Aquinas's Order of God's Attributes in the Two Summas; Testing Syllogisms in the First and Second Figures

Orientation #

He does not say what was done last time or what comes next, though “Remember, we had given something like that in the categories” and “Here you are with the four forms” pick up earlier material. The logic portion follows the handout “The Form of the Simple Syllogism”, pp. 3–10 (verified source). The previous class introduced Aristotle’s three figures from the Prior Analytics after treating conditional and disjunctive syllogisms.

The class, in order #

1. The five parts of the treatise on God’s substance (“comparing two treatises on the substance of God”) #

Point: preparing a Thomas Day talk, he compares how the two Summas treat the substance of God, which in both has five parts: simple, perfect (with good attached), infinite, unchanging, one; then follow God’s operations. Not quite the same order in the two works. He notes the coincidence of five: five ways for God’s existence, five attributes of his substance, and asks the class whether the five divide into two or three.

2. Simplicity and perfection belong together (“more simple and more perfect”) #

Point: in both Summas simplicity comes first and perfection right after, and he argues the pairing is not accidental.

1. Thomas notes in the Summa Theologiae that this is the reverse of the material world: a stone is simpler than a tree, a tree than a dog, a dog than a man, yet perfection increases with complexity; but God is most simple and most perfect. Hence, having negated composition, one must next show that perfection is not negated with it.
2. A student adds: Dawkins and other atheists assume God must be complex to be perfect; he agrees this is a weak point in their arguments.
3. His own argument, a Dante-like ascent: as one goes up the angelic scale (angels, archangels, principalities, virtues, powers, dominations, thrones, cherubim, seraphim) the angels become more perfect and simpler at once. Thomas: God understands everything by understanding himself; angels know their own substance far better than we know our soul but need other thoughts besides, and the higher angels have fewer thoughts yet understand more perfectly with them. So at the top of the scale one expects something most simple and most perfect.
4. In the immaterial world, then, more simple = more perfect and more perfect = more simple. Examples: Aristotle says tragedy is better than epic because a simpler, more perfect form of fiction (though Homer is “the poet”; Sophocles comes close); Mozart’s music is simple yet, a pianist told him, takes longer to practise because everything must be just so. He stresses the two notions are distinct (“simplicity isn’t the same thing as perfection, but they go together”).

3. Unity and infinity as the second couple (“God’s perfection is endless”) #

Point: in the Summa Contra Gentiles unity and infinity follow simplicity and perfection in that order, and he argues they correspond to them.

• One and infinite go together mathematically, “not married, but a couple anyway.”
• Evidence that one corresponds to simple: in the Compendium of Theology (written for his companion who wanted a brief exposition to carry with him) Thomas treats the unity of God in the middle of the consideration of simplicity. Reason: there can be only one God because he is entirely simple; there can be many men because of individual matter and composition.
• Evidence that infinite corresponds to perfect: asked whether one would sooner say God’s simplicity or his perfection is endless, students answer perfection (“perfection without limits”); goodness, attached to perfection, is endless; one can say how the cherubim exceed the thrones but not how good God is. The Fourth Lateran Council (inferred; “the fourth … Council”) lists God as immensus, almost a synonym for eternal; even an infinitely extended universe would be measurable in a sense. Thomas: God can make anything he is able to make, taken one by one, but not everything he is able to make at once, for then he would have a limit. Praise: he can say how much to praise Nixon, his teacher Kasurik [as heard], De Koninck, Aristotle, but God is beyond all praise (Psalms), and one praises him more for perfection and goodness than for simplicity; he is “the good of every good” (Thomas, after Augustine).

4. The order in the Summa Theologiae and the wild card (“Two twos and one”) #

Point: the Summa Theologiae puts infinity right after perfection (confirming the pairing) but unity last and unchanging between them; he gives reasons for both.

• Unity last: the Prima Pars goes on to the Trinity, De Deo Uno et Trino, so the last thing stressed in the substance of God is that he is one, so that the Trinity will not seem to contradict it. The Summa Contra Gentiles has no Trinity in its first three books (what natural reason can know), so no such need.
• Unchanging: first in the Contra Gentiles, because there the first two of the existence arguments are from motion and the argument is more expansive (three reasons for “whatever is moved is moved by another,” three against an infinite series), a fuller summary of Physics VII–VIII than the Summa Theologiae’s first way, to which he refers students.
• In the Summa Theologiae unchanging comes after simple, perfect, infinite, which fits the three reasons for saying God is unchanging (as in Kasurik’s Natural Theology course): (1) he is simple, and Physics I shows what changes must be composed; (2) he is perfect, and one moves because one lacks something (“what do you get God for Christmas?”; he does not need us); (3) he is infinite, and even the early Greeks saw an infinite principle has nowhere to move. Conclusion: the five divide into two twos and one wild card. Aside: “Verity is the soul of wit” [ed.: usually “brevity”], wisdom the most perfect knowledge is brief; “the fool multiplies his words” (Bible).

