Definition as Demonstration, the Rule of Two or Three, God's Ordered Likeness in Creatures, and the Four Tools of the Dialectician

Orientation #

The recording begins mid-argument (“notice what I was doing there”): he has just been reasoning from the end of a knife to its matter, and he sums up “the postulates… the four questions… demonstration propter quid and quia” before turning “now a little bit to dialectic.” Nothing is said about next time. Verified sources place about ten minutes of the class in his handout note on Physics I, reading 13 (the first-matter-by-proportion passage); the printed volume is DHB Vol. III, p. 364. The previous class treated demonstration vs. dialectical syllogism, propter quid vs. quia, and the four questions; the next continues the four tools of dialectic.

The class, in order #

1. Knife and definition: complete definition vs. demonstration (“almost the same thing as a demonstration”) #

Point: a complete definition contains what a demonstration contains, but in a different form (position).

• Knife argument, reasoning from end (cause of the cause) to matter: (1) a knife is a tool for cutting; (2) you want to cut something, not be cut; so (3) it needs a blade, and (4) to avoid cutting your hand, a handle, with the blade inserted in the handle. This is a demonstration: the cause, that of which it is the cause, and “it can’t be otherwise.”
• Definition of definition, in three forms: (a) “speech signifying what a thing is” (by purpose); (b) “speech composed of genus and differences” (by what it is made of); (c) the grand one: “speech signifying what a species is through its genus and differences.” Which is correct? All are; (c) has everything the demonstration has.
• Demonstration vs. grand definition: in the syllogism “speech signifying what a thing is” is the middle term, “speech composed of genus and difference” the major, “definition” the minor; the grand definition has the same content in the form of a definition. He finds it “kind of beautiful” that Aristotle thus unites the two kinds of questions, because there are many kinds of causes (define by inner purpose or by what it is made of).

2. The rule of two or three: Porphyry’s five and the ten categories (“you can’t understand distinctions of more than three”) #

Point: in his “doubting mood” he tests his rule that distinctions of more than three are understood only through distinctions of two or three, adding “for the most part.”

• Porphyry’s five names (Isagoge): genus, species, difference belong together as inside the nature (genus gives it in general, difference in particular, species combines both; genus and species correspond “like father and son”; difference is what the species has in addition to the genus); property and accident are outside the nature, accident having no connection with it (a green triangle), property having a connection. So: one distinction of two (inside/outside), one of three, one of two again.
• Aristotle’s ten highest genera: “Aristotle means what Thomas says he means” is his slogan, so he goes to two places where Thomas explains the ten, the fifth book of Wisdom [ed.: Metaphysics V], where being is divided into the ten “according to the figures of predication,” and the third book of the Natural Hearing [ed.: Physics III], where Aristotle does not put motion in some category other than acting upon and undergoing. In both Thomas divides the ten into three (or first into two, substance and accident): said of an individual substance (1) by reason of what I am (substance, not subdivided); (2) by reason of something in addition, inside me, divided into absolute (quantity and quality, corresponding to matter and form) and toward another; (3) by reason of something outside me. Of the outside ones, “habit,” being clothed, is divided off as belonging to man (other animals come with their clothing or armour; the turtle, a house on his back); he first says “five,” corrects to “six,” then settles on five remaining, divided by motion (acting upon, undergoing) and by quantity (where, when, position; Thomas: place and time, place subdivided because of position of parts in place). “He’s always dividing by two or three.”

3. The eight meanings of “in” (“what about these eight meanings of in”) #

Point: eight is understood as three, three, and two (act; passive ability; active ability).

• Actually in: (1) in a place (I am actually in this room); (2) part in whole (teeth in my mouth); (3) genus in species (actually there when you define the species).
• In by passive ability: (4) species in genus, not actually there, since “animal” would then mean something composed of cat, dog, horse, elephant, so “a dog is an animal” would say a dog is composed of all those; (5) form in matter, form to matter as species to genus; (6) whole in parts, whole like form, parts like matter, “that from which something comes to be, existing in it.”
• In by active ability: (7) in my power / “out of my hands”; (8) in the end: “I left my heart in San Francisco,” “where your treasure is, there your heart shall be.”
• Note: he says “three, three, and three” but has enumerated eight and earlier said “the seventh sense”; the count in his own list is 3 + 3 + 2.

4. The four causes and the four opposites (“Can you understand distinction of four?”) #

Point: four is not understood as four.

• Causes divided into two: inner (matter, form) vs. outside (mover or maker, end): three distinctions of two. Or into one and three: matter is ability in the passive sense, the other three are based on actuality. This is why God can be cause as end, mover/maker, and in a way as form in the sense of exemplar (not intrinsic form): “all three or two and a half,” because he is first act, pure act.
• Example of the inner causes: the word “cat” depends on the letters C, A, T (matter); since “act” has the same letters, “you’re forced by the truth itself” to add the order of the letters (form).
• Opposites, four senses: divided one and three, relation separated off because it does not eliminate its opposite but demands it, whereas living/not alive, virtuous/vicious, knowing/ignorant are incompatible; then the three subdivided. Thomas explains the four opposites very clearly this way.
• The second postpredicament, “before,” four senses: he is “not even sure how you divide those four up”; he is still thinking about the eight senses of before. Left open. The rule may have exceptions, but it is good and “makes you very thoughtful.”
• Aside: cat stories (his daughter’s guest from college petting the cats; Aunt Margaret bringing home a kitten; his daughter’s cat from the music teacher).

