Aquinas, Summa I q.85 a.4-5: Knowing Many Things at Once, Discrete vs. Continuous Time, and Why We Must Compose and Divide

Orientation #

He refers back to the handout text on before and after “from the categories” that he has already given the class, and to “the previous article” (a. 3) inside a. 5’s first objection; at the end of a. 4 ad 3 he says he will take up the case of a statement “in the next article”. Verified sources place this class in ST I q. 85 a. 4 and the beginning of a. 5. The previous class treated q. 85 a. 3 (universals before particulars, more known to us vs. by nature); the next continues a. 5’s replies and a. 6 on whether the intellect can be deceived.

The class, in order #

1. Prayer and an opening story (“trial by fire”) #

Aside before the text: an incident in the life of St. Dominic — a public debate with heretics the townspeople could not judge, so both parties’ books were thrown into the fire; the heretics’ burned, Dominic’s was untouched, and some singed wood is said to be kept in a church. A student mentions a donkey story; he is not sure it is Dominic’s.

2. Article 4, the objections (“we are able to understand many things together”) #

He reads the four objections that we understand many things at once, supplying the missing words as he goes.

1. Understanding is above time, as above the body; before and after belong to time (time = the number of the before and after in motion — three hours numbers the before and after of the sun’s motion around the earth); so the understanding does not know diverse things one after another but together.
2. Diverse forms not opposed can be together in the same thing — in the apple, the odor and the color at the same time. Understandable forms are not opposed; so nothing prevents one understanding being in act under diverse understandable forms.
3. The understanding at once understands some whole (a man, a house), and a whole contains many parts; so it knows many together.
4. One cannot know the difference of one thing to another unless both are grasped together (from the book about the soul), and the same for any comparison. His illustrations: I cannot know I am taller or shorter than you without knowing you and me at the same time; to know a square has more sides than a triangle I must think square and triangle together. Sed contra: the book of the Topics (“Aristotle’s book on dialectic”) says one understands one thing only, but scire — “kind of habitual knowledge” — can be of many.

3. The body: many by way of one, not many as many (“by way of being one those many”) #

The point: the understanding can understand many per modum unius but not per modum multorum.

• Dog and cat: when I understand the difference, or say “a dog is not a cat”, I think both together — but in one comparison, one negative statement. If I think simply what a dog is and simply what a cat is, “as many as many”, I cannot think both at the exact same moment.
• Argument, as he reads it: (1) the mode of any action follows the form which is the source of the action; (2) so whatever the understanding can know under one form it can know together — hence God sees all things at once, because he sees all by one thing, his own essence; (3) what it knows through diverse forms it cannot know together, because (4) the same subject cannot be perfected at the same time by many forms of one kind and diverse species.
• Illustrations of (4): the same body in the same part cannot be colored by diverse colors or shaped by diverse figures. Clay cannot be a sphere and a cube at once, though it can be a cube and brown at once; it cannot be brown and yellow in the same part at the same time. So the understandable form is to the mind “a little bit like the shape is to the clay or the wax”.
• Student question: does this have to do with truth as the mind’s identity with the thing? Answer: no, the reason is the one Thomas gave — no two forms of the same kind at once. The apple objection fails because color and odor are of different kinds; two colors in the same part are not possible.

4. All understandable forms are of one genus; the ladder from God to us (“as you go down from God”) #

Thomas adds: all understandable forms are of one genus, being perfections of the one power of understanding, although the things they are forms of are of diverse genera; so the same understanding cannot be perfected at once by diverse understandable forms and understand diverse things in act.

• The descent: God understands all things by understanding himself; angels understand themselves but not everything thereby, so need added thoughts; lower angels need more thoughts; we, at the bottom, need almost a separate thought for everything we want to know distinctly. “We’re always trying to be a little bit more like the angels and God” in knowing many at once, and to some extent can.
• Example from calculus: inscribe a square in a circle, bisect the chords, draw from the center, keep bisecting — the polygon approaches the circle as a limit never reached. In knowing the circle as the limit of polygons you know circle and polygon “somehow at the same time”, and see their distinction (no polygon ever equals the circle) — the mind “striving to be more like its guardian angel”.

5. Reply 1: the understanding is above bodily time, but there is another before and after (“the understanding is above time”) #

Reply as read: the understanding is above the time that is the number of the motion of bodily things; but the plurality of understandable forms causes a variation of operations in which one is before another, and this change Augustine calls time when he says (eighth book upon Genesis to the letter) that God moves the spiritual creature — even the angels — through time.

