Syllogism Figures, Wisely and Slow, and the Eight Recurring Forms of Argument

Orientation #

He opens mid-stride, recalling that in the first and second figures four of the sixteen arrangements were syllogisms, and that “as we mentioned before” the dici de omni / de nullo never apply directly in the second and third figures. The Meno if-then examples are “as we mentioned” (prev. lecture). The next class carries this analysis into further Euclid propositions and the “matter” of syllogisms.

The class, in order #

1. The third figure: four cases with two universals (“middle term is the subject in both cases”) #

Point: set up the third figure and the tool needed to test it.

• Recap: first figure has one mood for a universal affirmative conclusion; universal negative has one in the first figure and two in the second. Third figure “comes third because it’s third in power”: it has no universal conclusions.
• The four cases with two universal premises: every B is A / no C is B [ed.: he then catches himself — “Wasn’t thinking, was I?” — since in the third figure B must be subject of both premises]; the layout he settles on is every B is A & every B is C; no B is A & every B is C; no B is A & no B is C.
• Only question: does anything follow necessarily with C as subject and A as predicate?
• Conversion is the necessary tool, since the “set of all / set of none” [ed.: dictum de omni et nullo] never applies as the premises stand in figures two and three: universal negative converts simply; universal affirmative converts partially to a particular affirmative; particular affirmative converts to particular affirmative; particular negative does not convert.

2. The four most-used forms and the via negativa (“God is not a body, no body is God”) #

Point: the four forms on the board (one affirmative, three negative-concluding) are the ones theology uses constantly, because theology proceeds by the via negativa / via negationis.

• Aside on individuals: God is not a universal said of many, but for conversion an individual functions like a universal. Socrates is not a woman ⇔ no woman is Socrates; God is not a body ⇔ no body is God (both directions).
• Theological pattern: find something said of God and denied of other things, or vice versa. Everything corruptible has parts; God has no parts; therefore God is not corruptible. Whatever has parts is a composition of act and ability; God is not such a composition; therefore he has no parts.
• Phaedo: Socrates against the soul as harmony of the body seeks something affirmed of one and denied of the other: the soul resists the body, a harmony does not resist the body, so the soul is not the harmony; the soul has harmony, a harmony does not have a harmony. “They’re often the second figure. That’s very common.”
• Note: there are more ways to draw a negative conclusion than a universal affirmative (only one way).

3. Finding the middle term: the first road in our knowledge (“the road from the senses into reason”) #

Point: his own example (handout, “First Road in Our Knowledge”, p. 2) of finding a middle term and then manifesting each premise.

1. Conclusion sought: the first road in our knowledge (C) is the road from the senses into reason (A).
2. Middle term: the natural road. The first road is the natural road; the natural road is the road from the senses into reason.
3. Manifesting the minor: nature means what a thing is, and a thing must be what it is before it can be anything else; so the natural is first in the thing — “and vice versa for that matter.”
4. Manifesting the major: man’s nature is animal with reason; animal is defined by senses; what is general develops before what is particular; so the road is from senses (general, animal) into reason (particular).

4. Student question: “wisely and slow” (“They stumble that run fast”) #

Point: Friar Lawrence couples wise with slow; he is not recommending slowness as such (there is a slowness of stupidity), but the slowness of the wise man. When does the wise man proceed slowly? “Three or four places”:

• when many things must be considered before judging;
• when the thing is difficult to understand — from the “second book of wisdom” [ed.: Metaphysics II inferred]: difficulty is due either to the thing itself or to the weakness of our mind; in natural philosophy the difficulty is on the side of the thing, in theology on the side of our mind. Contrast Descartes, who “skips over” the definition of motion as too hard and treats God and thought as obvious;
• “the most subtle thing, and this is the very important thing”: the greatest minds are very slow in the beginning, in the fundamentals everything else depends on. De Koninck noted Poe (Purloined Letter): the law of inertia applies to minds as to bodies — a ping-pong ball is easily moved and easily stopped, a heavy body hard to start and hard to stop. Aristotle and Thomas: a man at a fork in the road who errs a little goes further astray the further he goes.
• Thomas “the dumb ox” (Chesterton’s title) as the greatest mind of the Middle Ages: slow in the fundamentals.
• Gamow on Bohr’s Copenhagen institute (Oppenheimer, Heisenberg, Gamow studied there; Bohr flown out of Denmark in the war): visiting physicists explained a new idea, everyone grasped it except Bohr; after long explanation Bohr said “Ah, now I see it. Isn’t it this way?” — they had it wrong, and ended agreeing with him. “The last man to get the idea was the first man to get the idea right.”
• His father, asked for advice by the boss alongside a quick-answering colleague: “I’ll tell you tomorrow” — and the boss followed him. A desert father who waited a month before answering.
• His remark on the Indian’s predominant passion being fear, especially fear of being mistaken about the fundamental.
• A second Friar Lawrence line on stumbling: “revolts from true birth, stumbling on abuse” — “birth” is being extended to mean nature, as nature comes from birth in Greek and Latin; to revolt from your nature is to stumble on abuse. Heraclitus: wisdom is to speak the truth and to act in accord with nature.
• Macbeth witches: one will be “a rat without a tail”; the Hudson edition notes there is always a defect in the animal form assumed, like the devil’s cloven foot — a sign of being twisted contrary to nature; good angels appearing to Abraham take a body with what it should naturally have.

