Summa I, Q.85, Articles 7–8: Why Some Understand Better Than Others, and Whether We Know the Indivisible First

Orientation #

He opens by saying “next time we’ll do seven and eight,” then does them in this class; the recording ends mid-flow with Spinoza’s geometrical method. Verified sources place the class in Summa Theologiae I, q. 85, aa. 7-8. The previous class did a. 6 (whether the intellect can be deceived); the next continues with q. 85 and the point/line question and knowledge of singulars.

The class, in order #

1. Article 7, the objections (“one is not able to understand the same thing better”) #

The point: three reasons why one man cannot understand the same thing better than another.

1. Augustine (Eighty-three Questions): whoever understands a thing other than it is does not understand it; so there is one perfect understanding, nothing more excellent, and no going “to infinity” in understanding one thing.
2. Truth is the equality of understanding and thing (recalled from before: say “what is is not” and you subtract from the truth, “what is not is” and you add; “what is is” equals reality). But equality takes no more and less: of three straight lines or three circles you cannot properly say one is more equal to a third than another. Aside: “we’re all equal, but some are more equal than others” (Animal Farm or Brave New World, he isn’t sure).
3. Understanding is what is most formal in man, what separates him from the animals; a difference of form makes a difference of species; so a man who understood more would not be of the same species. Joke: Thomas is called the Angelic Doctor, “doesn’t seem to be the same species as us.” Sed contra: experience shows some understand more deeply, as the man who leads a conclusion back to first beginnings and first causes understands it more than the one who reduces it only to proximate causes. Example: I know you hit me because you are angry; the man who knows why you are angry understands the hitting more.

2. The answer: “more” on the side of the thing vs. the knower (“of more power in understanding”) #

Distinction: “more” determining the act of understanding on the side of the thing understood vs. on the side of the one understanding.

• On the side of the thing: impossible; to understand it as more or less than it is would be to be deceived, as Augustine argues.
• On the side of the knower: possible, because one has more power in understanding, just as one with a more perfect visual power sees better. Examples of sharper senses (Thomas’s own comparison, “a similia… from the senses”): Mozart said to hear a trumpet faint others could not; a music student who could not name a chord the whole class recognised; his weekly wine tastings with his brother Mark at Saint Mary’s College (he himself right about half the time, Mark never wrong; Mark alone detected a mislabelled wine at Ron McArthur’s dinner); painters walking into a room seeing “a shade of red just like that”; women having more names for colours than men. So some have a better eye, ear, taste—and some a better understanding.

3. Two ways one understanding is better (“as the body is better disposed”) #

(a) On the side of the understanding itself, which is more perfect: as the body is better disposed, so it gains a better soul. He recalls what the soul is: the first act of a natural body composed of tools; body and soul are relative, so a finer body means a finer soul and a finer understanding. Most manifest in things of different species; this is why Aristotle always rejects the Platonic/Pythagorean transmigration of a soul from one body to another (asides: the cat book saying people who eat cats were rats in another life; Shakespeare’s characters alluding to it). Reason: an act or form is received in matter according to the capacity of the matter; so men with a better-disposed body get a soul of greater power in understanding. De Anima II: those of good touch and soft flesh are seen to be well disposed in mind. (b) On the side of the lower powers the understanding needs: those with better imagination, cogitative power and memory are better disposed to understand, since these prepare the images that are abstracted. Examples: his own weak imagination in Euclid’s solid geometry—he built a cardboard model and hung it from the kitchen lamp; contrasted with a high-school classmate (both 99th percentile in a national maths test) who could recite a five-page poem after one reading, and a professor with a photographic memory who read Aristotle in Greek, taught Arabic, Middle English, Italian, German, French, played the organ flawlessly at short notice, and “had to look at the book twice” for one difficult language.

4. Replies to the objections (“to be just as it is”) #

• Ad 1-2 (together): saying one understands better does not mean exceeding the object or being unequal to it. Truth of the understanding consists in understanding the thing to be just as it is; one man understands it as it is better than another. Example: when he tastes the wine and cannot recognise it clearly he is not tasting it other than it is, only less well.
• Ad 3: a difference of form arising only from a different disposition of matter makes diversity in number, not in species; forms are diversified as individuals according to matter. He draws out: separated souls are distinguished only because each soul is made for its body—otherwise there would be no many separated souls, they would each be a kind, like Gabriel and Michael (no two angels of the same kind). So “you have to appreciate your parents preparing your body”: another body would have had a different soul.
  • Student: does this require the body to pre-exist the soul in time, or only as a principle? Answer: the body is naturally generated first, then the soul is infused; exactly when the human soul is infused “we don’t know,” but since the soul is the first act of a body composed of tools you would expect some diversity of organs first.
  • Aristotle’s comparison against transmigration (the story of someone stopping a man beating a dog because he recognises his dead friend’s voice): a soul entering another body would be like one art taking up the tools of another—the carpenter using the tailor’s tools, sewing board to board; the glassblower does not use the hammer. Soul is to this body as art to its tools.
  • Moral aside: however displeased at your body’s defects, it is the only body your soul could have had; be thankful in some sense.

