Metaphysics VI: The Whole Truth, Contradiction, and Truth in the Mind, Good in Things; Predicates and Definition in Logic

Orientation #

He is reading the second, third, fourth and fifth paragraphs of a passage on being as true and false (verified: Metaphysics VI with Aquinas’s commentary, lectio 4, matched to his handout “Note for Sixth Book of Wisdom, Reading 4”), then previews what Books VII, VIII and IX will do. He refers back to a Macbeth text “last week” and says “when we start to do the Summas, like we do before in the year.” The next class turns to Porphyry’s five and Aristotle’s ten, and to definition.

The class, in order #

1. Two ways of departing from truth (“the truth, the whole truth, and nothing but the truth”) #

Point: falsehood has two contrary extremes, and truth lies between.

• The courtroom oath is not mere repetition: “the whole truth” excludes subtracting, “nothing but the truth” excludes adding. Faustus: those who say more or less than the truth “are villains, the sons of darkness.”
• Bartender example: Paul and John were at the bar 9–10. Saying only Paul was there subtracts (saying what is, is not); saying Paul, John and Tom adds (saying what is not, is).
• Trinity: three persons therefore three natures = adding; one nature therefore one person = subtracting. Incarnation reverses it: one person therefore one nature = subtracting; two natures therefore two persons = adding. Each error has an element of truth, neither has the whole truth.
• Kent in King Lear: “all my reports go with the modest truth, nor more nor less, but so.”

2. What a contradiction is (“both cannot be true, and both cannot be false”) #

Point: to divide a contradiction, in the strict sense, is to have the two statements one of which must be true and the other false.

• Strict contradictories: same subject, same predicate, one affirmative one negative, such that both cannot be true and both cannot be false. “President Bush is sitting / is not sitting” — and he does not know which is true.
• Student objection: suppose he’s lying down — wouldn’t both be false? Answer: no; lying down, he is not sitting, so the negative is true. Either sitting or not sitting.
• This rests on the two axioms of being: (i) it is impossible to both be and not be, at the same time in the same way; (ii) it is necessary to be or not to be. Middle terms exist between black and white (lukewarm between hot and cold), but no middle between hot and not-hot: cold or lukewarm, you are still not hot.
• Hamlet: “to be or not to be, that is the question” is a question precisely because you can’t do both and must do one. “To breathe or to philosophize” is not a question — you can do both.

3. Contradiction with a universal subject (“the two halves of a contradiction”) #

Point: grammatical likeness hides logical difference once the subject is said of many.

• “Man is sitting” is indefinite: does it mean every man, or some man? Socrates names one individual, man is said of many.
• Wrong answer corrected: “every man is sitting” and “no man is sitting” are not contradictories — both are false, as looking round the room shows; logic calls them contrary, “about as far away as you can get.”
• The contradictory of “every man is sitting” is “some man is not sitting” — one man suffices. Likewise the universal negative against the particular affirmative.
• The two particulars can both be true (because “some man” is indefinite); the two universals can both be false; the diagonals cannot both be true or both be false.
• Aside: since every affirmative has a contradictory negative and vice versa, of all possible statements, 50% are true and 50% are false — so any reason at all to prefer one gets you “over that half and half.” “She loves me, she loves me not” — one must be true and the other false, but you don’t know till the last petal.

4. True as composition, false as division (“the true has the affirmation to put together”) #

Point: truth affirms what is together and denies what is divided; falsehood reverses this.

• Man and animal are together: “man is an animal” is true, “man is not an animal” false. Man and stone are divided: the negative is true.
• Second paragraph alludes to On the Soul III: to think “man is not a stone” you must think man and stone at once; but you can think man without thinking stone. So in a way you make one out of man and stone by the negative statement.

5. How to read Aristotle: through Thomas (“like looking at a professor’s notes almost”) #

Point: the third paragraph is extremely important and extremely brief; its whole point could easily be missed without Thomas.

• His old teacher Kasurik (ASR uncertain): Aristotle wrote the book, then scratched out every other sentence. More reasonable: what we have is like an official record, a professor’s index cards for an hour’s talk.
• Monsignor Dionne on Cajetan’s mistake: commenting directly on Aristotle without going through Thomas. Like the angels, where each instructs the one immediately below: Aristotle → Thomas → De Koninck → “I’m just going to show you how to read Thomas.” Learn from the mind closer to your own and ascend to the greater mind.

6. True and false in the mind, good and bad in things (“not in things … but in the mind”) #

Point: a fundamental distinction — truth and falsity are primarily in the reason, good and bad primarily in things outside the mind; and within the mind, truth is not in the simple.

