Part 1: Put Together, Whole and Part: Number, Matter and Form, Composed and Universal Wholes

Orientation #

He opens mid-answer to a question a student (“she”) asked about matter and form, refers back to “our study of points and the continuous” and to “when we talked about the unity of body and soul”, and says he was reading the Sophist “just this morning” about the opinion that imagining is opinion with sensation (prev. lecture topic). The previous class treated imagination in De Anima III.3 and the next returns to whole and part and the interior senses.

The class, in order #

1. Three senses of “put together” (“original meaning of the word put together”) #

Point: “composed” is said in several ways, and its first meaning is tied to the continuous.

• Rubber ball put together from rubber and a shape: matter and form, in a sense.
• The original meaning of “put together” is tied to the continuous.
• Logic gives another: the definition puts together genus and differences (square = equilateral right-angled quadrilateral: genus quadrilateral, plus differences).
• Aside: the definition of syllogism contains positio (“some statements laid down / placed, another follows necessarily”); Thomas’s commentary on St. Paul’s Epistles happens to explain the word “placed”, and he borrows it.
• Geometry: parallelogram divided into two triangles, or two triangles put together make a parallelogram; circle into two semicircles. But the semicircles and triangles can exist by themselves; matter and form cannot. That was what she asked about.

2. Is 3 + 4 = 7 like continuous parts or like matter and form? (“what does put together mean here”) #

Point: putting numbers together is more like matter and form than like joining continuous things.

1. Two contains two ones, as a circle contains two semicircles.
2. Semicircles are put together by their boundaries becoming one boundary; number is not continuous, so ones have no boundary or limit (as in the earlier study of points: two points put together coincide into one point; two semicircles remain two yet also one circle).
3. So if the only way of two becoming one were the continuous way, the two ones would never be one two but always two ones.
4. Aside: a comic’s McMaster lectures (name unclear in recording) on numbers, that “you can’t make one out of two”; computers and calculating machines treat two as two ones, “just so many units”.
5. But regard one as able to be two, made actually two by the addition of one: then the added one is as act to ability, form to matter. Conclusion: “this is important now to see.”

3. Definitions are like numbers (“assimilates definitions to numbers”) #

Point: Plato and Aristotle (Metaphysics VIII) compare natures to numbers, and Shakespeare reasons the same way.

• Aside: he looked at the Sophist this morning; Plato there says a true or false logos is a noun and a verb, the basic thing of Aristotle’s Peri Hermeneias; “you realize how much Aristotle learned from Plato” (his teacher for twenty years).
• Adding or subtracting one gives a different number; so body + life = plant, + sensation = animal, + reason = man; take away reason from man and he is an animal; animal without sensation a plant, “no more”; plant without life a body. Body one, plant two, animal three, man four.
• Shakespeare: “What is a man, if his chief good and market of his time be but to sleep and feed? A beast, no more.” Restated: “What is a four if it be half of six? A three, no more.” Reasoning by proportion: half of eight is to four as half of six is to three; the chief good of man is to man as the chief good of the beast is to the beast; having or using reason is either what man is or a property of man. If man has no good greater than the beast (sleep and feed, “like a mopping back home”), he is no more than a beast.

4. Number as one thing, and the strict sense of “able” (“one step away from it”) #

Point: seen as ability actualized, number has more unity than a mere collection, but only if ability is taken strictly.

• Rubber is able to be a ball, but you must add a form; likewise the one added actualizes what one is able to be; two is able to be three, three to be four, actually four through receiving the next one. So number is one thing, a real species of quantity (how many), not a bringing together of things that cannot be put together for want of common boundaries or surfaces.
• Brother Mark: if number were just a bunch of ones there would be no significance in three, seven, ten, twelve, a hundred. Counting shows the order: ones not all on the same level.
• He notes he is reversing Plato and Aristotle’s analogy (natures like numbers), and that he is not saying number has as much unity as matter and form.
• Aristotle on ability in the strict sense: you are able to be something when one step away. Stairs climbed one at a time: not able to be on the second step until on the first. Reasoning: A obvious, A proves B, B proves C, C proves D; strictly you are not able to know C until you know B. A student who never studied geometry is not able, strictly, to know solid geometry; hence plane geometry as prerequisite. So two is able to be three, not (strictly) four; that added one is like the form making it actually three.