5. Why logic, and the said of all and said of none (“The said of all and the said of none”) #

Point: the necessity of a syllogism rests on two self-evident principles.

• Why logic at all? Because we do not know everything. Albert’s [ASR “Helbert”] division makes sense: simple unknown needs the art of defining, complex unknown the art of reasoning.
• Dici de omni and dici de nullo [ed.: dictum de omni / de nullo]; “I speak English”: the said of all and the said of none. Aristotle: A is said of all B when A is said of whatever B is said of (cf. Categories: animal said of dog, dog of retriever, so animal of retriever).
• His preferred statement, from his “great love of the A statement”: if every B is an A, then whatever is a B is an A. Obvious if one understands “every B is an A” (not “some are, some are not”), like seeing that a square is not a circle; “a statement known to itself” [ed.: per se nota], though not to all. So every B is A, every C is B, therefore every C is A “by the said of all.”
• Said of none: if no B is an A, then whatever is a B is not an A; otherwise A would be said of something B is said of. Aristotle knew and proved this. So no B is A, every C is B, therefore no C is A.
• Weakening the minor to “some C is B” gives some C is A, or some C is not A; but the two universals are the impressive cases.

6. Two negatives in the first figure give nothing (“You can’t get anything in two negatives”) #

Point: he suspects two negatives yield nothing, since even the said of none needs an affirmative premise, but “I’m from Missouri, you got to prove it.” Method, using if-then: if something follows necessarily it always follows (if four is necessarily half of eight, every four is). Find examples that satisfy two conditions: (a) the premises come out true, so the matter is perfect and any defect is in the form; (b) one example where every C is A and one where no C is A. The first kills every negative conclusion, the second every affirmative; affirmative and negative exhaust the possibilities; not always so, therefore not necessarily so (valid denial of the consequent), therefore not a syllogism, since a syllogism is speech in which from statements laid down another follows necessarily. Disjunctive syllogism also used to eliminate. Examples: B = stone, A = tree; C = oak tree (every oak tree is a tree) and C = cat (no cat is a tree); premises checked true. Result: no conclusion; “one of your parents must be affirmative.” Asides: Warren at Wisconsin, a mathematician denying certainty, told “two plus two is four” said it “depends upon the system” (binary); teachers who cite a triangle on the earth’s surface with more than two right angles use “triangle” equivocally, the most common fallacy. Simple examples are best.

7. Affirmative major, negative minor in the first figure (“nothing is said to be a C”) #

Point: every B is A, no C is B gives nothing with C as subject and A as predicate (the said of none cannot apply, since nothing is said to be a C; one could get “some A is not C” by turning it round, but that is not what is asked). Examples: A = animal, B = dog; C = cat (every cat is an animal) and C = stone (no stone is an animal). Both kinds of conclusion knocked out. Result for the four universal cases of the first figure: two syllogisms (AA, EA), two not.

8. The second figure: imperfect syllogisms (“Aristotle calls these imperfect syllogisms”) #

Point: with the middle term predicate in both premises, the said of all and of none do not apply as they stand, so these are imperfect; they must be reduced to the first figure by conversion, if conversion is necessary.

• Four cases: every A is B / every C is B; no A is B / no C is B; no A is B / every C is B; every A is B / no C is B.
• AA: to reduce one would need every B is A, but the universal affirmative cannot necessarily be converted (every two is half of four converts, but from the matter; every dog is an animal, every odd number is a number do not). Proof of invalidity: A = dog, B = animal; C = cocker spaniel (“copper spaniel” in the recording; every cocker spaniel is a dog) and C = cat (no cat is a dog). Nothing follows. “Don’t try to make the form invalid because the matter is bad.”

9. Converting the universal negative, proved (“I’m from Missouri”) #

Point: no A is B / every C is B works only if no A is B converts to no B is A, and he refuses to assume it (a student proposes assuming it: “you worked at Assumption College, so that works”). Proof: one cannot check the infinity of universal negatives one by one. Suppose it not necessary: then when no A is B, some B is A. Name that B “X”. X is both a B and an A, so some A is B, contradicting no A is B. So one is “forced by the truth itself.” Aside: De Veritate q. 22 (which he calls de bonitate, since it goes on to the good): the will cannot be coerced, but the mind in a way can, when it does not want to admit something and the truth forces it; a California student who came to every class with an objection and relaxed as it was resolved. Result: convert to no B is A, keep every C is B, and by the said of none no C is A, “by magic, by conversion”; it follows necessarily, but less clearly than in the first figure. That is why the first figure is called first. Fourth case, every A is B / no C is B: convert to no B is C, get no A is C, then convert again to no C is A; two conversions. So the second figure yields a universal negative only, in these two forms.