5. Back to definition: the end as cause of causes (“the end is the cause of all the other causes”) #

Point: it may be better to do the demonstration before the grand definition, so one sees the connection between “speech signifying what a thing is” and “speech composed of genus and differences.”

• Example: a Manhattan needs whiskey, sweet vermouth, cherries: what a thing is put together from is for its purpose. Aristotle: the end is the cause of the other causes.
• Augustine: “Because God is good, we are”; good is a notion of an end. Caution: strictly there is no cause and effect within God; Thomas says there is cause and effect “in the mode of” [unclear in recording].
• Why does God love himself? First cause of love: he is good, goodness itself, “the good of every good,” summum bonum, as Thomas shows “in his favorite book” (unnamed). Second cause of love: knowledge; God knows he is good.

6. God makes everything like himself, but not equally (“God hates equality”) #

Point: God cannot produce another God from nothing, so he produces himself in us by making us like him, in an ordered ladder, unequally.

• Ladder of likeness: the stone is like God only in existing (hence metaphors: “the Lord is my rock”); the tree more, since God is alive (Peter’s confession: “Son of the living God”); the dog and cat more, since they sense with more than one sense; man more, since he understands; but man needs discourse. Even axioms known without discourse (“the whole is more than the part”) presuppose discourse in coming to know what whole and part are, from experience of wholes and parts (Aristotle, book on demonstration, on the axioms). The angel, needing no discourse, is by nature more like God than we are.
• Why not equally? (1) His “old professor of Christianity” put it roughly: “God hates equality”; Thomas: no two angels are equal, each more or less perfect and more or less simple, in hierarchy from lowest to highest. (2) A student: there is no way he could put it all into one. (3) Two ways creatures are like God: to be good and to be a cause; if all were equal none could cause goodness in another. (4) There would be no order unless one were better than another; better is “the fourth sense of before”; and the better can move the lower: higher angels illuminate lower, down to “my guardian angel illuminating me” (why the class prays to the guardian angel). God orders by wisdom: Sapientis est ordinare, Aristotle’s line Thomas always quotes.
• Asides: he needed Thomas to break the ten down to fit his weak mind; his teacher Kasurik: “compared to Aristotle I’ve got the brain of an angleworm”; the chain Kasurik, De Koninck, Dionne, like angels illuminating in order (De Koninck answering questions Kasurik couldn’t; De Koninck on his thesis: “why did you bother to ask me?”). Thomas’s works on Aristotle are technically “expositions,” a laying out; necessary to proportion Aristotle to us, as the Church Fathers are for Scripture.

7. Wrap-up of demonstration and turn to dialectic (“four tools of the dialectician”) #

Point: of the postulates, the nice things to see are the four questions, the definition of demonstration, propter quid vs. quia, and the connection between the two sets of questions.

• Aristotle’s logical works are collected as the Organon, logic being the tool of philosophy; in the book of places [ed.: Topics] Aristotle gives four tools within the tool: “a very toolish subject.” He is more and more impressed as he follows the order of the four.

8. First tool: selection of probable opinions (“the selection of probable opinions”) #

Point: since dialectical reasoning is from probable opinions, “what else could be the first tool?”

• Select the opinions of all or most men, or of the most famous in an art or science speaking about its matter; under it come “our two old friends,” distinction (opinions pertaining to ethics, to the natural world) and order (from general to particular, since the general may be used to reason to or be applied to the particular).

9. Second tool: distinguishing the senses of words (“distinguish the senses of words”) #

Point: opinions are heard and read in words, and words have many meanings, so the second tool is the ability to distinguish senses; “the most common mistake” is not to.

• Shakespeare on reason’s “large discourse looking before and after”: before and after has many senses; Shakespeare does not mean all, and reason looks before and after in more than one.
• Aristotle gives places to look; one is the opposite. “Liberal”: in politics its opposite is conservative; in the liberal arts, conservative; for the virtue liberality, stingy. Many opposites, many meanings. (Joke reported: conservatives give more to charity, liberals are liberal with other people’s money; conservatives more interested in real liberal education.)
• Distinguishing senses also multiplies probable opinions: reason looks before and after in time, in cause and effect and being, in what comes before as principles of a science, in what is better.

10. Third and fourth tools: differences and likenesses of things (“the ability to consider likeness”) #

Point: distinguishing words brings you close to distinguishing things; the third tool is the ability to find differences of things (liberal with money vs. liberal in politics are different things), the fourth the ability to consider likeness, since one who knows differences must know similarities (a doctor who knows health and one who knows sickness are no doctor unless one knows both).