5. The eight forms that come up again and again (“there are really eight things you have to know”) #

Point: besides the four categorical forms, two if-then and two either-or forms exhaust what recurs (induction, enthymeme, example aside).

• If-then, from the Meno: affirm the antecedent — if virtue is knowledge it can be taught; it is knowledge; so it can be taught. Deny the consequent — if it can be taught there are teachers; there are none; so it cannot be taught.
• Either-or: (a) deny all but one alternative, knowing the thing falls under one of them; (b) deny all alternatives, to show the thing does not fall under the division at all.
• Example (b), from his philosophy of nature class: why Empedocles gave up one first matter. If one matter, either it has definite qualities or none. With definite qualities (sugar, water, fire) everything would be sweet/wet/hot — but the world is of contraries. With none (the Milesian move from water to air), how do qualities arise? Kool-Aid added to water gives taste and colour; water added to water never does — something from nothing. Both horns fail; so seemingly not one matter. “There’s a way out of that,” but that is how the argument proceeds.

6. Euclid, Elements I.1: three syllogisms of one form (“radii of the same circle are equal”) #

Point: a construction theorem (equilateral triangle on AB) needs three syllogisms, all of the same categorical form.

• Construction: circle BCD with centre A, distance AB; circle ACE with centre B, distance BA; join CA, CB.
• Syllogism 1: radii of the same circle are equal; CA and AB are radii of circle BCD; so equal. Syllogism 2: likewise CB and BA, radii of ACE.
• Syllogism 3 cannot use the same middle (AC, CB are not radii of one circle): quantities equal to the same are equal to each other (axiom); AC and CB are each equal to AB (the two prior conclusions); so equal.

7. Thomas: the good is the proper cause of love — finding the main syllogism (“you begin from the conclusion”) #

Point: analysis (the “Analytics” are about taking apart, not generating) starts from the chief conclusion, finds its immediate premises, and treats everything else as superfluous or backup.

• Setting: first article of the question on the causes of love, between the questions on love’s nature and its effects (four articles on causes, six on effects); used in his love-and-friendship course, where each article is preceded by a page of Shakespeare.
• He reads the respondeo (handout p. 6). “Whence it remains that the good is the proper cause of love” — whence marks the main conclusion.
• Being a trained logician: the conclusion is affirmative, so if categorical it must be every B is A / every C is B; the three negative forms are out.
• Middle term (student): the object of love. The good is the object of love; the object of love is the cause of love. Middle term compared to the middleman in economics or the matchmaker, who knows both parties.
• Grammar: the first paragraph ends by concluding the major (“it is necessary therefore that what is the object of love be properly the cause”); the second paragraph states the minor first and then gives its reason (“because”). Reason and conclusion are in opposite orders so that the two premises stand side by side in the reader’s mind. Minor is stated in reverse order but the terms are convertible.
• He calls the supporting arguments “backup syllogisms” (others say “post syllogism” [ed.: probably “prosyllogism”]).

8. Backing up the major: abilities acted upon by their object (“the heart as being wounded”) #

Point: “love pertains to the desiring ability, which is an ability that is acted upon” rests on a fundamental division of the soul’s abilities.

• Order of knowing: abilities are known through their acts (you don’t know you can walk until you walk; “I didn’t know I had it in me”), acts through their objects: seeing vs. hearing distinguished by colour vs. sound, so the abilities are not one.
• The fundamental either-or: either the ability acts on the object or the object on the ability; if neither, no connection at all. Digestion acts on its food (“crunch, crunch”); the senses are acted upon — the light acts on the eye, sound on the ear (kids going deaf, blinded looking at the sun in an eclipse).
• The heart (“for want of a better name”) is of the second kind: she “made a big impression on you”; the heart is wounded; Teresa of Avila and Thérèse of Lisieux receive love as being pierced by an arrow or lance. So it is a passive ability, and its object causes its act.
• Philosophical example, other acts of the same ability: the object of fear (a gunman who “hates monks,” the terrorist attack) causes the fear; the insult that is the object of anger causes the anger.
• Backup syllogism made explicit: what acts upon the heart arousing its love is the cause of love; the object of love acts upon the heart arousing its love; so the object is the cause. Middle term: acts upon. Thomas “doesn’t spell it all out fully, but that’s what he’s doing.”

