Part 2: God Without Parts, the Trinity and Number, Debate on Number, and History as Incomplete Inquiry

Orientation #

He opens mid-thought, continuing the discussion of part and whole and God’s lack of composition; he refers back to “the first reading there” on knowing confusedly before distinctly and to “the chapter on part and whole.” A student refers back to “this power of retaining images you talked about.” He does not announce next time. The previous class worked through the senses of part and whole in Metaphysics V and Aquinas on God’s freedom from composition; the next opens De Anima III.4 on the intellect.

The class, in order #

1. God has no parts, not even as a universal whole (“God the Father and God the Son”) #

Point: saying God is not composed and is not a part of anything is almost the same as saying God has no parts; but the universal whole must be excluded too.

• Mohammedans think Christians are polytheists because we say Father and Son; they misunderstand. Father, Son, Holy Spirit are one God, not three particular gods.
• If they were three particular gods, God would have parts in the sense in which the universal whole has parts (its particulars).
• “Extremely important”: Father, Son, Holy Spirit are in no way parts, not of God nor of the Trinity; “a part is always something imperfect.”
• Student: then in what sense do we use number, “one and three”? Answer: look at that in the treatise on the Trinity; but it is not the three studied in the science of numbers.
• Argument: (1) if the three were a number in that sense, Father + Son would be more than the Father, and Father + Son + Holy Spirit more than Father + Son; (2) but they are not more, because (Augustine, Boethius following him, Thomas following both) they are distinguished by nothing absolute, only towards each other; in what is absolute they are one and the same. Conclusion: to say the three together are more than the Father is to make the multiplicity something absolute, as in ordinary number.
• Aristotle in the Categories does not call father/son, double/half “relation” but pros ti, translated in Albert and Thomas ad aliquid, “towards something”: not something in itself.
• John’s Greek: en archē ēn ho logos, kai ho logos ēn pros ton theon, kai theos ēn ho logos; ton theon there stands for the Father. “The Father and I are one.”

2. “Put together” is equivocal; composed whole vs. universal whole (“the word put together right is what equivocal”) #

Point: a student presses, “you haven’t explained how parts of number are put together”; he replies that “put together” is one of those names placed first upon the continuous and then carried over.

• Any composed whole (not the universal whole) may be said to be put together from its parts. Thomas, and Aristotle “in the first reading,” distinguish composed whole from universal whole yet see a likeness of ratios.
• How Aristotle manifests that we know confusedly before distinctly, by three kinds of example (as Thomas explains): (a) a sensible composed whole, known indistinctly at first, the parts distinguished gradually; used to manifest the universal point, and also compared directly and in proportion to it. “That’s incredible! … shows how clearly he understands what he’s doing.” (b) the understandable composed whole, the definition: quadrilateral, equilateral, right-angled can be understood independently and then brought together, which helps imagination and reason. (c) He notes Aristotle leaves out the one Book One is most concerned with, matter and form, which is harder.
• What this shows for the chapter on part and whole: the words “whole” and “part” could be carried from the composed whole to the universal whole because there is a proportional likeness.

3. Number’s parts: composing, not subject parts; no common boundary (“parts that have a common boundary”) #

Point: what a number is, via the Categories division of quantity.

• Continuous vs. discrete: both have parts; continuous parts have a common boundary (parts of a line meet at a point, of a surface at a line, of a body at a surface); discrete parts do not meet. Seven divided into 2 and 5, or 3 and 4: no common boundary.
• Two and three are composing parts of five, not subject parts: you cannot say “two is a five” as you say “two is an even number” (two is a subject part of even number).
• First meaning of “put together”: placed side by side so that extremities become one, coincide, or touch. Matter and form, genus and differences do not meet like that (do right-angled and quadrilateral have a common boundary?), yet we still say the definition is put together from genus and differences; we could not say number is put together from odd and even (subject parts).
• So are a number’s parts put together like matter and form / genus and difference, or like two semicircles? “It’s sort of in between.” Number is a quantitative whole (circle more than semicircle, five more than three), so more like the semicircles or the triangles making a parallelogram; yet like the definition and matter–form it has no boundaries. A student thinks it is really more like the semicircles; he holds to the in-between.

4. Is the form of a number the last one? Ability and act (“Miles made my grandchildren be seven”) #

Point: a student urges there is a real matter–form composition in number where all the ones are matter and the form is something else (“fiveness”); he answers that what makes it five is the fifth one, because number arises by counting, which has order.

• Grandchildren: Kate the first has a special place, but Miles the seventh made them seven. Student: what if triplets? “The last, without the rule.” Counting seven books, seven chairs for seven people (six found, one short, “oh, there’s a chair over here, that makes seven”): the seventh chair makes it seven, though it is not the form of the others.
• If you look at seven ones as all equal, “democratic,” with no order, nothing makes them one: they remain seven ones, since they cannot come together like semicircles, having no extremity. Coming together does not mean what it means for the circle, nor exactly matter and form; it has a likeness to both, and you must put them together “in a way like matter and form” yet unlike.
• “The point is that you have to see ability and act there.” Seven becomes eight by addition of one, as adding reason to animal gives man; take one from eight and you have seven, take reason from man and you have a beast: “not just playing with words… real likeness.”
• Letters c-a-t are able to be “cat,” “act,” or the abbreviation for Thomas Aquinas; what makes them one or the other is the order. Order is like the form of the number as the order of the letters is like the form of the word; student: “that’s something other than the last one.” Reply: adding has the idea of actualizing that ability, otherwise you would have a seven and a one, not an eight. Student: suppose I add the seven to the one? Reply: in the strict sense a thing is able to be something when one step away: one is able to be two, two to be three, three to be four, not three to be five.
• Student: then adding differs from making actual, since I can add two and two. Reply: that is calculation, treating numbers as units, a collection of twos; strictly two becomes three by one, then four, and you run it together. Saying four is two twos is like saying two is two ones rather than one two: your “democratic mind and democratic customs” want two to be more than one.
• Student: the one added does not exist by itself. Reply: you must see that one in a certain order or you don’t understand what number is. Student: “I still think the form of the eight is not the last one.” Three at the table, a fourth makes four; a card game needs a fourth, “the three are made four by that fourth person.” The disagreement is left standing.
• Aside: a faculty wife once asked whether he played cards, to fit him into a card group.

