Summa I, Q.85 a.1, Replies: Two Kinds of Abstraction, Plato's Error, and Common vs. Individual Matter

Orientation #

He picks up at the objections of q. 85 a. 1, saying “we talked about before” of the central question whether the mind is false in understanding singulars universally, and “as we were doing before” of sense examples (prev. lecture); he ends: “we better say the next two articles for next time.” Verified sources place the whole class in q. 85 a. 1 with a handout (“The First Statement and King of Statements”, p. 3) and DHB Vol I p. 103 read alongside. The previous class concluded q. 84 a. 8 and opened q. 85 a. 1 on abstraction from phantasms; the next takes up whether the species is what is understood, and universals before particulars.

The class, in order #

1. The first objection: is the mind false in understanding singulars universally? (“the mind false in understanding singulars universally”) #

The objection (read): whatever understands a thing other than it is is false; forms of material things are not abstracted from the particulars whose likenesses are the images; so abstracting forms from images yields falsity. He says this touches “that central question of philosophy that we talked about before.”

• His setup: I understand you, a singular, to be a man, something universal. In doing so I do not grasp what is unique to you (the other student is a man in the same sense), so my knowledge is incomplete — but is it false? No. “The mistake would come if I said that the universality of man belongs to you.”

2. Reply to the first: abstracting in two ways (“to abstract happens in two ways”) #

Thomas’s reply (read): abstraction (a) by way of composition and division, when we understand something not to be in another or separated from it; (b) by way of simple and absolute consideration, when we understand one thing considering nothing about another.

• He connects (a) to statement: Thomas’s Peri Hermeneias (Aristotle’s “second act”), putting together (“man is an animal”) or dividing (“man is not a stone”).
• Argument: 1. To abstract by the understanding, in way (a), things not abstracted in reality is not without falsity — e.g. “man is not an animal.” 2. To abstract in way (b) is without falsity — understanding animal while understanding nothing about man. 3. Same is true of secundum rem undivided things.
• Perfect number: Augustine and Thomas explain the six days by six being the first perfect number; his students don’t know what a perfect number is but do know what a number is — not false; false only if one said a perfect number is not a number.
• Thomas’s own example (read): to say colour is not in the coloured body is false; to consider colour and its properties, considering nothing about the apple, is without falsity, “for apple is not of the definition of colour.”
• Applied: what belongs to the definition of the species (stone, man, horse) can be considered without the individuating principles, “and this is to abstract the universal from the particular,” the understandable form from the images. “This is not to say that it is without them, but to understand it without them.”
• Plato’s mistake: he says what a man, a dog, a cat is exists by itself outside the mind, separated from this man and the next; Aristotle says it exists in separation only in the mind — hence in the De Anima “the soul is the place of forms,” not the world.
• The “otherwise” (read): if “other than it is” refers to the thing understood, the understanding is false (as if it abstracted stone from matter so as to understand it not to be in matter — Plato); if “otherwise” is on the part of the one understanding, no falsity — the mode of understanding differs from the mode of the thing’s existing.
• Student’s question, in his words: “Does truth require that the way we know be the way things are?” Plato answers yes, Aristotle no. Reason (read): the understood is in the one understanding in an immaterial way, not materially as in the thing. Student: so the form of the individual object really exists in our mind, in a different way? — Yes, truly; what you all have in common can be understood without your differences, though outside my mind it does not exist without them.
• His simpler sense example: sugar is white and sweet together; sight knows the whiteness without the sweetness, taste the sweetness without the whiteness (a blind man’s knowledge of sugar) — incomplete, not false; false only if I say “this white thing is not sweet.”
• Hitler, Saddam Hussein, John Paul II: “he was a man” is not all that can be said, but not false; I can know what they have in common, though man does not exist apart from what is unique to each; to say it does is “to be with Plato there in my world of forms.”
• Why people answer that question wrongly: they are not thinking of this distinction. Truth means saying what is in things is in things and what is not is not — that is statement; this other business is understanding one without that in which it is.
• Cube: the shape can be understood without ice, wood, plastic, so there is a science of the cube into which nothing sensible enters; but to say a non-material cube exists is Plato’s mathematical world. Plato’s “three-decker universe”: sensible world, mathematical world, forms. Student: how does the mathematical world differ from the forms? — In the mathematical world there is still individuation, many of a kind; among forms only one “what a man is.” Plato gives a hint, though: if there were immaterial things each would be what it is and there could not be two of a kind — an introduction to the angels, and why there can be only one God.

3. Digression: how Marx proceeded (“See the way Marx proceeded”) #

Aside on a modern error, chained: 1. In experimental science we know by making; 2. Marx (as moderns do) says this is the only way of knowing; 3. so we know only what we make; 4. we are the beginning and end of all we make, so of all we know — “we are the alpha and omega.”

