Reason Knowing Itself; The Second and Third Figures of the Syllogism

Orientation #

He says of next time only: “we can go into this maybe next time a little bit” — syllogizing about God in the Summa. The verified sources put the class on his handouts “The Form of the Simple Syllogism” (pp. 3–4), “Reasoning and the Four Kinds of Argument” (p. 6) and “Know Thyself” (p. 8). The previous class worked the first figure and the rules of conversion; the next reviews compound statements and Aristotle’s definition of syllogism against enthymeme and example.

The class, in order #

1. Order among senses of “before”; distinction before order (“one sense of before is before another sense”) #

Point: a name equivocal by reason has an order among its meanings, and reason, which looks for order, can find it.

• “Before” has four senses; the order among them is itself in one of those senses — “it’s the third sense” (he does not spell the four out here).
• Distinction vs. order: distinction means “this is not that”; order means “this is before or after that”. Their order: distinction comes before order, known “by the axiom of before and after that nothing is before or after itself” — you must see the distinction before the order.

2. Reason knows itself: “know thyself” and the definition of definition (“reason can come back upon itself”) #

Point: logic is “the philosophy of reason”, and what is marvellous about reason is that it can know itself.

• Shakespeare’s “reason is the ability for a large discourse, looking before and after” is reason defining reason, obeying the seven wise men of Greece who put up at Delphi “know thyself” and “nothing too much”.
• To whom is “know thyself” addressed? An exhortation, not a statement. Not to God or angels (they know themselves first and most), not to trees or the dog (the dog cannot know what a dog is), but to man — “more precisely, to your reason”: anger doesn’t know what anger is, digestion doesn’t know what digestion is, reason can know what reason is.
• Definition of definition: “speech signifying what a thing is”. His teaser: is the definition of definition a definition of the definition of definition? No: it is a definition of definition in general, true of the definition of square, of the soul, etc. Likewise “a statement is speech signifying the true or the false” is a statement about statements.
• Distinction of distinction (recalled from Thomas on the Trinity): formal distinction, by opposites (being divided into substance and accident: accident exists in another as in a subject, substance does not) vs. material distinction, division of the continuous (Euclid dividing a straight line into equal parts).
• Reason “is really the only part of me that can know itself”: does love know what love is? — but reason to some extent knows what understanding and reasoning are.
• Aside: a philosophy teacher at a Western university told him students’ faces say “why are you doing this to me?”

3. “Nothing too much” and names equivocal by reason (“one of them keeps it as its own name”) #

Point: one way a name becomes equivocal by reason is that of many things it is said of, one keeps the old name and the other gets a new one.

• Can you love God too much, if the wise men said “nothing too much”? Answer attempted: God is not a thing — but he is something; Boethius even says the Trinity is three things. Parish talk divides “person” against “thing” (don’t treat the girl as a thing), yet a person is something, not nothing; “to resolve it, person is something”.
• Examples of the pattern: (a) Aristotle sometimes calls habit a disposition firm and not easily lost, and disposition one easily lost; other times divides habit against disposition — the easily-lost one keeps “disposition”, the firm one gets the new name “habit”. (b) In the “book of places” (Topics, on dialectic): property is what is convertible with something (half of four converts with two); sometimes property is divided into property and definition — definition is convertible speech (“every square is an equilateral right-angled quadrilateral” and back; “every man is an animal that has reason” and back) but “does something more”, brings out what the thing is, so it gets the new name and the rest keeps “property”. (c) His mother disliked “man is an animal” because “animal” is sometimes kept for the beasts — biology teacher saying you’re an animal is no insult; girlfriend saying it probably is.

4. First figure recap: valid vs. invalid known differently (“You can’t prove these are valid by examples”) #

Point: of the four universal pairs in the first figure two are syllogisms, one giving a universal affirmative — “the only way you can” in direct syllogism — and one a universal negative; the other two yield nothing.

• Validity is not shown by examples; invalidity is, because an example never shows something is always so, let alone necessarily so (“I’m a philosophical grandfather, so every philosopher is a grandfather? No”).
• Preview: the second figure can give a universal negative but never a universal affirmative.

5. Deception by matter: mother, woman, man (“Every mother is a woman. No man is a mother”) #

Point: students say “no man is a woman” follows, but the form (every B is A; no C is B) yields nothing.

1. Same form with dog/animal/cat: every dog is an animal, no cat is a dog — nobody concludes “no cat is an animal”, because they know it is false.
2. So the student is deceived by the matter: he knows “no man is a woman” is true and that there is some connection between not being a mother and not being a woman — “see how subtle it is”.
3. In this form sometimes every C is A (every cat is an animal), sometimes no C is A (no man is a woman); nothing affirmative or negative is always so; “if nothing is always so, then nothing is necessarily so”.