5. Article 8, the objections and sed contra (“knows the indivisible before the divisible”) #

1. Physics I (“Natural Hearing”): we know scientifically from principles and elements; indivisibles are the principles and elements of divisibles; so they are known first.
2. Topics VI: what is put in a definition is known before, since a definition is from things prior and more known. Point is in the definition of line (Euclid: length without breadth, whose extremities are two points); unity is in the definition of number—number is a multitude measured by one (Aristotle, tenth book “after the books of Natural Philosophy”). Aside on the word: meta ta physika, “after the natural books,” so “metaphysics means nothing to us”; call it the tenth book of first philosophy or of wisdom. Euclid too defines number as a multitude composed of ones.
3. Like is known by like; the understanding is simple (De Anima III), so the indivisible, being more like it, is known first. Sed contra (De Anima III): the indivisible is shown as a privation or lack—Euclid’s point is “that which has no part.” But privation is known per posterius: you know knowledge before ignorance, sight before blindness, since blindness is defined as lack of sight. The word “indivisible” itself is negative.

6. The answer begins: our object, and the continuous (“the indivisible or undivided is said in three ways”) #

Object of our understanding in its present state (soul in body): the what-it-is of a material thing, taken from images—“the what it is of something sensed or imagined.” Since what is first and per se known by a power is its object, we must see how each indivisible stands to this. First way: the continuous is “indivisible”—he corrects to undivided, “not the best way of translating it”—undivided in act though divisible in ability.

• Continuous vs. discrete quantity (Categories, chapter on quantity): both have parts, but in the continuous the parts meet at a common limit—left and right halves of a line at a point, the semicircles at the diameter, the halves of a body at a surface; in seven, the three and the four do not meet. Aside: de Broglie’s book On the Discrete and the Continuous in Modern Physics goes back to this chapter.
• Physics definition: the continuous is divisible forever. Seven is not: you reach one. Argument that bisecting a line never ends: (1) you cannot cut something into nothing (Anaxagoras: you cut a thing into what it is made of, and it is not made of nothing); (2) you cannot end in two points, since a line cannot be made of points—points have no length, so if two (or a million, or infinity) touch, the whole of one touches the whole of the other, i.e. they coincide, and have no more length than one. So every cut gives two shorter lines.
• Consequence: Aristotle says thoughts are more like numbers than lines—not divisible forever, and there is a next thought as there is a next number (seven after six): “every mother is a woman, no man is a woman,” and the next thought is “no man is a mother.” But there is no next point: two points cannot touch without coinciding, so a line always lies between them—the geometric postulate that between any two points a straight line can be drawn would be false if points could touch and remain two, like two circles. Likewise no next now in time: “very strange.”

7. The three indivisibles and their order of knowing (“a confused knowledge is before a distinct knowledge”) #

1. The continuous (undivided in act, divisible in potency, indeed forever): known before its division into parts, because confused knowledge precedes distinct, “as has been said.”
2. One in species: the definition of man is indivisible; known before its division into the parts of the definition (we name a thing confusedly before breaking it into its defining parts), and before the understanding composes and divides by affirming and denying—I understand man and animal before “man is an animal,” man and stone before “man is not a stone.” Reason: this twofold indivisible the understanding knows per se as its own object.
3. The altogether indivisible, point and unit (the beginning of number): neither divided in act nor divisible. The unit is simpler than the point, which has position: three points may be collinear or not, three ones have no such difference. The Platonists said a point is a unit with position; hence geometry is less certain than arithmetic, and Euclid sometimes has more than one case in a theorem, which arithmetic never has. This indivisible is known afterwards, through privation of the divisible: Euclid’s first definition, a point is that of which there is no part; or “neither length nor width nor depth.” Body → surface → line → point: body has length, width, depth; surface no depth (one negation); line no width or depth (two); point none (three). More negations as you go to the simpler—a sign the point is known after. Body known before surface, surface before line, line before point. How to force a student who denies points exist (since what exists must have size) “by the truth itself”: take a cube, a finite body; it has an end, the surface; if the surface had depth you would not yet have reached the end, so the surface has length and width, no depth, yet exists as the end. The square too ends; its end has length but no width. The line ends; its end has no length. “Now you got the existence of a point.” The more negation, the longer it takes to reach certitude about its existence.