10. Converting singular negatives about God (“God is not a universal”) #

Point: as a young philosopher (taught logic by Richard in high school, given credit for the college course) he asked whether singular negatives convert, since God is not a universal (“every God is pure act” makes no sense, only “this individual God”). Same proof: if something composed were God, call it X, then God is composed, contradiction; so “God is not composed” converts to “nothing composed is God,” and “God is infinite” to “nothing finite is God.” Simpler: Socrates is not a woman, so no woman is Socrates, else some woman X is Socrates and Socrates is a woman. In the Peri Hermeneias Aristotle was concerned with universal statements.

11. Two negatives in the second figure (“What do you do with negative premises”) #

Point: nothing, since even the said of none needs an affirmative; proved by examples. A = animal, B = stone; C = cat (every cat is an animal) and C = tree (no tree is an animal); premises checked true. No affirmative or negative always the case; not a syllogism. The class ends here.

His words #

• “substance of God”: the five attributes treated after God’s existence and before his operations.
• “wild card”: God’s unchangingness, the fifth attribute placed differently in the two Summas.
• “the good of every good”: Thomas’s (after Augustine) name for God.
• “immensus”: conciliar attribute of God, near-synonym of eternal.
• “verity is the soul of wit” [ed.: usually “brevity”]: brevity as mark of wisdom.
• “simple unknown / complex unknown”: Albert’s division grounding defining and reasoning.
• “dici de omni / dici de nullo” [ed.: dictum de omni / de nullo]; “the said of all / the said of none”: the principles of syllogistic necessity.
• “A statement”: the universal affirmative.
• “a statement known to itself” [ed.: per se nota].
• “the matter is perfect”: premises true under the chosen examples, so any defect is formal.
• “imperfect syllogism”: Aristotle’s name for second-figure syllogisms, needing conversion.
• “Natural Hearing” [ed.: Physics].
• “turn it around” [ed.: convert].
• “I’m from Missouri”: refusal to accept without proof.

Texts #

Read in class

• Handout, “The Form of the Simple Syllogism”, pp. 3–10 (verified): the four universal cases of the first and second figures.

Mentioned

• Aquinas, Summa Theologiae, Prima Pars: existence of God (five ways), simplicity, perfection, infinity, immutability, unity; De Deo Uno et Trino.
• Aquinas, Summa Contra Gentiles: first three books; the two arguments from motion; the five attributes.
• Aquinas, Compendium Theologiae: unity treated within simplicity.
• Aquinas, De Veritate q. 22 (“de bonitate”): whether the will can be coerced.
• Aristotle, Physics I (what changes is composed), VII–VIII (unmoved mover).
• Aristotle, Categories: animal said of dog, dog of retriever.
• Aristotle, Prior Analytics (inferred): said of all, figures, imperfect syllogisms.
• Aristotle, Peri Hermeneias: universal statements.
• Aristotle on tragedy vs. epic (Poetics, inferred).
• Fourth Lateran Council (inferred): God as immensus.
• Psalms (praise beyond all praise); “the fool multiplies his words” (Bible).

His questions #

• Would you divide those five into two or three? Two twos (simple–perfect, one–infinite) and a wild card, unchanging.
• Which is more perfect, the stone or the tree, the tree or the dog? The tree; the dog: in matter perfection grows with complexity, the reverse of God.
• As you go up the angelic scale, they get more perfect, but also what? Simpler; so at the top, something most simple and most perfect.
• Would you say God’s simplicity is endless, or his perfection? Perfection without limits; perfection and goodness are endless.
• Could God make everything he is able to make? No, for then he would have a limit.
• Is Thomas just not as good at order in the Summa Theologiae? No: unity is last because the Trinity follows; unchanging after the three reasons for it.
• What do you need logic for? Because you don’t know everything.
• Can you get anything from two negatives? No; even the said of none requires an affirmative; proved by counterexample.
• Can you necessarily turn around the universal affirmative? No (every dog is an animal); so the second figure AA is invalid.
• How do you know you can turn around “no A is B”? Suppose some B is A, call it X; then some A is B, contradiction.
• Can you convert a singular negative like “God is not composed”? Yes, by the same proof: nothing composed is God.