.

• Look at the opposite of the word: “doesn’t see” of a blind man (lacks the capacity) vs. of the husband who “doesn’t see” the new dishes (doesn’t use it): act and potency. His story: moving cars out of the one-car garage, he put his son’s car in the street, then found the same car with the wife’s keys — “I didn’t see it” though he had looked at it. Last time he used contraries (wet, dry); contradictories work too. “Liberal education” might be misread as making political liberals.
• Look at the word in combination: liberal politician vs. liberal arts; define each whole, drop “politician” and “arts”, and what is left is not the same (arts pursued for their own sake vs. a politician who follows the left).

11. What a place is: “where you look” (“where you look to find an argument”) #

He resists reducing places to “more universal premises” and keeps the concrete sense.

• Student suggests the places are just more universal statements; answer: yes in a way, but that may not express the whole use; better to say a place is where you look, and you may not find an argument there — like looking for glasses or keys in the places they might be (the pants in the closet; the house rule of key slots for Duane, Rose, his son).
• Prior Analytics gives more general places for finding a syllogism: look at definitions, properties, what things follow upon and what follows upon them, and see if something is common. The more proper the place is to the matter, the more you leave dialectic toward demonstration: his comedy reasoning from contraries was dialectical; from Thomas’s principal passions it was closer to demonstration and to what is proper to the passions — boldness arises from hope of victory, despair from fear; fear of the Lord without hope makes despair, hope without fear makes overconfidence.
• Macbeth’s witches: “security is mortal’s chiefest enemy” — security as confidence, boldness. Aristotle: the young man is deceived more than the old because full of hope; the quantum physicists after their success hoped to take over biology; after one great accomplishment one gets bold, but there is always another difficulty.
• The four tools are basic; his special course in dialectic worked only with them; you can exercise yourself without knowing all the places. Proportions also fill industry hiring tests and IQ tests (“A is to B as X is to…”), a gauge of intelligence, and the Platonic dialogues.

His words #

• fourth tool: the ability to see a likeness; exercised on things further apart, hence proportional likeness
• proportion: “this is to that as that is to that”; alternating a proportion (Shakespeare exhortation)
• continuous proportion: God is to you as you are to your offender
• highest genera / ten categories: to defining what axioms are to reasoning
• statements known through themselves: axioms; the first statements we reason from
• hypothetical or if-then syllogism: reasoning from one ratio to another with four terms
• induction: the dialectician’s other argument
• golden mean: virtue and art between too much and too little
• childish vices: Thomas’s name for forms of intemperance in the concupiscible appetite
• principal passions: joy, hope, fear, sadness (Thomas)
• place: where you look to find an argument; contains many things as a place does [ed.: topos]
• a fortiori place: if a predicate belongs where less apt, it belongs where more apt
• “material logic”: the coming sophistry lectures
• “sees” as capacity vs. use: act and potency

Texts #

Read in class

• Handout, “On Dividing Shakespeare’s Plays”, p. 3 (verified source): Shakespeare’s exhortation, the proportional argument on man’s chief good
• Shakespeare, Romeo and Juliet: “death lies on her like an untimely frost…” (quoted); King John: “Heaven take my soul, and England keep my bones” (quoted); Macbeth: “security is mortal’s chiefest enemy” (quoted)
• Our Father petition and parable of the forgiven servant (quoted)

Mentioned

• Aristotle, Topics I (four tools; places); Prior Analytics (where to find a syllogism); on metaphors (Rhetoric/Poetics, inferred); reason ruling emotions as father or master (Politics, inferred); young men deceived by hope
• Plato, Meno; Republic; Phaedo (inferred) on the soul’s immortality; likeness as cause of deception
• Euclid, Elements, definition of square; theory of proportions
• Thomas Aquinas on the four principal passions and childish vices; John of St. Thomas; St. John of the Cross
• Vatican II on the Word of God; Gaudium et spes opening
• Homer, Agamemnon “shepherd of the people”; Pericles’ funeral speech; Terence’s comedies; Molière
• Pierre Duhem; Einstein, The Evolution of Physics; Faraday; Newton (inverse square law); Chesterton
• Printed volume DHB Vol. III, The School of Aristotle, p. 1465 (verified source)

His questions #

• What is the middle part of the Meno about? What is common to defining and reasoning: coming to know what you don’t know through what you do know.
• Does defining go on forever, every part needing definition? No; then nothing could be defined, just as nothing could be proved if every premise needed proof.
• Why does Aristotle give the tool of difference before the tool of likeness? Because of the danger of seeing a likeness without the difference (likeness deceives), and because difference is closer to the second tool.
• Should reason rule the emotions as a master rules a slave or as a father rules a son? As a father a son, for the good of the emotions themselves.
• Which is more apt to be destroyed, the composed or the simple? The composed; the soul seems simpler than the body.
• Is the place like a major premise? (student) In a way you can construct the premise from it, but a place contains many things, as a place does.
• Does the word “to see” have more than one meaning? Yes: to have the capacity, and to be actually using it.
• Is the place just a more universal statement of the premise? (student) In a sense, but better approached concretely as where you look, where you may or may not find an argument.
• What does comedy purge us of, if tragedy purges pity and fear? First thought joy and boldness; corrected to joy and hope, the principal passions.