8. The definition of one, and the Platonists (“such an indivisible has a certain opposition to a bodily thing”) #

The one is defined as the indivisible (Metaphysics X). Reason it is known after: such an indivisible is opposed to a bodily thing, whose what-it-is the understanding takes first and per se. If we understood by partaking of separate indivisibles, the Forms, as the Platonists held, the indivisible would be understood first, since for them what is prior is first partaken. Application, “very important”: in the Summa the first question is on theology’s necessity and character, the second on God’s existence, the third (eight articles) on the simplicity of God; “simple” is not grammatically negative like “indivisible,” but to say God is simple is to say God is not composed—he negates each kind of creaturely composition, then composition in general. The Contra Gentiles does the reverse: composition in general first, then most of the particular kinds.

9. Why Euclid begins with the point; geometry imitated wrongly (“go from the simple to the composed”) #

Euclid begins with the point though it is not first known: in geometry, because we are constructing and restrict ourselves to quantity and shape, going from simple to composed (point before line, angle before figure, triangle before quadrilateral) is appropriate, but it is not characteristic of our mind. Biology textbooks imitate it: cell, tissues, organs, then the whole animal—though the animal is more known to us. “That’s a big mistake of Descartes and Spinoza”: proceeding everywhere as in math—what is meant by “panmathematizing.” Spinoza’s title: Ethica Ordine Geometrico Demonstrata, with axioms and postulates. Recording ends here.

His words #

• equality of the understanding and the thing: his rendering of truth; more and less do not apply to equal [ed.: adaequatio]
• most formal in man: the understanding, what separates man from animals
• Angelic Doctor: Thomas; joked as “not the same species”
• Natural Hearing: [ed.: Physics]
• about places: [ed.: Topics]
• about the soul: [ed.: De Anima]
• the tenth book after the books of natural philosophy / of first philosophy / of wisdom: [ed.: Metaphysics X]
• first act of a natural body composed of tools: the soul [ed.: organic body]
• ability: [ed.: potency]
• what it is: the object of understanding, of something sensed or imagined [ed.: quod quid est]
• undivided: his preferred rendering of indivisibile for the continuous, since it is divisible in ability
• continuous vs. discrete quantity: parts meeting at a common limit vs. not (line/point, circle/diameter, body/surface vs. seven = 3 + 4)
• divisible forever: Physics definition of the continuous
• per posterius: privation known after
• next number / next thought / no next point / no next now
• parts of reason: parts of the definition
• panmathematizing: the error of Descartes and Spinoza

Texts #

Read in class

• Thomas Aquinas, Summa Theologiae I, q. 85, a. 7 (objections, sed contra, respondeo, replies)
• Thomas Aquinas, Summa Theologiae I, q. 85, a. 8 (objections, sed contra, respondeo; no replies read)
• Euclid, Elements, definitions of point, line, number (quoted)
• Spinoza, Ethica Ordine Geometrico Demonstrata (title)

Mentioned

• Augustine, Eighty-three Questions
• Aristotle, Physics I (principles and elements); Physics on the continuous as divisible forever; three ways of “one”
• Aristotle, Topics VI (definition from things prior and more known)
• Aristotle, De Anima II (soft flesh, good touch); De Anima III (understanding simple; indivisible shown as privation; three ways of indivisible)
• Aristotle, Categories, chapter on quantity
• Aristotle, Metaphysics X (number a multitude measured by one; the one as indivisible)
• Thomas Aquinas, Summa Theologiae I, qq. 1-3 (order: theology, existence of God, simplicity of God); Summa Contra Gentiles (reverse order on simplicity)
• Louis de Broglie, On the Discrete and the Continuous in Modern Physics
• Anaxagoras (nothing is cut into nothing)
• Orwell, Animal Farm / Huxley, Brave New World (“more equal”), unsure which
• Shakespeare (allusions to transmigration)

His questions #

• Can one thing be “more equal” to another than a third? No; properly speaking a thing is either equal or not, as truth is either had or not.
• Did Mozart hear better than we do? Yes; a more perfect sense power perceives the same thing better, and likewise a better understanding.
• What is the soul? The first act of a natural body composed of tools; body and soul relative, so a finer body gets a finer soul.
• Does the body have to pre-exist the soul in time? (student) The body is naturally generated first and the soul infused; when, we do not know.
• How does Aristotle argue against a man’s soul passing into a dog? It would be like one art using the tools of another—the carpenter with the tailor’s tools.
• Can a line be made of points? No; points touching must coincide, so infinitely many have no more length than one.
• Is there a next point, or a next now? No; between any two points there is always a line—unlike numbers and thoughts, which have a “next.”
• How do you force a student who denies points to admit they exist? From the finite body: its end is a surface without depth, whose end is a line without width, whose end is a point without length.
• What does it mean to say God is simple? That God is not composed; the Summa negates every kind of creaturely composition in q. 3.
• Which is more known to us, the cell or the whole animal? The whole animal; textbooks starting with the cell imitate geometry wrongly.