• “What is time?” vs. “What time is it?”: “two twenty-three” is no time; three minutes, days, years is an amount of time — a number of the before and after in the most continuous and regular motion known, the sun’s around the earth; the clock only imitates that motion (hand on six before seven, seven before eight).
• The mind is not continuous, so its thinking is not continuous, but there can be a before and after in thinking: one thing then another. Shakespeare’s definition of reason as the ability “for large discourse, looking before and after” — discourse is knowing one thing after another, eventually one thing from another. So a “discrete time” is spoken of for the angels; “time” there is equivocal with our time, the number of a continuous locomotion, which has nothing to do with angels.
• Aside on purgatory: the separated soul is “not really in this time”; yet the delay in seeing God must be very painful, the body no longer distracting from him — a fitting purgation for dilly-dallying on the way (which is what venial sin is: not leaving the road to God but dilly-dallying on it).
• He ties this to the handout text on before and after: the first sense of before is in time (bodily); a third sense is before in the discourse of reason. A student asks whether the angels’ before is the third sense; “it’d be like that, yeah, rather than the first one”.

6. Digression: continuous vs. discrete, and why thinking is like number (“there is a next thought”) #

The point: reasoning is discrete, not continuous, which is a sign the understanding is not a body.

• Continuous: between any two points infinitely many stopping places; two points cannot touch (having no parts, no edge distinct from interior, touching would be coinciding, leaving one point); so between two points there is always a line, always divisible — no next point. Likewise no next parallel line on a surface (two lines cannot touch without coinciding; between them is always a surface); no next longer or shorter line.
• Discrete: from “every mother is a woman” and “no man is a woman” the next statement is “no man is a mother” — there is a next thought, nothing between the premises and the conclusion. In defining, from quadrilateral to square you add just two things, equilateral and right-angled, and you are there. Numbers: after six comes seven, a next bigger and a next smaller.
• Aristotle’s order of senses of before: first in time, to which before in anything continuous is reduced; second in being (one before two); third in the discourse of reason — the second and third are discrete. Between the proemium and the tractatus of a work “there’s nothing”; the most rigorous case is the syllogism (“speech in which some statements laid down, another follows necessarily because of those laid down”).
• So Aristotle in the first book about the soul says thoughts are like numbers. We say “a line of thought” because the continuous is more manifest to sense than number, which is more abstract — why Euclid begins with geometry before arithmetic. The soul is touched by continuous time only insofar as its images are in time; thinking itself, not in a body, is above it, with only the discrete before and after that Augustine also called time by likeness. “Before and after” is equivocal by reason (Categories).
• Aside: in showing the Athanasian Creed’s “no before and after in God”, Thomas eliminates all Aristotle’s senses of before — the Father is not before the Son in time (even discrete time), nor in being better, nor in knowledge; the Son is from the Father but not after him. “I’ll leave that to the study of Trinity someday.”

7. Replies 2-4: same-kind forms, parts in a whole, comparison (“under a certain confusion”) #

• Reply 2: not only opposite forms but any forms of the same kind cannot be together in the same subject, as the colors and shapes show. Sphere and cube are not opposites like black and white, but both are shapes; the clay can be molded into one and then the other, not both at once — so the mind cannot be fully informed in act by two understandable forms.
• Reply 3: parts can be understood in two ways: (a) somewhat confusedly, insofar as they are in the whole, known through the one form of the whole, and so together; (b) distinctly, each through its own form, and so not at the same time. Painting: standing back and taking in the whole vs. focusing on how he did this bit, which is “a different seeing”. Anatomist: seeing the human being with arms and legs vs. studying the arm one day and the foot another, separate knowledges. Thomas does not altogether deny the objection; he distinguishes. The case of understanding a statement is deferred to the next article.
• Reply 4: knowing a difference or comparison, the understanding knows both under the one thought of the comparison or difference, as parts under the notion of the whole — “this is what the big thing is”. Universal: I know dog, cat, horse confusedly by knowing animal; to know each distinctly is a separate thought each. This “shows the lowliness of our mind”: it must go from one to the other, “large discourse”.
• Aside: his Mozart collection, some six hundred pieces — he cannot hear them all at once, nor the first movement with the second, so he goes through in rotation (symphonies, then violin concertos, then sonatas), and gets “kind of panicky”; “it’s like with the mind”.

