Two Senses of Induction (God's Simplicity), the Senses of 'Body' and Touch, and the Three Figures of the Syllogism

Orientation #

He refers back to earlier work in this course: “we talked about the if then syllogism right again today”, “you were here when you did the conversion”, and “we’re taking last class examples for A, B, and C” (prev. lecture). The last part of the class works from the handout “The Form of the Simple Syllogism”, p. 3 (verified source). He does not say what comes next time. The previous class treated simple and compound statements and Aristotle’s definition of syllogism against induction, enthymeme and example.

The class, in order #

1. Induction from singulars is not necessary (“Go home and wash your face”) #

Point: an argument from many singulars to a universal does not follow necessarily, because you never see all the singulars.

• Examples: a boy from Watertown, Minnesota (his mother’s town, no blacks there) meets a black boy in Minneapolis and tells him to wash his face; missionary children who spoke Spanish only to black people; living in darkest Africa you would conclude all men are black. Each shows induction settled by the singulars one happens to have met.
• His sister’s Mars cases: pink snow on Mars would surprise us but is not impossible; “half a loaf is as much as a whole loaf” up there would be impossible. Marks the line between what induction merely fails to show and what is necessary.
• A fortiori the rhetorical argument [from example] is not necessary either. Question raised: are there some inductions that are necessary? He answers by distinguishing two kinds of induction: (a) from many singulars to a universal; (b) from the less universal to the more universal. In (b) the less universals can be exhausted, so the argument is much stronger.

2. Thomas on God’s simplicity: eight articles as an induction (“God is not composed in any way”) #

Point: the seventh article of the Summa’s question on God’s simplicity is an induction in the second sense, and a syllogism as well. He walks the articles (reading from the text, “I’m cheating, I have it here”):

1. God is not a body.
2. Not composed of matter and form (a different composition from that of bodily parts).
3. Not composed of subject and nature: in me there is “what a man is” and something peculiar to me (this flesh and bones); if I were the same as what a man is I would be the only man. Angels are not composed this way: each angel is his own species, has “the fullness of his species” (“My angel’s probably laughing at me now”).
4. Not composed of nature and being (essence and existence): creatures receive existence from God, so they are not their existence; angels are composed this way, God is not.
5. God has no genus and difference; not in the category of substance.
6. Not composed of substance and accident (Boethius: God is his substance).
7. Concludes God is not composed in any way. Student asks: by syllogism or induction? “He does both.”
   • Induction: having argued against each of the six kinds of composition found in creatures, he concludes to none at all: an argument from particulars to universal, but particular kinds, not singulars. Stronger than induction from singulars because one can be complete about the kinds.
   • Syllogism: (i) whatever is composed is a mixture of act and ability — either one part is to another as ability to act (matter to form, subject to nature, nature to existence, substance to accident, genus to difference in another sense) or all the parts are to the whole as ability to act; this is the passive ability of book IX of Wisdom; (ii) God is pure act (already shown); therefore God cannot be composed.
   • Why both: Thomas proportions himself to beginners, who understand induction more easily; “He’s a very thorough guy.”
8. Why an eighth article? He shows God does not enter into composition with something else. Aside: he was reading De Veritate q. 20 (on Christ’s knowledge) this morning, where some held the divinity took the place of Christ’s soul or intellect; that is impossible because God cannot be a part of something, sharing its potency.

3. Axioms: known first by induction, but not by induction alone (“the whole is more than the part”) #

Student: don’t we reach “the whole is greater than the part” by induction, and isn’t it certain? Reply: Aristotle says we first come to the axioms (statements known through themselves by all men) by induction, but we understand enough of what a whole and a part are to see it must be so; if known by induction alone we would not be sure. Contrast: knowing what a right angle and a triangle are does not show that a triangle’s angles equal two right angles; that needs syllogism (Euclid I.32; book I has 48 theorems, 47 the Pythagorean, 48 its converse).

4. Why Wisdom has a whole book of dialectic and a whole book of equivocal names (“names equivocal by reason”) #

Point: dialectic and the distinguishing of equivocal names appear in Aristotle’s other books, but only Wisdom gives each a whole book, because of Wisdom’s universality and subject.

• Thomas’s exposition of Wisdom III: Aristotle gives four reasons for proceeding dialectically before determining the truth, and (Thomas says) does so in his other books too; but in Natural Hearing IV he has a particular dialectic about place, then determines the truth, then about time — not a whole book. Wisdom has a whole dialectical book because of the affinity of dialectic and Wisdom in universality (Thomas had made this point earlier in the commentary).
• Wisdom V: a whole book distinguishing senses of words equivocal by reason and their order. Aristotle does this elsewhere too — his own point, “Thomas doesn’t make this point”: On the Soul II distinguishes three senses of “sensible”: private [ed.: proper] sensible, known by one sense only (your colour); common sensible, known by more than one (your size and shape, seen and felt); accidental sensible (I am “said to see you”, but what I see is colour and shape, in quality, and size, in quantity; you, an individual substance, I recognise rather than see). Natural Hearing IV gives eight senses of “in”, and Thomas takes the order Aristotle starts with as a clue to the order of all.
• Why a whole book in Wisdom: Wisdom is about first causes and immaterial things, which can be spoken of only with words equivocal by reason; the wise man considers and defends the axioms, which are expressed in such words; the subject of Wisdom is being and one, “very equivocal by reason.”