5. Student objection: is the added triangle a form? (“triangle is able to be the parallelogram”) #

Objection: a triangle is able to be the parallelogram by addition of the other triangle, so the other triangle would be like form too. Reply: you could say it that way, but triangles come together in the first sense, extremities touching or becoming one; numbers have nothing like that, and neither do matter and form. The point of comparison is precisely that.

• Digression, unity of body and soul: no problem for Aristotle as it is for others who take body and soul as two complete substances, “like a man and his car”: then transmigration of souls follows, since nothing stops the man leaving the car. If soul is to body as form to matter, the unity of man is understood and transmigration does not make sense: this soul is the act of this body, this kind of soul of this kind of body. Plato’s position: “the sailor in the boat”; moderns: “the ghost in the machine”. Contradicted by experience: the one feeling pain in his foot is the one thinking what to do about it.
• So man is “put together” from body and soul, yet the first meaning of “put together” goes back to the continuous: “this seems to be very fundamental in our thinking.”

6. “Not composed” vs. “no parts”: the continuous and the separable (“God is not composed in any way”) #

Point: Thomas’s “God is not composed in any way” is not exactly the same as “God has no parts”, but very much alike, because the first meaning of both is quantitative and continuous.

• Aristotle, Metaphysics V, defining the continuous: divisible into things each of which can be a “this something”, an individual substance. Chalk broken in half: each half by itself; but chalk and its shape cannot be put one here and one there. There is a real distinction (the shape can change) but they cannot exist by themselves.
• The other side, putting together: nut and bolt, screwing, gluing, bricks with cement, fitted stones; bodies put together can each exist without the other.
• The old materialist: “I’ve dissected bodies for years, liver here, stomach here, eyes there, never found the soul.” But soul is not a part like that.
• Student: is composition more general than having parts? Left in the question; he turns to the four meanings.

7. Four meanings of part and Physics I (“four meanings of the word part”) #

Point: three of the meanings in Metaphysics V are of a composed whole, one is the universal whole, and Physics I uses the first two as examples.

• Physics I: go from general to particular because we know things confusedly before distinctly (he gives a reason “now so difficult”). Examples: (a) a sensible composed whole, continuous or at least touching (salad dressing, a painting with parts); (b) an understandable composed whole: we name before we define. These are two meanings from Book V: the quantitative whole and the genus-difference composition.
• Then the universal whole, which is not put together from its parts but said of its parts; Aristotle compares: the general is to the particular as the whole is to the parts (whole taken in the first, composed sense).
• Words: English “particular” from “part”, not by chance. Aristotle’s Greek for particular (kath’ hekaston, garbled in recording) is not from “part”, though later commentators use merikon, from the word for part; the Greek for general, katholou, is kata holou, “according to the whole”.

8. Mapping Thomas’s question on simplicity (“God has what? No quantitative parts”) #

Point: the articles denying composition in God follow the senses of part.

• No quantitative parts: not a body (first sense). No matter and form (second sense, “the second thing shown in the Summa”).
• The third and fourth senses are not in Book V but led back to matter and form by similarity: Socrates and what-a-man-is are not identical, and what-a-man-is is to Socrates as form to matter (hence “species”, from form); substance and existence are as ability and act. SCG II: angels have composition of substance and existence, not of matter and form; a further chapter shows this composition is not that of matter and form but similar.
• So articles two, three, four take the central sense with two attached; the fifth denies genus and difference.
• To exclude every sense you would also deny the universal whole: not many particular gods, only one God. That is easily deduced from God being identical with what he is, or being his own existence, but explicitly “you’d have to have another article there.” He leaves whether it belongs to sacra doctrina as a problem.
• Quadrilateral divided into square, oblong, rhombus, rhomboid, trapezium; triangle into equilateral, isosceles, scalene: the genus is not put together from these, “unless you’re a John Locke”. Aside: metaphysics classes give the Locke passage; Berkeley quotes it and says he can make no sense of it.