8. Article 5, the objections and sed contra (“by putting together and dividing”) #

The question: does our understanding understand by composing and dividing? He identifies this with the second act of reason in Thomas’s proemium to logic: putting together in an affirmative statement (man is an animal), separating in a negative (man is not a stone).

1. Composition and division are only of many things (nothing is put together with or divided from itself); but per the previous article the understanding cannot know many at once. His anticipation: Thomas will say they have been made one, forming one statement.
2. Every composition or division has present, past or future added (reflected in our verbs); but the understanding abstracts from time as from other particular conditions — is man’s being a man past, present or future? (Even the definition of time is timeless.)
3. The understanding understands by being made like things; but composition and division is nothing in things — only the thing signified by predicate and by subject, which are one and the same if the composition is true (man truly is that which an animal is). Sed contra: vocal sounds signify the conceptiones of the understanding (Peri Hermeneias I), and in vocal sounds there is composition and division, as affirmative and negative propositions show. Aside: the word conceptio matters because the thought of God is also said to be born or generated, in likeness to our conception.

9. The body: why the human mind must compose, divide and reason (“goes forth from potency to act”) #

Argument as read and glossed:

1. The human understanding goes from potency (ability) to act, so it is like generated things, which do not have their perfection at once but acquire it by degrees.
2. So in its first grasping of a thing it does not get perfect knowledge: it first grasps something about the thing, e.g. the what-it-is — “quiddity”, a “terrible word they make up in Latin” from the word for what — which is the first and proper object of the understanding (De Anima III makes it more precise: the what-it-is of something sensed or imagined, e.g. what a man, dog, triangle, square is). This is the first act of reason, “simple grasping”.
3. Then it understands the properties, accidents and relations of the thing; so it must put together or divide one thing grasped with another, and then proceed from one composition or division to another, which is to reason. Example: understanding what two is does not show at once that two is half of four, a third of six, a fourth of eight.

• Three acts of reason, as in the proemium to logic, which logic directs. Reasoning is like calculating: two numbers give a third by adding, subtracting, etc.; two statements give a third. “A little bit like sexual reproduction”: two of a kind give a third of the same kind — two dogs a dog not a cat, two numbers a number not a statement, two statements a statement not a number.

4. The angelic and divine understanding (Thomas may speak of them here, being in theology; Aristotle in De Anima has not yet reached angels or God) are like incorruptible things which have their whole perfection at once; so in knowing the what-it-is they know at once whatever we know by composing, dividing and reasoning.

• Aside: this is why the angels could fall immediately with no chance of recovery — a mature choice made at once; a child hardly chooses, having no deliberation. Shakespeare: “since my dear soul was mistress of her choice and could of men distinguish” — it takes a while before the soul is mistress of her choice.
• Geometry: knowing what a triangle is, we must reason that its angles equal two right angles (Euclid I.32): a line through the vertex parallel to the base, alternate angles equal — itself proven in I.27 — resting on the marvelous I.16, that an exterior angle is greater than either interior opposite. The angel sees it on understanding what a triangle is.
• Asides: his old teacher Kasurik (name as heard) described your angel watching you make a decision like watching an inchworm find its way. Another teacher (name unclear in recording) said that meeting your guardian angel after death you will say “This is God!” and he will reply he is not, God is even more marvelous, but he’ll take the admiration.

10. Reply 2: turning back to images adds time (“turning back again towards images”) #

Reply as read: the understanding abstracts from images, yet does not understand in act except by turning back to images; from that side it adds time to its composing and dividing. Even now, thinking what a triangle is, I imagine a triangle, and images are in time.

