Isagoge vs. Categories, What a Thing Is, and Metaphysics VII: Defining Substance, Accident and Motion

Orientation #

He is between Book VII and Book VIII of the Metaphysics: he says he will “spare you the going through book seven,” giving instead two things from it that stick in his mind, and announces that in Book VIII Aristotle approaches substance not logically but from natural philosophy, matter and form — he will bring ten copies of the text. Verified sources place the class between Aquinas’s commentary on Metaphysics VI (lectio 4) and Metaphysics VIII (inferred), with a short reading from the handout “The Skopos or Aim of the Categories,” p. 20.

The class, in order #

1. A student’s question: two different distinctions of “said of” (“there’s five in the Isagoge, right, and ten in the categories”) #

Point: the Isagoge and the Categories both distinguish “said of,” but not the same distinction — numerically five against ten — so what is an accident in the Categories’ sense need not be an accident in Porphyry’s sense.

• Student’s first try: Porphyry looks at the relation to the subject (per se or accidental), the Categories merely defines the accidents. He allows this “gets in there” but reframes it.
• Aside: Fr. Delac, teaching logic at Collège Saint-Thomas when he was a student, despaired of ever getting students to see accident-opposed-to-substance against accident-opposed-to-property — “99.99 percent of the students will never get in their head straight.”

2. The clue from the Summa Contra Gentiles (“my favorite book”) #

Point: the Isagoge is a distinction of names said univocally of many things.

1. Thomas argues that no name is said univocally of God and creatures by a disjunctive (“either-or”) syllogism: every name said univocally of many things is either genus, difference, species, property or accident.
2. He then eliminates all five.
3. Therefore he takes Porphyry’s five as a complete division of names said univocally of many — which is the clue to what Porphyry is dividing.

• Difficulty he raises: Porphyry’s proemium and his definitions (“genus is that which is said of many differing in species and answers the question what is it,” in quid praedicatur) do not say name. Maybe Porphyry doesn’t know what he’s doing; maybe he wants genus and species both for the name and for the general or particular kind of thing itself. But Aristotle treats definition as a logos, a speech composed of names, genus and difference being names — “it seems you got to begin there, the sensible name.”
• He took this to Monsignor Dionne: should Porphyry not first have distinguished names said univocally of many from names said equivocally of many? Dionne said yes. Then a further part would divide equivocals by chance from equivocals by reason — and he says he has himself distinguished the different ways a name is said equivocally by reason, doing for those what Porphyry does for univocals.
• Example of univocity: “the dog is an animal,” “the cat is an animal” — same meaning in mind, a living body with sensation, and the same reason for calling each. Against this his boundary case of bats: bats in here last night and bats in the church belfry — [he says “then I have the same meaning in mind,” apparently inverting his own example; as he leaves it, the contrast to equivocation is left unmade].

3. What the ten are names of (“names said of individual substances”) #

Point: the Categories divides names said of individual substances, by the manner of saying.

• Before the ten, Aristotle distinguishes substance/accident and universal/individual, giving four: universal substance (man), individual substance (this man), universal accident (shape), individual accident (my shape).
• Thomas’s division (following the rule of two or three): a name is said of individual substances either (a) as regards what they are, (b) by reason of something existing in them in addition to what they are, or (c) by reason of something outside them.
  • (a) gives substance: man said of you and me; animal of man; living body, body, substance up the line.
  • (b) you and I are said to be white, or healthy.
  • (c) you and I are said to be in this room, clothed, sitting.

4. Ousia and to ti esti (“in both he gives exactly the same ten”) #

Point: substance signifies what a thing is.

• Only two places he knows where Aristotle lists all ten: the Categories and the Topics. Same ten, same order, one exception: the Categories calls the first ousia (substance), the Topics calls it to ti esti, what it is. “Very very revealing” — “what it is, how much, how, towards what, very concrete.”
• Hence in Book VII Aristotle talks so much about what-it-is and about definition, since the definition tells what a thing is.

5. Book VII: is a thing the same as what it is? (“would there be more than one circle?”) #

Point: in material and mathematical things the individual and what it is are not identical — otherwise there could only be one of each kind.

1. What a circle is is something one.
2. If a circle and what a circle is were identical, there could not be more than one circle; likewise one man, one dog, one cat.
3. But there are many. So they differ.