9. Backing up the minor: the good as what fits (“the shoe fits”) #

Point: the middle uniting good with object of love is fitting/agreement.

• Three acts of the desiring ability toward the good: love (most basic), desire (love in the absence of what is loved), pleasure or joy (love in its presence).
• Love itself is the agreement of the heart with its object; so the object of love is what fits you; and the good is what fits you (what is proportioned to you is good for you). Fitting is the link.

10. Euclid and Thomas compared (“one main syllogism”) #

Point: both use three syllogisms of the same form, but ordered differently.

• Euclid has three things to prove, two by parallel syllogisms whose conclusions supply a premise of the third; there is an order, but no single “main” syllogism.
• Thomas has one thing to prove and one main syllogism; the other two back up the major and the minor respectively — the major proved before it is stated, the minor stated then proved. Easy matter in one, “very difficult” in the other, but one kind of argument in both.

His words #

• set of all / set of none: his rendering of dici de omni / de nullo [ed.: dictum de omni et nullo]; never applies directly in figures two and three.
• via negativa / via negationis: theology’s procedure of showing what God is not.
• ability: for potency [ed.: potency, power]; “composition of act and ability.”
• the first road in our knowledge: the road from the senses into reason; middle term “natural road.”
• wisely and slow: the slowness proper to the wise man, in three or four situations.
• second book of wisdom: [ed.: Metaphysics II inferred]; difficulty from the thing or from our mind.
• desiring ability / the heart: his names for the appetite [ed.: appetitive power]; “for want of a better name.”
• passive ability: one acted upon by its object, as against one that acts on its object (digestion).
• backup syllogism / backup manifestation: a syllogism proving a premise of the main one [ed.: prosyllogism]; “post syllogism” as heard.
• philosophical example: proceeding by parallel cases (fear, anger) to manifest a premise.
• fitting / agreement: what is proportioned to something and good for it; the middle between good and object of love.

Texts #

Read in class

• Euclid, Elements I.1 (construction of an equilateral triangle), read through and analysed.
• Thomas Aquinas, Summa theologiae, question on the causes of love, art. 1, respondeo (I-II q.27 a.1 inferred; handout “Causes of Love”, p. 6).
• Berquist, “An Introduction to the First Road in Our Knowledge”, p. 2 (handout; his own argument).
• Shakespeare, Friar Lawrence lines “wisely and slow” and “revolts from true birth, stumbling on abuse” (Romeo and Juliet inferred).

Mentioned

• Aristotle, Prior and Posterior Analytics (as “analysis”).
• Aristotle, “second book of wisdom” (Metaphysics II inferred).
• Plato, Phaedo (soul not the harmony of the body); Plato, Meno (virtue and teachers).
• Descartes (definition of motion; God, thought).
• Poe, The Purloined Letter, via De Koninck; Chesterton, “The Dumb Ox.”
• Gamow on Niels Bohr; Heraclitus on wisdom; Shakespeare, Macbeth (Hudson edition note); Teresa of Avila, Thérèse of Lisieux; Empedocles and the Milesians (from his philosophy of nature class).

His questions #

• Is there anything that follows necessarily with C as subject and A as predicate? That is the only question for each arrangement; conversion is the tool for answering it in figures two and three.
• What is the middle term uniting “first road” and “road from the senses into reason”? The natural road in our knowledge.
• When does the wise man proceed slowly? When many things must be considered; when the matter is difficult (from the thing or from our mind); and, most subtly, in the fundamentals.
• Why would the greatest mind of the Middle Ages be called the dumb ox? Because Thomas was slow in the fundamental things on which everything else depends.
• What’s the middle term to see that AC and AB must be equal? And for AC and CB? Radii of the same circle; things equal to the same thing.
• What does Thomas use as a middle term to unite “good” and “cause of love”? The object of love (student answer).
• Does the object act upon the ability, or the ability upon the object — which kind is the heart? The heart is acted upon by its object, like the senses, unlike digestion.
• What is the middle term uniting good with the object of love? Agreement, fitting: what fits you is good for you and is what the heart agrees with.
• Does the reversed order of reason and conclusion in the two paragraphs confuse you? No; it puts the major and minor together so the conclusion can be drawn at once.