• Dialectical materialism: matter is the beginning of everything (an old opinion), and everything develops out of matter by the clash of opposites — Hegel’s dialectical method taken over; Marx thought Hegel stood on his head (thought first, then matter). In the mind there is the same knowledge of opposites; Marx transposed into matter what is in the mind, so opposites struggle in matter — partly in the idea of evolution too; Marx dedicated Das Kapital (he thinks) to Darwin, and Darwin’s copy survives.
• Applied to society: take what is most material (technology, mode of production) and explain everything else from it.
• Quebec joke: hesitation before jumping into cold water — “this is how speculative philosophy began” — Marx’s account of Thales (“water is the beginning of all things”): the speculative man as one who won’t get his hands dirty and daydreams.

4. Reply to the second: matter twofold, and the three abstractions (“matter is what twofold”) #

The difficulty: material things are defined by matter, yet here we abstract from matter.

• Thomas (read): some thought the species was form only, matter no part of it, so matter would not enter definitions of natural things. Rather: common matter (flesh and bone) vs. designated/individual matter (these fleshes and these bones “that you can feel yourself”). The understanding abstracts the species from individual sensible matter, not from common — leaves out his, your and John Paul II’s flesh, blood and bones but keeps flesh and bone in general; cites Metaphysics VII (“seventh book of wisdom”). “The species of man cannot be abstracted from flesh and bones in general.”
• Mathematical species (circle, sphere, cube) are abstracted not only from individual but from common sensible matter, but not from common intelligible matter (hyle noete), only from individual intelligible matter. Student asks the distinction between common sensible and common intelligible matter: intelligible matter, “more clearly stated as imaginable matter,” is extension, “part outside of part” — any imagined triangle or sphere is extended.
• Locke and Berkeley (mentioned before): Locke’s general idea of triangle — are the three sides equal or unequal? He says both and neither. Any imagined triangle is individual, its sides equal or unequal, never both or neither; the understood triangle abstracts from equal/unequal. Proper answer: in the definition the three lines are able to be equal or unequal but are actually neither. Locke confuses the universal the reason understands with imagined triangles; Berkeley concludes there are no universal ideas.
• Geometry as experience of the universal: the interior angles equal two right angles, shown by drawing through one vertex a line parallel to the opposite side and using the parallel theorem (alternate angles equal); the demonstration holds of any triangle, whatever you imagined, since it uses only what is common — “if you’ve done geometry you have an experience of your mind as understanding the universal.” Imagination is still bodily, part outside of part.
• Plato assimilates natural species to mathematical, and sometimes geometrical to arithmetical: point one, line two, surface three, body four — adds up to ten.
• Back to the paragraph (read): sensible matter is bodily matter as subject to sensible qualities (hot, cold, hard, soft); understandable matter is substance as subject to quantity. Quantity is in substance before sensible qualities, so numbers, dimensions, figures (terminations of quantity) can be considered without sensible qualities, but not without substance subject to quantity (that would be to abstract from common intelligible matter); they can be considered without this or that substance (abstracting from individual intelligible matter). Some things — being, one, ability, act — are abstracted even from common intelligible matter and can be without any matter, as in the immaterial substances: these are considered in wisdom.
• Plato, not considering the two ways of abstraction, laid down that all things abstracted by the understanding are abstracted in reality — mathematicals and universals alike.

5. Objection and reply three: images act on the intellect as colours on sight? (“as colors to sight”) #

Objection (De Anima III): images are to the understanding as colours to sight; sight does not abstract a species from colours, the colours are impressed on it; so neither does understanding abstract.

• Reply (read): colours have the same way of existing, in individual bodily matter, as the power of sight, so they impress their likeness; images, likenesses of individuals existing in bodily organs, do not have the intellect’s way of existing, so cannot impress themselves on the possible intellect; by the power of the agent intellect turning upon the phantasms a likeness results in the possible intellect representing only the nature of the species — this is called abstraction. Not that the same form in number passes over as a body transfers to another body: “you’re making in a sense a likeness… like it only in a universal way.”
• Order of our knowledge: sensing, memory, many memories collected into experience, then the agent intellect separates out what many dogs have in common — the beginning of understanding (mother pointing out the dog). Boethius: the thing is singular when sensed or remembered, universal when understood.
• Student: Helen Keller’s breakthrough with water poured on her hand — grasping that opened her world.
• Defining a Shakespearean sonnet on one’s own: read the individual sonnets, compare, notice same length, 14 lines, meter, until: a likeness of thought and feeling in 14 lines of iambic pentameter, three quatrains with alternate rhyme, completed by a couplet — except a couple where Shakespeare plays on the Italian form (octet answered by sextet), grouping four with two.
• Aside: 154 sonnets in 14 lines — the discipline forces better expression, like Mozart’s respect for the musical forms (minuet where Beethoven goes to the scherzo).

