How Forms Admit More and Less: Species as Numbers, Health, Substance and Figure, and Knowledge That Broadens and Deepens

Orientation #

He picks up mid-article (“So, therefore, that the truth of this thing might be made known…”) and says of a later class only that “later on we’ll talk about… virtues in particular, where they can grow.” He ends: “We have to stop here now.” The previous class turned to whether habits increase and the analogical transfer of “growth”; the next continues Question 52 through the four opinions and the replies.

The class, in order #

1. Species are fixed, like numbers (“species of things are as numbers”) #

The point: that by which a thing obtains its species is fixed, standing, “as it were, indivisible”; whatever exceeds or falls short belongs to another species (Metaphysics VIII; Plato had said it before Aristotle).

• Shakespeare’s “if his chief good and market of his time be but to sleep and feed, he beast no more”: he flags the word “no more” — man has more than the beast, and the play goes on to find it is reason.
• Subtraction/addition series: take reason from man, you have a beast; take sense from a beast, a plant; take life from a plant, a body. So body = 1, plant = 2 (body + life), beast = 3, man = 4: natures are like numbers, varied by adding or subtracting. “There’s nothing between four and three.”
• Application: this is a simple way to explain how God knows other things by knowing himself — if four knew itself it would know three, two and one; creatures partake of God more or less, and he knows them so, “because He’s everything.”
• Aside: his mother disliked his saying “man is an animal” until he added “an animal that has reason.”

2. Forms absolute vs. forms ordered to another (“cannot said in order to another”) #

The point: a form that by itself sorts the notion of a species has a determined ratio that cannot exceed or fail; of this sort are heat, white and qualities “not said in order to another,” and much more substance, which is being per se. But forms that receive their species from being ordered to something can be diversified in more or less while remaining one in species, because of the unity of that to which they are ordered. “This is a difficult thing he’s saying.”

• Motion: coming into the room is ordered to being in the room; one can be coming more or less into the room, yet it is still the same species of motion.
• Health: the body is healthy by a disposition suitable to the nature of the animal, and diverse dispositions are suitable, so health varies in more or less and always remains health. One of us can be stronger, and also healthier, than another: better disposed toward the same thing.
• Ethics X: health receives more and less, “there is not the same measure in all things, nor in one the same thing always”; being less, health remains usque ad aliquid. His own case: he now needs the pew to genuflect (“I’m becoming unhinged”).
• The measurements of health stand as exceeding and exceeded; if the name of health were imposed only on the most perfect commensuration, it would not be said to be more or less. Same with beauty: two girls both beautiful, one more beautiful, and the less is not thereby ugly; two strong men or two fast runners or horses, one a little better.
• His summary of the distinction: health, ordered to preservation of the body, can be more or less in itself; heat, not ordered to anything as such, can be partaken of more or less by the subject, “but the heat itself is not a different kind of heat” — “kind of hard to see.”
• Student aside: Eskimo tribes having many words for snow; he allows it is not a great example.

3. Partaking of the subject; Simplicius on substance, quantity, figure (“substance by itself cannot receive more or less”) #

The point: considered according to the subject’s partaking, again some forms receive more and less and some not; Simplicius gives the cause.

1. Substance by itself cannot receive more or less: you cannot be more a man than I (unless “man” is used equivocally for courage, which is a quality); one dog is not more a dog; my soul is not more a soul than yours. So every form partaken substantially lacks intension and remission.
   • “All men are created equal” (Declaration of Independence): not equal in size, health, strength, beauty — the truth is substantial equality; in slave-owning Athens, free and slave was not a difference of substance. Today’s egalitarianism has lost this and wants everyone to have the same.
2. Quantity is propinqua, near to substance (in the Categories the order is substance, how much, how), and figure is the termination of quantity and follows it; hence in these too nothing is said more or less.
   • One ten-inch line is not more ten inches long than another; “more or less ten inches” means you are reading something other than ten inches. Two men of the same height: one is not more that height.
   • Figure: one circle not more circular than another; loosely we say the Earth is more a sphere than a box, but strictly the Earth (mountains, valleys) is not a sphere, and a rubber ball is not more a sphere than a sphere.
   • Student: Animal Farm, “some are more equal than others.” He takes it up: “equal” is originally tied to quantity; if one could be more equal than another, the axiom “quantities equal to the same are equal to each other” would fail. Euclid’s first theorem (equilateral triangle on a line, two circles from the endpoints, radii equal) assumes exactly this.
   • Physics VII: when something takes on a form or figure it is not said to be altered but to come to be.
3. Other qualities, more distant from substance and joined to passions and actions, receive more and less by the subject’s participation: water on the stove more or less hot.