• Put as an if-then syllogism: if necessarily so then always so; nothing is always so; therefore nothing is necessarily so (A and B standing for premises).

6. Second figure, the four universal cases (“the middle term is in the second place”) #

Point: middle term is predicate in both premises; question in each case: does anything follow with C as subject and A as predicate?

• AA (every A is B, every C is B): the said-of-none needs a universal negative; the said-of-all needs a universal affirmative plus something said to come under its subject — but nothing is said to be an A or a C. Converting “every A is B” to “every B is A” would give the first figure, but a universal affirmative converts only partially. “I give up” — then prove nothing follows by examples, satisfying two conditions: (1) examples for A, B, C making both premises true (“no defect in matter”); (2) one set where every C is A and one where no C is A. Since statements are affirmative or negative, universal affirmative knocks out both negatives, universal negative both affirmatives — “kills two birds with one stone; Aristotle does it a lot”. Examples: A dog, B animal; C cocker spaniel (every cocker spaniel is a dog — circled) and C cat (no cat is a dog — underlined). Check the homework: every dog is an animal, every cocker spaniel is an animal, every cat is an animal — condition one met. Nothing follows.
• EE (no A is B, no C is B): two negative “parents”, no offspring, “but I want to make sure”: A animal, B stone; C dog (every dog is an animal) and C tree (no tree is an animal); premises no animal is a stone, no dog is a stone, no tree is a stone all true. Nothing follows. A student asks him to go through the second condition again; he restates: affirmative/negative is a complete division of simple statements, so one example each ends “the ball game”.
• Aside on two ways of going wrong, like a checkbook: wrong numbers (false premises) or wrong adding (conclusion not following), or both “if you’re really stupid”; Aristotle in book I of Natural Hearing on Melissus [ed.: transcript “Listens”; likely Melissus] — premises false and conclusion doesn’t follow, which “finishes the guy off”; “the bad happens in many ways, the good in one way”; ice-cream cones for 19 grandchildren need the right price, the right number and correct multiplication. The Greeks called calculating logistikē, reasoning logic; both from reason.
• Definition of syllogism recalled: speech in which, some statements laid down, another follows necessarily because of those laid down. Shakespeare’s “it must follow as the night the day” is not a syllogism: night follows day not because of day but because of the sun going round the earth (“I don’t believe the earth turns on its axis”).
• AE (every A is B, no C is B): convert the universal negative — it stays universal — to no B is A; with every C is B you are “back in the first figure”: no C is A. This is why the second figure can give a universal negative: “to do so, you got to convert and you run back in the first figure”, which is more powerful and clearer, so it is put first.
• EA (no A is B, every C is B): convert to no B is A? He instead reads it as no B is C and every A is B, giving no A is C, then converts that to no C is A — left to last because “you had to convert twice”. Student: did you switch minor and major? Yes — he needs C as subject, so two conversions.
• “The power is going down”: first figure gives universal affirmative and negative; second only universal negative. Student’s aside about painful freshman logic; his: “my favourite class in high school”.
• Student: is it only two negatives that give nothing in every figure? He: mixed affirmative-negative always gives a negative conclusion, two affirmatives an affirmative.

7. Third figure: middle term subject in both (“your middle term is the subject in both cases”) #

Point: every case that concludes here concludes only particularly — “the weakness of it”.

• AA (every B is A, every B is C): nothing is said to be a B, but convert the minor partially to some C is B, “and lo and behold, by magic” first figure; said-of-all gives some C is A — the most affirmation you get. This is “reasoning out” a conclusion; epistēmē, reasoned-out knowledge: geometry of lines, angles, figures; arithmetic of numbers.
• EA (no B is A, every B is C): convert to some C is B; said-of-none gives some C is not A.
• EE (no B is A, no B is C): no said-of-all (no universal affirmative), no said-of-none either since it needs an affirmative part. Examples: B stone, A animal; C dog (every dog is an animal — circled), C tree (no tree is an animal — underlined); premises no stone is an animal/dog/tree true. “Two stones, I’ve killed four birds.”
• AE (every B is A, no B is C): converting the major gives some A is B, no B is C, hence some A is not C — but a particular negative cannot be converted, so no conclusion with C as subject. Examples: B dog, A animal; C cat (every cat is an animal — circled), C stone (no stone is an animal — underlined); premises every dog is an animal, no dog is a cat, no dog is a stone true. Nothing follows; not a syllogism.
• Summary: first figure both universals, second only universal negative, third “no universality, feeble” — hence its place.