• Man, animal, stone taken simply are not yet true or false, though you understand something by them. Truth arises in putting together or dividing.
• Where do you find truth or falsity? Not if you dig in the ground (rocks and soil), not in the ocean, not in the air — in the mind, and there only in statements.
• The Parmenidean system is funny: its parts (being, non-being, becoming) are simple, no statements, so no falsity in it — which simplifies life, but you get no truth either.
• Knowing vs. loving: knowing happens by the thing known being in the knower; love is more the heart being in the thing loved. “I left my heart in San Francisco”; “Where your treasure is, there your heart shall be”; Augustine: the soul is more ubi amat than ubi animat [as he gives it: “ubi amata … ubi animata”].
• Augustine on the shore and the boy pouring the ocean into a hole: you cannot get the ocean (or the Trinity) into the little hole of your mind — but you can jump into the ocean. St Teresa of Avila seeing the sea as a metaphor for God’s infinity. Fr Boulay: the will in this life is more proportioned to God.

7. Same knowledge of opposites, but not the same love (“the same knowledge of opposites”) #

Point: because knowing takes opposites into the mind and love follows the condition of things, one opposite is in the knowledge of the other, but love of one excludes love of the other.

• Knowing high blood pressure requires knowing proper blood pressure; knowing virtue is knowing vice.
• A clever student’s argument against teaching ethics at St Mary’s: ethics teaches not only virtue and how to become virtuous, but vice and how to become vicious — and since men are inclined to vice, you make them worse. “The best argument I knew against teaching ethics.” He does not answer it here.
• Parallels: rhetoric persuades to good or bad, makes a man seem just or unjust; Politics V teaches how to preserve a government and how to overthrow it; medicine can save the baby or kill it — “nobody could kill it better, maybe, than a doctor.”
• The reason for the difference: blindness is defined by sight (a lack of sight in an animal apt to have it), so one opposite is in the knowledge of the other; but in things, blindness excludes sight, and so loving sight excludes loving blindness.

8. Why Thomas treats God’s goodness early and God’s truth late (“a very interesting order”) #

Point: the order of the Summa confirms that good is in things while truth is in the mind.

• Order on God: first the substance (simple, perfect, unchanging, infinite, one), then the operations (understanding, willing), then the Trinity — one must see that God understands and loves Himself before the procession of the Word and the Holy Spirit.
• God’s goodness is attached to the consideration of the divine perfection, within the substance (as eternity is attached to unchangeableness) — before the divine will is even treated. But God as truth itself comes only after God’s understanding.
• Plato likewise puts the good itself (Republic), the same as the beautiful itself (Symposium), at the beginning of all things, and does not explicitly see that it understands and wills — a mistake — yet the order is the same: the good itself seen before mind and will. Thomas (with Dionysius) treats good and beautiful together.
• Why: good and bad, being in things, can be considered in the perfection of God’s substance; truth, being primarily in the mind, must wait on God’s understanding.
• Note on our two thoughts: God’s substance and operation are one, like the centre of a circle, but in creatures they are two points; starting from creatures we have two thoughts, neither adequate.
• Aside: a talk at TAC a few years ago on the contrariety of love and knowledge; the Macbeth text last week — speaking figuratively is more appropriate to love, and “the perfect sign of love is music,” which can even do without words. To know well you must analyze, a Greek word for taking apart; the lover does not take apart.

9. Setting aside two senses of being (“the cause of the one is indeterminate”) #

Point: with accidental being and being as true set aside, what remains is the being of the figures of predication, and its causes and beginnings are what must be considered.

• Composition and division are in the mind, not in things; so being as true is another being than being most properly. The mind joins and divides what it is (substance), how (quality), how much (quantity), and the other divisions of being according to the figures of predication.
• Accidental being is set aside because its cause is indeterminate; being as true because it is something undergone by the mind, and rests on being in things. Neither shows any existing nature of being outside.
• This presupposes the fifth book, where it was distinguished in how many ways each thing is said.

10. Preview of Books VII, VIII, IX (“book nine is the one”) #

Point: how Aristotle will proceed on being according to the figures of predication.

• VII and VIII: substance, chiefly material substance, more known to us — VII starting from what is said in logic about substance, VIII from what is said in natural philosophy.
• IX: the division of being into ability and act [ed.: potency and act]; “it’s primarily the ninth book that you see how he’s going to go all the way to the first cause from a knowledge of being as being” — the first cause as pure act. He usually takes Book IX when going through one of these; they will do something of VIII.

11. Said-of and subject (“that which is said as something”) #

Point: predication is being said of, and students never get clear the difference between what is said as something and what is said to be something.

• “Man is an animal”: man is said to be an animal; animal is not said to be an animal. Man is the subject, the underlying; animal the predicate, the Latin for that which is said as something. Hence the genus is written above the species on the board.

12. Why Thomas assigns predicate, not definition, to the first act (“the ten said-ofs”) #

Point: the puzzle of the Posterior Analytics text, and his suspicion of the answer.