5. Senses of “body” (“what are the three or four main meanings of body”) #

Point: “body” is equivocal by reason and its senses are constantly confused.

1. Species of substance: substance divided into material (bodies) and immaterial (spirits, angels, “separated substances”).
2. Integral part: “I have a body and I have a soul”; Aristotle’s soul is the first act of a natural body having life in ability, a body composed of tools [ed.: organic]. This body is not the genus.
3. Species of continuous quantity: line, surface, body (with place and time). People confuse the three-dimensional with the substance, since quantity is the genus closest to substance.
4. Body of an article in the Summa (corpus): the “substance” of the teaching is in the body — because the only substance we think of is body. Students add: body politic; a body of water (Lake Quinsigamond next to Worcester); the mystical body (Paul’s comparison) — with a short dispute whether that is a political body or “supernatural in character”, and whether they are equivocating on “polis” (city of God). Aside: Gilbert and Sullivan, “everybody’s somebody, no one’s anybody.”

6. Return: proportional induction, and words for knowing taken from sight and touch (“Teacher leads you by the hand”) #

Point: induction in the second sense is not purely equivocal but proportional; and our words for the mind’s acts are carried over from sight and, better, from touch.

• Thomas’s manuductio in the article on teaching: the teacher leads by the hand with less universal propositions and sensible examples.
• Sight: being the most spiritual sense, “see” is carried to the mind’s eye (Hamlet, “In my mind’s eye”: memory or imagination), then to understanding (“I see, said the blind man”, his mother’s joke), then to “seeing God face to face.” Aside: de Broglie’s title Matter and Light — light is not matter, though he may think it is.
• Touch: simple apprehension is “simple grasping”. Grasping shows that the thing known is in the knower (contrast love, which is in the thing loved), and that to grasp a thing one must separate it from what surrounds it (he can grasp his glass, since air gives way, not the centre of a solid). Touch is “the most material” sense yet the sense of certitude: De Koninck’s talk on sight and touch; doubting Thomas trusts his hand on the Lord’s side, not his eyes; Dr Carroll on the fitness of sending Thomas to India, where they deny what they can see; St John’s epistle, “what we have held with our hands.” Moderns prefer the visual (the film in which a man in a tower sees people as little moving things and asks what money one makes); touch, not sight, is the sense of sympathy — to know the good you have to feel the suffering.

7. Only one way to conclude a universal affirmative (“here’s one way of syllogizing”) #

Point: the universal affirmative can be syllogised in the first figure alone.

• First figure by the “set of all” [ed.: dictum de omni]: if every B is A, whatever is B must be A; told every C is B, conclude every C is A; told only some C is B, conclude only that those C are A.
• Second figure (middle term predicate in both): every A is B, every C is B. No set of all, since nothing is said to be A or C; converting every A is B yields only some B is A. “There’s no way to get the set of all.” (Student’s proposal that it concludes to some C is B: rejected on the same ground.)

8. Three ways to conclude a universal negative (“the universal negative converts simply”) #

Point: because the universal negative converts without losing power, it can be concluded in the first figure and twice in the second.

• First figure by the “set of none”: no B is A, every C is B, therefore no C is A; with some C is B, only some C is not A.
• Conversion reviewed: universal affirmative converts only partially (every dog an animal, not every animal a dog; every odd number a number) — “loses power.” Universal negative converts simply. Proof: if no B is A but some A could be B, name that A “X”; X is both A and B, so some B (X) is A, contradicting the start. So the universal negative is more useful for conversion — “That’s why you get more universal negative conclusions.”
• Second figure, no A is B, every C is B: convert once, no B is A, and you are in the first figure. Aristotle calls second-figure syllogisms imperfect (one must convert to see the necessity), first-figure perfect (set of all/none applies as it stands); converting always lands back in the first figure.
• Two universal negatives (no A is B, no C is B): invalid, shown by examples satisfying two conditions — premises true, and one case where every C is A, one where no C is A. A = animal, B = tree; C = dog (every dog an animal), C = stone (no stone an animal). Check both conditions aloud “to make sure I make no stupid mistakes.” One true universal affirmative knocks out every negative as always true, hence as necessary; one true universal negative knocks out every affirmative; together nothing follows. Supporting principle: what is necessary is always so (two is necessarily half of four); “man is white” is not necessary because not every man is white.
• Every A is B, no C is B: convert the negative (no B is C), reorder, get no A is C, then convert again to no C is A. Valid, but “I have to convert twice to see the necessity.” Total: one way for the universal affirmative, three for the universal negative.

9. The third figure yields only particulars (“middle term is the subject”) #

Point: with the middle term subject in both premises, only particular conclusions follow.