6. Reply to the fourth: images illuminated by the agent intellect (“illuminated by the acting upon understanding”) #

Aristotle compares the agent intellect to light in the eyes, but not similar in every way. Reply (read): images are illuminated, since as the sensitive part is made more powerful by conjunction with the intellectual, so images by the agent intellect are made able to have understandable intentions abstracted from them; and the agent intellect abstracts in that through its power we consider the natures of species without individual conditions, whose likenesses inform the possible intellect.

• “So what’s our little prayer? Strengthen the light of my mind, order illumined my images.”

7. Reply to the fifth: still turning to the images (“except by what turning to the images”) #

Reply (read): the understanding both abstracts forms from the images, as it considers natures in general (clearest in geometry: the demonstration says nothing about equal or unequal sides), and yet understands them in the images, since it cannot understand even what it abstracts except by turning to the images.

• Proportion: to see the colour of your clothes I must turn to your clothes, though the seeing is in my eye, not the garment; remove the clothing and my seeing is affected. Likewise the “what it is” is of something sensed or imagined, so I must turn to the image; if the object existed out there in separation we wouldn’t have to. So affect the imagination and thinking is affected.
• Student: “Very subtle.” He: the next two articles next time. Closing aside: his other students now meet Thursday nights.

His words #

• “images” — phantasms [ed.: phantasmata].
• “understanding” — intellect; “acting upon understanding” / “agent intellect” — [ed.: intellectus agens]; “possible understanding” — possible intellect.
• “composition and division” — abstracting by statement, putting together or separating (the “second act”).
• “simple and absolute consideration” — understanding one thing considering nothing about another.
• “secundum rem” — in the thing, in reality.
• “perfect number” — six, the first; used by Augustine and Thomas on the six days.
• “the soul is the place of forms” — De Anima, against Plato’s separated forms.
• “three-decker universe” — Plato: sensible world, mathematical world, forms.
• “common matter” vs. “designated” / “individual matter” — flesh and bone vs. these fleshes and these bones [ed.: materia signata].
• “intelligible matter”, “hyle noete”, “imaginable matter” — extension, part outside of part; substance as subject to quantity.
• “seventh book of wisdom” — Metaphysics VII.
• “wisdom” — the science of being, one, ability, act [ed.: metaphysics].
• “ability” — [ed.: potency].
• “sensing, memory, experience” — the order in which knowledge develops before understanding.
• “singular when sensed… universal when you begin to understand” — Boethius, as always quoted.

Texts #

Read in class

• Thomas Aquinas, Summa Theologiae I, q. 85, a. 1, objections 1 and 3 and replies to objections 1-5 (verified source).
• handout “The First Statement and King of Statements (Commentary on First Statement)”, p. 3 (verified source; not named in the transcript).

Mentioned

• Thomas, commentary on the Peri Hermeneias (Aristotle’s “second act”, statement).
• Aristotle, De Anima (“the soul is the place of forms”; III, cited in obj. 3).
• Aristotle, Metaphysics VII (“seventh book of wisdom”).
• Augustine and Thomas on the six days and the perfect number six.
• Boethius (singular when sensed, universal when understood).
• Marx, Das Kapital (dedication to Darwin); Hegel; Darwin.
• Locke and Berkeley on the general idea of triangle.
• Shakespeare’s sonnets (154); Mozart, Beethoven.
• DHB Vol I, The First Philosophers, p. 103 (verified source; Thales, “water is the beginning of all things”).

His questions #

• Am I false in understanding you, a singular, to be a man, something universal? No — incomplete, not false; false only if I said the universality of man belongs to you.
• If I understand animal without understanding man, is that false? No; that is the second kind of separation; “man is not an animal” would be false.
• Are my students false in knowing what a number is without knowing what a perfect number is? No; false only if they said a perfect number is not a number.
• Does truth require that the way we know be the way things are? Plato yes, Aristotle no: the understood is in the knower immaterially, not as in the thing.
• Is the sense of sight mistaken in knowing the whiteness of sugar without the sweetness? No; false only if it said this white thing is not sweet.
• How is Plato’s mathematical world different from the world of forms? In the mathematical world there is still individuation, many of a kind; of the form only one.
• What is the distinction between common sensible and common intelligible matter? Intelligible (imaginable) matter is extension, part outside of part; sensible matter is subject to hot, cold, hard, soft.
• Are the three lines of the understood triangle equal or unequal? Able to be either, actually neither; an imagined triangle must be one or the other.
• How would someone define a Shakespearean sonnet on his own? Read and compare the individual sonnets until what is common appears: 14 lines, three quatrains and a couplet.
• Why must we still turn to the images to understand what we abstract? Because the “what it is” is of something sensed or imagined, as seeing your clothes’ colour requires turning to your clothes.