• Distinction: in the first act of reason one is more separated from time than in the second. “What a man is” is neither past, present nor future; “Socrates walks / walked / will walk” has a tense. In the Peri Hermeneias, noun and verb are defined first and the verb always signifies with time.
• Digression on names: Latin nomen and Greek onoma mean both name and noun. Nomen broadly is a vocal sound with no parts signifying by themselves, so both noun and verb are nomina; when distinguished, the noun keeps nomen and the verb gets a new name (verbum; Greek rhema), so onoma becomes equivocal — Ammonius (teacher of Boethius, “teacher of Thomas in a sense”, in Alexandria) constantly notes which sense he is using. English has separate words: name, noun, verb. Why does the verb get the new name? Because it adds time, something beyond the common meaning of name. His standard example: five fingers, or four fingers and a thumb — the thumb stands out (holding a glass) and gets the new name. Likewise “man” is said of man and woman; Latin and Greek have different words for the human being and the male, English does not, so “man” is equivocal by reason, and attempts to change the language miss this. A student offers an etymology that “woman” adds something — a veil over the face — so gets the new name; joking exchange (the professors should wear veils; the Mohammedans would like the explanation).
• Close: so the human understanding knows by putting together and dividing, as it knows by reasoning. In the Summa Contra Gentiles (and perhaps the Summa Theologiae) there is a chapter showing God does not understand ratiocinando; God and the angels know composition, division and reasoning, but by an understanding of a simple what-it-is — “see it all at once”. Geometry again: understanding what a triangle is does not show the angle sum; you put things together and reason, “and then oh yeah”.

His words #

• “number of the before and after in motion”: his definition of time (Physics IV).
• “understandable forms” [ed.: intelligible species].
• per modum unius / “by way of being one” vs. “by way of being many”: Thomas’s distinction in a. 4.
• scire, “kind of habitual knowledge”: the knowing of many in the Topics sed contra.
• “ability” [ed.: potency].
• “large discourse, looking before and after”: Shakespeare’s definition of reason, used for discursive knowing.
• “discrete time”: the before and after of angelic operations; equivocal with bodily time.
• “equivocal by reason”: said of “before and after”, onoma, “man”.
• “putting together and dividing” [ed.: composition and division], the second act of reason.
• “the what it is”, “whatness”, “quiddity”: the first and proper object of the understanding; “simple grasping” [ed.: simple apprehension].
• conceptio: the thought signified by vocal sound; linked to the generation of God’s Word.
• nomen / onoma / rhema / verbum: name-noun-verb, with onoma equivocal.
• ratiocinando: by reasoning, which God does not do.

Texts #

Read in class

• Thomas Aquinas, Summa Theologiae I, q. 85, a. 4, whole article.
• Thomas Aquinas, Summa Theologiae I, q. 85, a. 5, objections, sed contra, body, reply 2.
• Handout “Note for Book One of Natural Hearing, Reading I”, p. 9: Aristotle’s senses of before and after (Categories), commented on. Mentioned
• Aristotle, Physics IV (definition of time).
• Aristotle, Topics (one understands one thing only).
• Aristotle, De Anima I (thoughts like numbers), III (the what-it-is as proper object).
• Aristotle, Peri Hermeneias I (vocal sounds signify conceptions; noun and verb, verb signifies with time).
• Augustine, De Genesi ad litteram VIII (God moves the spiritual creature through time).
• Thomas Aquinas, proemium to logic (three acts of reason) (inferred: proemium to the Posterior Analytics commentary).
• Euclid, Elements I, propositions 16, 27, 32.
• Thomas Aquinas, Summa Contra Gentiles, chapter on God not understanding by reasoning (locus not stated).
• Thomas on the Athanasian Creed, “no before and after in God” (locus not stated).
• Ammonius, commentary on the Peri Hermeneias.
• Shakespeare, Hamlet (“large discourse”; “mistress of her choice”).
• DHB Vol III, The School of Aristotle, p. 316 (verified source; not named in transcript).

His questions #

• Time is defined as the number of the what? Before and after in motion.
• Can a piece of clay be a sphere and a cube at the same time? A cube and brown? Not sphere and cube; yes, cube and brown — two forms of the same kind cannot be together.
• Is the reason that the mind must be identical with reality (student)? No; the reason is Thomas’s: no two forms of the same kind at once, as with the apple’s color and odor vs. two colors.
• Between two points, how many points could you stop at? Can two points touch? Is there a next point? Infinite; no (they would coincide); no next point.
• Every mother is a woman, no man is a woman — what is the next statement? No man is a mother; there is a next thought, so reasoning is discrete.
• Is the angels’ before the third sense of before? It’d be like that, rather than the first.
• When you understand what two is, do you see at once that it is half of four? No; you must put things together with two.
• Why does the verb get a new name while the noun keeps nomen? Because the verb adds time, as the thumb stands out among the fingers.
• When you understand what a triangle is, do you see that its angles equal two right angles? No; you compose and reason (Euclid I.32 via 27 and 16); the angel sees it at once.