• He flags the wording: Aristotle says “find” differences but “consider” likeness. Near likeness (cat and dog both four-footed; a child calls a dog a cat) vs. likeness of ratios, more distant; most scientific discoveries are made by likeness of ratios, and Aristotle’s works are full of them.
• Mathematics, first meaning of “proportionally”: 2 is to 3 as 4 is to what? Students say 5 (same distance), but distance is not likeness; imagine 4 as two twos and 6 as three twos: 4 is to 6 as 2 to 3. Misuse: “4 to 6 is even to even, so 2 to 3 is even to even,” or “2 to 3 is prime to prime, so 4 to 6 is”; that is not the way they are alike. Strictly: 4 is the same parts of 6 that 2 is of 3.
• Aristotle’s “most difficult thing”: first matter, underlying substantial change, is known by proportion: first matter is to man and lion as clay to sphere and cube. Not alike in that man and lion are substances while sphere and cube are species in the genus of quality; not alike in that clay is an actual substance while first matter is not. Alike in this: clay can be sphere or cube, not both at once; when one, able to be the other; if it becomes the other it ceases to be the former. First matter likewise can be man or lion (the lion eats the man), not both, ceasing to be the former. Likewise man to healthy and sick.
• Earlier proportion recalled: definition is to the first act as statement is to the second; a statement is not a definition, but as the definition lets you understand what a thing is, the statement lets you understand true and false.
• Virtue by proportion: virtue, a stable disposition making a power and its work good; the virtue of a knife is sharpness, its vice dullness; you would not want a knife without its virtue, why a man without his? The recording ends here.

His words #

• demonstration: giving the cause, that of which it is the cause, and that it cannot be otherwise
• definition of definition: “speech signifying what a species is through its genus and differences” (grand form)
• rule of two or three: distinctions of more than three understood only through distinctions of two or three, “for the most part”
• book of the five names: Porphyry’s Isagoge; book of the ten names: the Categories
• fifth book of Wisdom [ed.: Metaphysics V]; Natural Hearing [ed.: Physics]
• figures of predication: Thomas’s principle for dividing being into the ten
• habit: the category of being clothed, proper to man
• ability [ed.: potency], active and passive; actuality, pure act, first act
• exemplar: the exterior form by which God is cause “in a way like form”
• “two and a half”: God as cause in the senses of end, mover, and exemplar-form
• summum bonum; “the good of every good”
• Sapientis est ordinare: it belongs to the wise to order
• exposition (not commentary): Thomas’s laying-out of Aristotle
• Organon: the tool; the four tools of the dialectician within it
• probable opinions: those of all or most men, or of the most famous in an art or science
• places: where you look to see if a word has more than one meaning (e.g., its opposites)
• likeness of ratios: distant likeness, “four is the same parts of six that two is of three”
• first matter: the matter underlying substantial change, known by proportion
• virtue: stable disposition making a power good and its work good

Texts #

Read in class

• Aristotle, Physics I, Thomas’s commentary lectio 13, via his handout “Note for Book One, Reading Thirteen,” p. 4 (first matter known by proportion; verified source, ~10 min)
• Shakespeare on reason’s “large discourse looking before and after” (Hamlet, inferred)
• Augustine: “Because God is good, we are” (locus not given)

Mentioned

• Porphyry, Isagoge (five names)
• Aristotle, Categories (ten names; postpredicaments: opposites, before)
• Thomas, exposition of Metaphysics V (division of being into ten)
• Thomas, exposition of Physics III (motion, acting upon, undergoing)
• Aristotle, book on demonstration [ed.: Posterior Analytics] (the axioms; the four questions)
• Aristotle, book of places [ed.: Topics] (four tools)
• Thomas, “his favorite book” (God as goodness itself, good of every good; not named)
• Thomas on the angels (no two equal; illumination)
• Peter’s confession, “Son of the living God”; “the Lord is my rock”; “where your treasure is”

His questions #

• Which definition of definition is correct? All are; the grand one includes everything the demonstration has, in the form of a definition.
• How do you understand the distinction of five in Porphyry? Inside/outside the nature; the inside into three; the outside into property and accident.
• Can you understand a distinction of four (causes)? No; as inner vs. outer, each into two; or as one (passive ability) and three (actuality).
• How do you divide the four senses of before? Left open; he is still thinking about it.
• Why does God love himself? Because he is good, goodness itself; and because he knows he is.
• Can God produce himself in us? Not as God from nothing; by making us like him.
• Why does he make everything like himself but not equally? No order without one better than another; the better can cause goodness in the lower (illumination); “God hates equality.”
• What else could be the first tool of the dialectician? Nothing: reasoning from probable opinions requires selecting them.
• Is “liberal” the same in politics, the arts, and the virtue? No: its opposites differ (conservative, conservative, stingy).
• Two is to three as four is to what? Six, not five: four is the same parts of six that two is of three.
• In what way is clay to sphere and cube like first matter to man and lion? Each can be one or the other, not both at once, and ceases to be the former in becoming the other.
• What is the virtue of a knife? Its vice? Sharpness; dullness.