5. Historia is by nature incomplete (“history is always more complicated than we think”) #

Point: the student asks about the power of retaining images “you said is separate”; he first finishes a remark on why Aristotle uses historia.

• Thomas explains Aristotle’s word: it is the nature of a historia, an investigation, to be incomplete; Aristotle is not determining every question about the soul.
• This shows why the name “history,” originally just investigation, is given by antonomasia to the investigation of human affairs: nobody can know all a man thought, felt, or did, even in a biography with letters and witnesses. A historian (Mr. Stage): “American history? which century? which decade? which aspect?”; endless.
• Constant revision: a new “True Lincoln” (he teases a Lincoln-admiring colleague), biographies of Churchill, MacArthur, Teddy Roosevelt, Kennedy; Keegan on WWII; disputes over when Shakespeare wrote his plays; Mozart’s catalogue dated and re-dated by the paper he used. Same history book gives three scenarios. Contrast geometry, which reaches closure.
• Example of revision: many historians say the Balkan and Crete campaign delayed the invasion of Russia (twenty miles from Moscow when snow came, no winter clothing issued, frostbite amputations); Keegan says the start was determined by waiting for spring rains to dry, nothing to do with Greece; he does not know who is right.

6. The four inward senses (“he distinguishes four inward senses”) #

Point: Thomas in the Summa Theologiae, following Aristotle, distinguishes four inward senses.

• Common sense: knows the per se sensibles, the common centre of what the outward senses see.
• Estimative power (in other animals; “a little bit like what we’d call instinct”): perceives what the outward senses do not perceive as such, that this shape is an enemy, this smell is to be eaten or not, these young to be fed. The sheep sees the shape of the fox and estimates it fearful, but the shape as such is not dangerous.
• Imagination and memory: Thomas uses memory for retaining these estimations; today we might use memory for retaining the image and imagination for the ability to manipulate images, so bear in mind what he is distinguishing.
• Two reasons for the distinctions: one distinguishing common sense from estimative (something not sensible as such), another distinguishing the retaining powers from the apprehending ones. The class breaks off here.

His words #

• universal whole; the whole whose “parts” are its particulars; God has no parts even in this sense.
• part; “always something imperfect.”
• pros ti / ad aliquid; “towards something,” Aristotle’s word (Albert’s and Thomas’s translation) for what we call relation [ed.: relation].
• put together; equivocal, first said of the continuous where extremities coincide or touch.
• composing parts vs. subject parts; two and three compose five; two is a subject part of even number.
• common boundary; what distinguishes continuous from discrete quantity.
• ability and act; his rendering for what makes a number one [ed.: potency and act].
• democratic; his jibe for treating the ones of a number as equal and unordered.
• historia; investigation, by nature incomplete; given by antonomasia to human history.
• common sense, estimative power (≈ instinct), imagination, memory; the four inward senses; he notes his own usage of memory/imagination differs from Thomas’s.

Texts #

Read in class

• John 1:1, Greek quoted: en archē ēn ho logos… kai theos ēn ho logos.
• “The Father and I are one” (John, inferred).

Mentioned

• Aristotle, Categories: quantity into continuous and discrete; pros ti.
• Aristotle, Physics I, “first reading” (inferred): knowing confusedly before distinctly, three kinds of example, Thomas’s explanation.
• Aristotle, Metaphysics V, chapter on part and whole (inferred).
• Thomas Aquinas, Summa Theologiae: treatise on the Trinity; the four inward senses (loci inferred).
• Augustine and Boethius on the Trinity (no locus given).
• Keegan, book on the Second World War; “The True Lincoln”; biographies of Churchill, MacArthur, Roosevelt, Kennedy; Shakespeare and Mozart chronologies.

His questions #

• In what sense do we say God is one and three? Not the three of the science of numbers; the persons are distinguished only towards each other, not absolutely.
• Are two and three composing parts or subject parts of five? Composing parts; two is a subject part of even number.
• Do right-angled and quadrilateral meet at a common boundary? Do matter and form? No; yet we still say the definition is put together from genus and differences.
• Are a number’s parts put together like matter and form, or like two semicircles? In between: quantitative like the semicircles, boundaryless like matter and form.
• What makes seven ones to be one seven? The order, the seventh one, seen through ability and act; the student still holds the form is “something else”: left open.
• How would seven become eight? By addition of one, as animal plus reason gives man.
• What does “add” mean? Actualizing an ability; strictly a thing is able only for what is one step away.
• Why is the name “history” given to the investigation of human affairs? By antonomasia, because such investigation is most of all incomplete.
• What does the estimative power perceive that the senses do not? That something is an enemy, food, or to be fed (the sheep and the fox’s shape).