4. Thomas’s own account: two ways a form is not partaken of more or less (“possible also to more explain the reason”) #

The point: Thomas seems to accept the Commentator but gives a fuller reason from the principle that what gives species must remain fixed and indivisible, like number.

1. Because the partaking thing has its species from the form: so no substantial form is partaken of more or less. Metaphysics VIII: as number has no more or less, neither does substance according to species. His daughter has ten children; another has ten too; neither has “more ten.” But with matter, according to material dispositions, more or less is found in substance (my body more or less disposed).
2. Because indivisibility belongs to the ratio of the form itself, so whatever partakes of it must partake indivisibly. Cases:
   • species of number: three is two plus one, and that third unit is as indivisible as a point;
   • species of continuous quantity taken by numbers (two cubits, three cubits);
   • relations such as double and triple: five is not “more double” of two than four; it is not double at all;
   • figures: triangle and quadrilateral. Aside: triangle is named from the angle, quadrilateral from the side; Greek tetragonum from the angle; “trilateral” and “quadrangle” (the campus quadrangle) also exist — “probably custom.”
   • Aristotle in the Predicaments gives this reason: things that receive the ratio of triangle or circle are alike triangles and circles, not more or less, because of the indivisibility of their ratio.

• Aside: a garbled remark about birds feeding worms into a nest [unclear in recording].

5. “The grand conclusion”: two ways habits have intensity and remission (“two ways of growing”) #

The point: since habits and dispositions are said by an order to something (Physics VII), intensity and remission in them can be considered two ways, and habits give neither species to the subject nor include indivisibility in their notion, so nothing prevents more or less.

• By themselves: more or less health, or more or less science, “which extends to more or fewer.” Example: at the medieval University of Paris you reportedly needed the first book of Euclid (48 theorems) to study theology; he has read books seven and eight, so his geometry extends to a couple hundred theorems.
• By the subject’s partaking: equal science or health received more in one than another, by aptitude from nature or from custom. Example: he follows Euclid’s theorems but might not manage to demonstrate them at the board — extends to them “in some way” but does not partake fully.
• Illustrations of the second way, “deepening rather than broadening” (student’s phrase, which he accepts): rereading every chapter of the Summa Contra Gentiles and understanding the same things better; De Koninck, teaching the Physics since the 1930s, still seeing something new each time; hearing all Mozart’s symphonies many times and hearing more in them, though knowledge cannot extend to more symphonies than he wrote (there is no 37th — it is Michael Haydn’s with a Mozart introduction; the second and third perhaps by his father).
• Extending vs. consolidating, by analogy: Alexander “no more worlds to conquer,” his Hellenizing and Persian marriages; Hitler overran Poland, France, Czechoslovakia, then made the mistake of Russia instead of digging in and bringing what he had more firmly under control.
• Memorising Shakespeare’s first twenty sonnets on a drive with his brother Mark, since half forgotten; memorising a few psalms and coming to understand them better vs. going on to all the psalms superficially: “two ways of growing.”
• Flag: “later on we’ll talk about… virtues in particular, where they can grow.”

6. Reply to the first objection: “large” carried over from quantity (“the name of magnitudo is derived”) #

The point: as magnitudo is derived from bodily quantities to the understandable perfections of forms, so is the name of growth, whose term is the great.

• Large and small belong first to quantity (a large man, the little box houses vs. the expensive large ones on the drive back from church in Shrewsbury).
• Shakespeare’s “large discourse”: three senses in order of distance from quantity. (a) A discourse covering a large area — close to the quantitative origin. (b) More precisely, reason’s discourse is about the universal, said of many, even infinitely many; “no odd number is an even number,” “no prime is composite” cover infinitely many. In Plato’s Parmenides the young Socrates is stuck in the quantitative picture of a blanket, only part of which covers each thing, whereas the whole of animal is said of dog and of cat — different from quantity, yet a likeness. The wise man’s discourse is largest here, being about being and one, said of everything. (c) Large = great, meaning perfect: large discourse vs. “small talk” about insignificant things; discourse about the soul, human happiness, the universe, and greatest of all about God.
• Einstein: special relativity 1905, general 1915, an explosion of cosmology; he wanted to understand the cosmos as a whole, the greatest thing in the world around us, though ordered to God. Galileo gives reasons too.
• His teaching habit: he “smooths over” the transition by starting with the universal sense, which is closer to quantity.
• Asides: Betelgeuse could hold the whole solar system (sun 93 million miles away) — “wow”; his kids admiring that he could count to 100, then 1,000, then stopping.