9. The sophism “the part is more than the whole” (“here is a part including more than the whole”) #

Argument he gives students: man is an animal, but animal with reason, so animal is only part of what man is; but animal includes man, dog, cat, horse, elephant; so a part is more than the whole. Resolution: animal as part of man is a composing part of the definition; animal including more than man is a universal whole. The universal whole is always said of more than any one part; the composed whole is always composed of more than one part. Students, and he when first meeting it, are deceived; “unless you know that chapter, you could be deceived.”

10. Equivocal words in the axioms, and wisdom (“nothing is before or after itself”) #

Point: sophistical objections to axioms mix senses of common words, so knowing those senses is presupposed to wisdom.

• Axiom: if A is before B and B before C, A is before C; nothing is before itself. Chaucer before Shakespeare (in time, the first sense); critics put Shakespeare before Chaucer (the fourth sense, better); so Chaucer before Chaucer. Same with yesterday/today/tomorrow and “today was much better than yesterday”. Each argument runs only in one sense.
• Aristotle was the first man to fully understand the words he uses everywhere (Plato says “until we know this, we won’t understand this word” but cannot quite do it), and almost the last; “the only man after him maybe Thomas.”
• “If you know the meanings of the words you use, you are wise”: false. “If you don’t know them, you are not wise”: true. So this is before wisdom in another sense of before.
• Moderns take Metaphysics V for a dictionary to stick anywhere; but it is presupposed to wisdom, to the defense of the axioms, and to all philosophy.

His words #

• “put together”; composed; first meaning tied to the continuous.
• “the fifth / eighth book of Wisdom” [ed.: Metaphysics V, VIII].
• “Natural Hearing”, “the so-called Physics” [ed.: Physics].
• “ability” and “act” [ed.: potency and act]; “able to be” strictly = one step away.
• positio, “laid down / placed” in the definition of syllogism.
• “a this something” [ed.: tode ti]: what each part of the continuous can be.
• “composed whole” vs. “universal whole”: put together from its parts vs. said of its parts.
• “sensible composed whole”, “understandable composed whole” (Physics I examples).
• katholou (kata holou, according to the whole); merikon; kath’ hekaston (inferred from garbled “Echosthenes”).
• “the sailor in the boat” (Plato), “the ghost in the machine” (moderns).
• “species, from form”.

Texts #

Read in class (commented, not quoted at length):

• Aristotle, Metaphysics V: four meanings of part; definition of the continuous.
• Aristotle, Physics I: general before particular, confused before distinct.
• Thomas, Summa theologiae I q.3 (inferred), articles on body, matter-form, subject/nature, substance/existence, genus/difference.
• Shakespeare, Hamlet (inferred): “What is a man, if his chief good and market of his time be but to sleep and feed? A beast, no more.” Mentioned:
• Aristotle, Metaphysics VIII: definitions assimilated to numbers (following Plato).
• Plato, Sophist: logos as noun and verb; imagining as opinion with sensation.
• Aristotle, Peri Hermeneias.
• Thomas, Summa contra Gentiles II: composition of substance and existence in angels.
• Thomas, commentaries on the Epistles of St. Paul (on “placed”).
• Locke, and Berkeley quoting Locke, on the general triangle.
• The comic’s McMaster lectures on number (name unclear in recording).

His questions #

• Is “putting together” three and four more like two continuous things or like matter and form? More like matter and form: the added one actualizes what the number is able to be.
• Can two ones become one two by coming together as semicircles do? No: they have no boundaries; they would always remain two ones.
• What is a four if it be half of six? A three, no more (Shakespeare’s reasoning by proportion).
• Is two able to be four? Not in the strict sense; two is able to be three, three to be four.
• Is the other triangle like the form of the parallelogram? You could say so, but triangles join by extremities; numbers and matter-form do not.
• Is “God is not composed in any way” the same as “God has no parts”? Not exactly, but very much alike; both go back first to the quantitative and continuous.
• If you wanted to eliminate every sense of whole and part from God, what more would be needed? Denial of the universal whole (only one God): easily deduced, but would need another article.
• Can a part be more than the whole? Only by mixing composed whole (definition) with universal whole; the sophism dissolves.
• If you know the meanings of the words you use, are you wise? False; but if you do not know them, you are not wise: true.