• The three acts: (1) understanding what a thing is, (2) understanding true or false, (3) reasoning. Normally: definition → first act, statement → second, syllogism/argument → third. But in the Posterior Analytics text Thomas says syllogism, enunciation, predicate — predicate to the first act. Why not take the perfect thing, definition? Socrates in the dialogues is always trying to get someone to define, so as to understand distinctly what something is; the predicate does not do that.
• Student suggestion: because we predicate the definition of that of which it is a definition. His reply: partly true, but in syllogism and statement you also say something of something.
• His suspicion: Thomas is thinking of the books actually handed down to us. Most of the logical books are in the third act (demonstration, dialectic, fallacies); one book on the statement, the Peri Hermeneias; and in the first act only the Categories — category being the Greek for predicate, so “the ten said-ofs” — plus Porphyry’s Isagoge, whose five are also said-ofs. The five are called predicabilia (predicables), the ten praedicamenta; both words from the same root as predicate.
• Albert the Great’s logic of the first act (“the simple and unknown”) has four parts: the predicables (Isagoge), the categories, division, and definition.

13. Why Aristotle left no book on definition (“more than enough”) #

Point: three possible reasons — he thought it unnecessary, never got around to it, or it was lost — and his own answer is the first.

• Definition is treated in Posterior Analytics II because definition is the beginning of demonstration; there he says what definition is and distinguishes two ways of arriving at one. Even in the Prior Analytics he sees a connection between syllogism and definition; and in the Metaphysics he takes Socrates’ constant desire to define as a sign that Socrates wanted to syllogize.
• The eight books of Places (Greek topos; “topics” in English tells you nothing): the third and fourth tools of dialectic, difference and likeness, are useful for definitions; the first tool gathers definitions others have made. The places in books II–VII all contribute to the examination of definitions — places about whether something belongs to something, whether it is said essentially, whether it is convertible (a definition must be all three), and then the book on the places about definition proper, on what it adds beyond these, bringing out the nature. Dialectic is useful for the beginnings of reasoned-out knowledge, i.e. definitions — as Euclid opens Book I with definitions, and gives more in later books as needed.
• Balance: he does not say a treatment of definition in the first act is out of place; in a general logic course he treats it there, following Albert, borrowing from the Posterior Analytics — “kind of redundant,” a point of view, not simply a mistake. Understanding what something is has very much to do with the first act.

His words #

• “the two halves of a contradiction” — the pair of statements one of which must be true, the other false.
• “indefinite” — a statement whose universal subject is not marked as every or some (“man is sitting”).
• “said of” / “said-ofs” — his English for praedicata; the ten categories are “the ten said-ofs.”
• “that which is said as something” vs. “that which is said to be something” — predicate vs. subject.
• “figures of predication” — the divisions of being: what it is, how, how much, etc.
• “ability and act” [ed.: potency and act] — the division of being in Book IX.
• “the Places” [ed.: Topics].
• “the eighth/ninth book” of Wisdom [ed.: Metaphysics].
• “logic of the first act, the simple and unknown” — Albert’s name for it.

Texts #

Read in class

• Aristotle, Metaphysics VI, on being as true and false — paragraphs 2–5 (Aquinas’s commentary, lectio 4; his handout “Note for Sixth Book of Wisdom, Reading 4”).

Mentioned

• Aristotle, On the Soul III (thinking man and stone together); Metaphysics V (being said in many ways), VII, VIII, IX; Rhetoric; Politics V; Prior Analytics; Posterior Analytics II; Topics I–VIII; Categories; Peri Hermeneias.
• Thomas Aquinas, commentary on the Posterior Analytics (syllogism / statement / predicate); Summa Theologiae I, treatise on God (inferred).
• Porphyry, Isagoge; Albert the Great on the logic of the first act; Cajetan (via Msgr Dionne); Charles De Koninck; Dionysius.
• Plato, Republic (the good itself), Symposium (the beautiful itself).
• Shakespeare, King Lear (Kent), Hamlet, Macbeth; Marlowe’s Faustus (inferred); Euclid; Augustine; St Teresa of Avila.

His questions #

• Are “the whole truth” and “nothing but the truth” just repeating “the truth”? No: one excludes subtracting from the truth, the other adding to it.
• Can “President Bush is sitting” and “is not sitting” both be false? No — if he is lying down, he is not sitting, so the negative is true.
• What is the contradictory of “every man is sitting”? “Some man is not sitting” — not “no man is sitting,” which could be false along with it.
• Of all possible statements, how many are true and how many false? Fifty percent each, since every statement has its contradictory.
• Where do you find truth or falsity — in the ground, the ocean, the air? In the mind, and there only in putting together and dividing, i.e. in statements.
• Is there the same love of opposites as there is the same knowledge of opposites? No: in things one opposite excludes the other, and love follows the thing.
• Why does Thomas treat God’s goodness under the divine substance but God’s truth only after the divine understanding? Because good and bad are in things, but truth is primarily in the mind.
• Why does Thomas say predicate rather than definition for the first act of reason? Probably because the books handed down to us in the first act — the Categories and the Isagoge — are all about things said of others.
• Did Aristotle write no book on definition because he thought it unnecessary, never got to it, or because it was lost? His suspicion: unnecessary — the Posterior Analytics II and the eight books of Places were more than enough.
• Is the student’s argument against teaching ethics (it teaches vice too) answerable? Left open — he calls it the best argument he knows against it.