7. Reply to the second objection: habit is a perfection without a terminus (“a habit is a certain perfection”) #

The point: a habit is a perfection but not one that is a terminus of its subject giving its specific being, nor does its notion include a limit as the species of number do; hence nothing prevents more or less.

• Coming back over Euclid’s theorems and seeing better how they fit; reading the same matter in the Summa Contra Gentiles, the Summa, the Sentences, the disputed questions, or from a second professor explaining differently — understanding “even better now.”

8. Reply to the third objection: alteration first in the third species of quality (“alteration is first found in the qualities”) #

The point: alteration is first in qualities of the third species (sensible: hot and cold, white and black); in the first species there is alteration per posterius: alteration in hot and cold alters the animal in health and sickness (heat a man too much, cool him too much); alteration in the passions of the sense appetite or the sensitive powers is followed by alteration in sciences and virtues (when his passions cool, “I get a little more virtue”; he imagines the Euclid figures more clearly).

• Closing note: “undergoing” is likewise carried over; understanding is an undergoing, and is “named from under.” “We have to stop here now.”

His words #

• fixed and standing, as it were indivisible: what gives species; species “as numbers” (Metaphysics VIII).
• “no more” (Shakespeare): man is beast plus reason; natures added and subtracted like 1–4.
• not said in order to another: heat, white, substance — absolute forms with a determined ratio; vs. forms ordered to another (motion, health, habits).
• ratio / reason: his rendering of ratio as “reason” or “notion” throughout [ed.: definition, formal account].
• usque ad aliquid: health remains “up to something” though lessened.
• most perfect commensuration: if the name were imposed only on this, health would not admit more or less.
• intention and remission: his phrase for intensio et remissio [ed.: intensification and remission].
• propinqua: quantity as “near” to substance; figure as “termination of quantity.”
• Predicaments: his name for Aristotle’s Categories.
• the Commentator: here used of Simplicius, whom Thomas “seems to accept.”
• extends to more or fewer: growth of a habit “in itself”; vs. partaking of the subject by aptitude “from nature or from custom.”
• deepening rather than broadening: the student’s gloss he accepts for the two ways of growing.
• magnitudo / magnum: greatness carried from bodily quantity to understandable perfection.
• large discourse vs. small talk: three senses of large (area, universal, great/perfect).
• per posterius: alteration in first-species qualities as consequent on sensible alteration.
• undergoing: understanding as an undergoing, “named from under.”

Texts #

Read in class

• Aquinas, Summa Theologiae I-II q.52 a.1, body (from “that by which something obtains a certain species”) and replies to objections 1–3 (inferred locus; he does not name the question).
• Aristotle, Ethics X (quoted through Thomas): health receives more and less.
• Aristotle, Predicaments (Categories): figures do not receive more or less.
• Shakespeare, “beast no more” / “large discourse” (Hamlet, inferred).

Mentioned

• Aristotle, Metaphysics VIII (species as numbers; number has no more or less).
• Aristotle, Physics VII (taking on form or figure is coming to be, not alteration; habits said by order to something).
• Aristotle, Categories: order substance, quantity, quality.
• Simplicius on the Categories (via Thomas); Boethius named once in the same connection.
• Plato: species as numbers; Parmenides (blanket image).
• Euclid, Elements I.1 and the 48 theorems of Book I; Books VII–VIII.
• Declaration of Independence; Orwell, Animal Farm (student).
• Shakespeare’s sonnets; the Psalms; Aquinas, Summa Contra Gentiles, Sentences, disputed questions; Mozart symphonies.

His questions #

• What does man have more than the beast? Reason; take it away and you have a beast, and so down to plant and body — natures like numbers.
• Can there be more or less in regard to what the nature of a thing is? No; then they have different natures.
• Can one of us be stronger than the other? Healthier? Yes to both; better disposed toward the same thing.
• If health were named only from the most perfect commensuration, could it be more or less? No; same for beauty.
• Can you be more a man than I am? Is one dog more a dog? No, as to substance; only as to qualities like courage.
• In what sense are all men created equal? As to substance; not in size, health, strength, beauty, or freedom.
• Is one ten-inch line more ten inches long than another? One circle more circular? No; quantity and figure, near substance, admit no more or less.
• Is five more double of two than four? Five is not double at all; relations like double are indivisible.
• Does De Koninck’s (or his own) knowledge extend to more things, or is it the same things understood better? The same things better — the second way of growing, by partaking.
• What is a large discourse? A discourse covering much, about the universal, or about great things — three senses, in order from quantity.