• Every B is A, every B is C: converting the second loses power (some C is B), so only some C is A. “If you can’t get a universal affirmative conclusion from two universal premises, how the hell are you going to get it from the other ones” — no need to run all sixteen.
• No B is A, every B is C: convert to some C is B; some C is not A.
• Every B is A, no B is C: convert to some A is B; some A is not C — and no conclusion with C as subject, since a particular negative cannot be converted.
• No B is A, no B is C: set of none requires one affirmative (“if your parents are both negative, you won’t have any children”); shown invalid by examples: A = animal, B = stone, C = dog (every dog an animal) and C = tree (no tree an animal), conditions checked as before. Aside: his freshman maths teacher worked round blackboards on every wall.

10. Why the figures are ordered first, second, third (“It was a falling off”) #

Point: the order is a descent in power and evidence.

1. First figure: set of all and set of none apply as it stands; both universal affirmative and universal negative conclusions.
2. Second: necessity seen only by conversion, which returns to the first; only negative conclusions among universals.
3. Third: only particulars.

• The invalidity proofs use the if-then syllogism: if something follows necessarily it is always so; nothing here is always so; therefore nothing follows necessarily. “I love that if-then syllogism” — as Augustine’s “our hearts are restless until they rest in thee” can be cast as an if-then.
• Notice: examples cannot prove a form valid — that would be proving by induction, which shows neither always nor necessarily; but one example disproves, as one black man disproves the racist’s “all men are white” (the Watertown boy again). Aside on Shakespeare as one who “could look before and after”; closing anecdote of Father Reed, the town’s one priest, brought over on Christmas Eve.

His words #

• induction (first sense); argument from many singulars to a universal; never necessary.
• induction (second sense); from the less universal to the more universal; can be exhaustive; proportional, “not purely equivocal.”
• torque/rhetorical argument [ed.: argument from example]; a fortiori not necessary.
• ability; what is actualised, “passive ability” of Wisdom IX [ed.: potency].
• pure act; God, premise of the syllogism in article 7.
• Wisdom; Aristotle’s fourteen-book work [ed.: Metaphysics]; Natural Hearing [ed.: Physics].
• exposition; Thomas’s word for “laying out the book” [ed.: expositio, commentary].
• names equivocal by reason; one word, several ordered senses [ed.: analogous names].
• private sensible; known by one sense only [ed.: proper sensible]; common sensible; accidental sensible.
• separated substances; the philosophers’ name for spirits/angels.
• body composed of tools; his rendering of Aristotle’s definition of the ensouled body [ed.: organic body].
• manuductio; “lead you by the hand”, Thomas’s word in the article on teaching.
• simple grasping; his rendering of Thomas’s simple apprehension.
• set of all / set of none; dici de omni [ed.: dictum de omni / de nullo]; the first-figure principle.
• converts partially / converts simply; “loses power” vs keeps universality.
• perfect / imperfect syllogism; Aristotle’s names for first-figure vs second-and-third-figure forms.
• if-then syllogism; the hypothetical form used to prove invalidity.

Texts #

Read in class

• Thomas Aquinas, Summa Theologiae, question on whether God is simple (I q. 3, inferred), aa. 1-8, read article by article.
• Handout, “The Form of the Simple Syllogism”, p. 3 (verified source), worked on the board.

Mentioned

• Thomas Aquinas, De Veritate q. 20 (Christ’s knowledge).
• Aristotle, Wisdom [Metaphysics] III (dialectic, four reasons), V (equivocal names), IX (passive ability); Thomas’s exposition of book III.
• Aristotle, Natural Hearing [Physics] IV (place, time, eight senses of “in”).
• Aristotle, On the Soul II (three senses of sensible; definition of soul).
• Euclid, Elements I.32 (angles of a triangle), I.47-48.
• Boethius (God is his substance); Thomas, article on teaching (manuductio).
• Shakespeare, Hamlet (“in my mind’s eye”); Augustine, Confessions (restless heart); 1 John (what we have held with our hands); de Broglie, Matter and Light; Charles De Koninck’s talk on sight and touch; Gilbert and Sullivan.

His questions #

• Does induction from many singulars follow necessarily? No; you never see all the singulars, and one contrary singular disproves it.
• Aren’t there some inductions that are necessary? Induction from less universal to more universal can be exhaustive and so much stronger; the axioms are first reached by induction but seen through their terms.
• How does Thomas argue in the seventh article, by syllogism or induction? Both: an induction from the six kinds of composition and a syllogism from pure act.
• Why is there an eighth article? To show God does not enter into composition with something else.
• Why does Wisdom have a whole book distinguishing equivocal names? Because its subject (being and one), the axioms, and immaterial things can be spoken of only with such words.
• What are the three or four main meanings of body? Species of substance; integral part against soul; species of continuous quantity; body of an article (with body politic, body of water, mystical body added).
• How many ways are there of syllogizing a universal affirmative? One, in the first figure by the set of all.
• How do we know the universal negative converts simply? Name the supposed A that is B “X”: it is both, so some B is A, contradicting the premise.
• Can you get a negative conclusion from two universal negatives in the second figure? No: animal/tree with dog and stone shows no conclusion is always, hence necessarily, true.
• Why does Aristotle call the figures first, second and third? The first is evident as it stands and gives both universals; the second needs conversion and gives only negatives; the third only particulars.