• Plato anticipated this wrongly: one form of man, one of dog, existing by themselves, and we “partake” in unexplained ways. Aristotle’s objection in Book VII: if I am a man by partaking of the form of man, “what do you need your parents for?”
• Why many of a kind: Euclid starts from the point — how two points, exactly alike? One at the beginning of the line, one at the end; one here, one there. So continuous quantity is involved. Two definitions of continuous: that which is divisible forever (worked out in Book VI of the Natural Hearing [ed.: Physics]) and, in the Categories, that whose parts meet at a common boundary — two semicircles meeting at the diameter. Continuity involves part outside part.
• “Why can you have many windows exactly the same kind?” — “You have enough glass.” Many metal chairs: enough metal; wooden chairs: enough wood. Two things needed: a material, and that it be extended, divisible, so one can be here and one there.
• Therefore if a substance is not material, has no length, width, depth, the basis for many individuals of the same kind disappears — the way to immaterial substance, “by way of negation at least.”

6. Angels, inequality, and the poets’ gods (“God hates equality”) #

Point: the negation just reached is what Thomas asserts of the angels.

• Thomas denies any two angels of exactly the same kind; in each of the three hierarchies and each order, beginning, middle and end, but never two alike.
• Thomas’s question whether angels would love each other more if they were of the same kind: they love each other more because they are not. Reason: the more understanding a creature, the more it is concerned with the common good, the order of the universe; and that order is more satisfied by inequality than by equality.
• Old teacher Casaubon: “God hates equality.” No two saints equal even in heaven — “star differs from star” — and so the envious will not be in heaven, envy being contrary to what heaven is like.
• Plato’s error compared to the poets: Homer’s gods with domestic disturbances, the wife on the other side in the Trojan War; Xenophanes — if cattle made statues their gods would look like cattle; Ethiopians make their gods black, Greeks blonde, and the Thracians. Not knowing the gods’ nature they imagine them like themselves but perfected. So with “man himself,” “dog itself.” Yet Plato saw something true: that each immaterial thing would be of a different kind — “a wonderful discovery,” against what the man in the street thinks of angels.

7. Book VIII and the two ways of leading by the hand (“per modum motus”) #

Point: Book VII leads us to substance from logic, Book VIII from natural philosophy.

• The wise lead us by the hand from the lower sciences to wisdom. Thomas contrasts the two: proceeding per modum motus, the way of motion, proper to the natural philosopher — against the logical way.
• Why the first way is logical: only in the mind is something said of something; outside the mind nothing is said of anything. So the whole distinction of being according to the figures of predication distinguishes beings by the way they can be said of individual substances; and the Isagoge too distinguishes by the way something is said of something (same meaning in mind or different).
• Logic’s two affinities to wisdom: universality (what logic talks about is said of everything, as the mind is in some way all things) and immateriality. Monsignor Dionne quoted Heath’s Euclid: mathematics purificat oculum mentis, purifies the eye of the mind — but, said Dionne, logic purifies it even more, being more immaterial than [mathematics]. Natural philosophy, by contrast, is very material.
• Book IX starts act and ability from motion; so Book VIII stands in the middle, matter and form preparing act and ability while looking back to Book VII’s substance. “Interesting the way Aristotle ordered these.”
• Aside: at Laval the two greatest minds taught logic and natural philosophy — he (Charles De Koninck, inferred: unnamed) natural philosophy, Dionne logic. Also: at TAC, the first time out, they wanted Book VII, “the last thing I’d slept to do.”

8. Definition as a limit (“a definition is a tight fit”) #

Point: definition, from finis / Greek horos, horismos (whence horizon, the line separating sky from ground), is a limit and so exact.

• City limits of Worcester: no part of Worcester should be outside them, and no part of Shrewsbury or Holden within. So a definition should include only the thing defined and nothing else.

9. Aristotle’s dilemma: can an accident be defined? (“definition has two meanings”) #

Point: either only substance is definable, or “definition” is said in two senses — and that difference corresponds to a difference in being.

1. An accident is something of another.
2. So you cannot say what it is without bringing in something other than itself — health is “the good disposition of the body,” bringing in the body.
3. But a definition should contain only the thing defined.
4. Therefore either only substance is defined (substance not being of another), or definition has two meanings: the definition of substance contains only substance, that of accident contains that of which it is an accident.

• This difference in being definable corresponds to a difference in things: substance is a thing in its own right, an accident “a strange kind of reality,” something of another.
• It gets stranger with privations: blindness excludes sight yet cannot be defined without it; ignorance without knowledge. And with motion, which lies between accident and privation — learning is not knowing, yet cannot be defined without bringing in knowing, something “more there than motion.” Further, motion is indeterminate while to define is to make precise. So perhaps more than two meanings of definition, moving from substance to accident to motion to privation — “kind of an amazing thing,” that Aristotle uses definability to bring out differences in things, substance being being primarily.
• Thomas on the fifth book: the modi essendi correspond to the modi praedicandi — “you got to be careful because there’s not exactly one to one” — my being in this room, my being a man, my being a geometer are really different kinds of being.
• He notes this is not the logician’s usual sorting of definitions (by effect or by cause, more perfect by the cause; by genus and difference, or genus and property), which divides ways of defining the same thing.