8. Singular negatives convert; syllogizing about God (“Socrates is not a woman”) #

Point: God is not a universal strictly (a universal is said of many with quite separate existence; Father, Son and Holy Spirit have the same existence — “I am who I am”), but a singular negative converts like a universal negative, so one can syllogize with God as a term.

• Socrates is not a woman → no woman is Socrates; otherwise some person X would be both, and some Socrates would be some woman. Tabitha (his daughter’s cat) is not a dog → no dog is Tabitha. So in the Summa: God is pure act, nothing composed is pure act — maybe next time.
• Logic is not studied for its own sake: Thomas says it is ordered to philosophy as a tool, not a chief part. The two main distinctions of being — act and ability, and being according to the figures of predication (substance, quantity, … : what are you, how big, how, towards what, where) — come from natural philosophy and logic respectively: Thomas says Aristotle leads us “by the hand” from logic in book eight (substance) and from natural philosophy in book nine; natural philosophy proceeds per modum motus (grade-school clay moulded into sphere or cube gives ability and act), logic by the way something is said of something (Isagoge: five predicables; Categories: ten predicaments; said-of-all and said-of-none). Something is really said of something only in reason; language signifies that.
• His graduate teachers: Charles De Koninck (leading in from natural philosophy) and Monsignor Dionne (from logic); neither would teach metaphysics before those — “get the second grade guys to teach metaphysics”.

His words #

• equivocal by reason: a name said of many with an order among the meanings; also when one thing keeps the old name and another gets a new one
• distinction / order: “this is not that” / “this is before or after that”
• philosophy of reason: logic
• definition of definition: speech signifying what a thing is
• statement: speech signifying the true or the false
• formal vs. material distinction: by opposites vs. division of the continuous
• property: what is convertible with something; definition: convertible speech that brings out what a thing is
• ability [ed.: potency], act
• set of all / set of none [ed.: dictum de omni et nullo], also “said of all / said of none”
• matter vs. form of a syllogism: truth of premises vs. the following of the conclusion
• two conditions (for showing invalidity): true premises; one example concluding affirmatively, one negatively
• convert: universal negative wholly, universal affirmative partially, particular negative not at all; singular negative wholly
• syllogism: speech in which, some statements laid down, another follows necessarily because of those
• reasoning out / thinking out: epistēmē, reasoned-out knowledge
• logistikē: the art of calculating; logic: the art for reasoning
• Natural Hearing [ed.: Physics]
• book of places [ed.: Topics]
• per modum motus: by way of motion (natural philosophy); logic by way of predication

Texts #

Read in class

• Handout “The Form of the Simple Syllogism”, pp. 3–4 (verified): second and third figure cases worked on the board
• Handout “Reasoning and the Four Kinds of Argument”, p. 6 (verified)
• Handout “Know Thyself”, p. 8 (verified)

Mentioned

• Shakespeare: “large discourse, looking before and after”; “it must follow, as the night the day … thou canst not then be false to any man” (Hamlet, inferred)
• Seven wise men at Delphi: “know thyself”, “nothing too much”
• Thomas on the distinction of the Trinity (distinction of distinction)
• Boethius: the Trinity is three things
• Aristotle on habit and disposition; Topics on property and definition
• Euclid, dividing a line into equal parts
• Aristotle, Physics I, on Melissus (inferred reading of “Listens”)
• Thomas Aquinas, Summa: God is pure act
• Aristotle, Metaphysics VIII and IX with Thomas’s commentary (leading by the hand)
• Porphyry, Isagoge; Aristotle, Categories
• DHB Vol. I, The First Philosophers, p. 11 (verified)

His questions #

• Is the definition of definition a definition of the definition of definition? No; it is a definition of definition in general.
• To whom is “know thyself” addressed? To man, more precisely to reason, which alone can know itself.
• Can you love God too much, if “nothing too much”? Left open, beyond: God is not “nothing”, he is something.
• Every mother is a woman, no man is a mother — what follows? Nothing by form; “no man is a woman” is a deception by matter.
• Why are they deceived by this and not by the dog/cat case, which is the same form? Because they know “no man is a woman” is true and see a connection in the matter.
• What two conditions must the examples satisfy? Premises true; one example where every C is A, one where no C is A.
• Can anything come from two negative “parents”? No — checked by examples in both figures.
• In the second figure, what can you conclude and how? Only a universal negative, by converting back into the first figure.
• What can you conclude in the third figure? Only particular conclusions.
• Socrates is not a woman — can you convert it? Yes, no woman is Socrates; singular negatives convert like universal negatives.