10. Descartes and Locke on motion, and what is known without definition (“you can’t define act”) #

Point: denying that motion can be defined closes the road from motion to a mover, and so to God.

• Descartes and Locke both say motion cannot be defined; for Locke it is a simple idea. Objection met: a definition needs multiplicity, never one word.
• Reply: motion is something of another — “walking doesn’t go for a walk,” it is always something other than walking that is walking. So you can say what it is of another, and that twoness suffices for something more distinct than the name.
• Parallel case, the point: a point has no parts, so you cannot make a speech out of its parts — unlike the knife, “a tool composed of a blade and a handle,” where parts can be spelled out. But the point is the end or limit of a line, something of another; saying what it is of the other is more distinct than “point.”
• Where it stops: in Book IX Aristotle says act cannot be defined — you can know what it is, but not by definition. Motion is defined by ability and act; act by nothing else. “Aristotle knew where the thing stopped.”
• The parallel in statements: some statements are known but not through other statements, else an infinite series of statements would have to be proved before any could be used. “Statements exist” proves itself: the man who says statements do not exist has made a statement — “the ball game is over.”
• Descartes quotes the definition of motion in an obscure translation and asks who understands those words, making himself look ridiculous. But once you give up defining motion you lose one of the main middle terms for showing motion’s dependence on a mover, the beginning of knowing that God exists — while the First Vatican Council teaches as an article of faith that God’s existence can be known by reasoning. “A very serious mistake.” Later philosophers do not even bother to try, or to say it cannot be done; it is now their custom.

His words #

• “Said of” — the phrase whose pluralization (“names said of many things”) he uses to pin down what each book divides.
• In quid praedicatur — Porphyry’s Latin for genus answering “what is it.”
• Disjunctive syllogism — “either-or syllogism”; “I use a big word.”
• Equivocally by chance / equivocally by reason — his two divisions of names said equivocally of many.
• Ousia / to ti esti — the Categories’ and Topics’ names for the first category.
• “Natural Hearing” — [ed.: Physics], for the sixth book’s definition of the continuous.
• Per modum motus — Thomas’s phrase for the natural philosopher’s way of proceeding.
• Purificat oculum mentis — Heath’s Euclid quotation, of mathematics; Dionne extends it to logic.
• Horos, horismos, finis — limit; the root of “definition,” hence “a definition is a tight fit.”
• Modi essendi / modi praedicandi — ways of being and ways of predicating, Thomas on Book V.
• “Act and ability” [ed.: act and potency] — the subject of Book IX.

Texts #

Read in class

• Handout, “The Skopos or Aim of the Categories,” p. 20 (brief reading).

Mentioned

• Porphyry, Isagoge, proemium and the definitions of the five.
• Aristotle, Categories (the four-fold division before the ten; the continuous as parts meeting at a common boundary).
• Aristotle, Topics (the ten, with to ti esti first).
• Thomas Aquinas, Summa Contra Gentiles, chapter that no name is said univocally of God and creatures.
• Aristotle, Metaphysics VII (what it is, definition, against Plato’s forms); VIII (matter and form); IX (act and ability; act undefinable); Thomas’s commentary on V (figures of predication).
• Aristotle, Physics VI, the continuous as divisible forever (inferred).
• Euclid, Elements, in Heath’s edition; the point.
• Thomas Aquinas on the angels: no two of a kind, their love and inequality.
• Homer; Xenophanes on the gods.
• Descartes; John Locke, on the indefinability of motion.
• First Vatican Council, on knowing God by reason.

His questions #

• What is the difference between the “said of” of the Isagoge and that of the Categories? Five against ten: the Isagoge divides names said univocally of many things; the Categories divides names said of individual substances.
• Should Porphyry not first have distinguished univocal from equivocal names said of many? Yes (Monsignor Dionne agreed); and equivocals then divide into by chance and by reason.
• Are a circle and what a circle is the same? No — if they were, there could be only one circle, one man, one dog.
• Why can you have many chairs of exactly the same kind? Because you have enough wood or metal: a material that is extended and divisible, so one is here and one there.
• Would the angels love each other more if they were of the same kind? No — they love the common good most, and the order of the universe is more satisfied by inequality.
• Can an accident be defined? Either only substance is defined, or definition has two meanings, since an accident’s definition must bring in its subject.
• Can motion be defined? Yes: motion is something of another, and saying what it is of that other gives the multiplicity a definition needs.
• What can be known without definition? Act, which cannot be defined by anything else — as some statements (“statements exist”) are known but not through other statements.