Summa I, Q7, Article 4 and Q8, Article 1: No actual infinite multitude, Weizsäcker on a finite universe, and how God is in all things

Orientation #

He refers back to “the previous article” (infinite magnitude) when reading the reply about species of multitude, and says of q. 8 that Thomas “has excluded the infinite body” in “the third article” (prev. lecture). At the end he asks “should we stop?” and the class continues into q. 8 a. 1. The previous class treated q. 7 aa. 2-3; the next continues q. 8 on God’s presence in things and everywhere.

The class, in order #

1. The three objections and the sed contra (“infinite multitude in act”) #

Point: he reads q. 7 a. 4, whether there is an infinite in things according to multitude.

• Obj. 1: what is in ability can be reduced to act; number is multipliable forever; so an actual infinite multitude is possible. He notes Aristotle in the “ninth book of wisdom” [ed.: Metaphysics IX] says some abilities are by nature never fully actualized.
• Obj. 2: of any species some individual can exist; species of figure are infinite (“hexagon, seven figure, eight figure, nine figure”); therefore infinite figures in act.
• Obj. 3: things not opposed do not impede each other; any posited multitude admits another not opposed to it, and so forever.
• Sed contra: Wisdom 11:21, all things disposed in weight, number and measure.

2. Thomas’s answer: no infinite multitude, per se or per accidens (“twofold opinion”) #

Point: Avicenna and Algazel allowed an infinite multitude per accidens; Thomas rejects even that.

• Per se infinite multitude: required for something to be; impossible, since the thing would depend on an infinity and its generation could never be completed.
• Per accidens: not required, but happens to be so. Example (his gloss “the metalworker, I guess”): per se the work needs the art in the soul, the moving hand, the hammer; multiply these forever and the work is never completed; but many hammers, one breaking and another taken, is a multitude per accidens, and “doesn’t differ at all whether by one or by two or by many or by infinity” if he works in infinite time.
• Thomas’s first reason: (1) every multitude is in some species of multitude (“sounds like they’re meant to be used in the previous article”); (2) species of multitude are species of number; (3) no species of number is infinite, since each number is a multitude measured by one. Conclusion: no actual infinite multitude, per se or per accidens.
• Aside: the Oxford translation of Aristotle read “infinite number”; his teacher said that is a contradiction in terms — “Dwayne, look it up in the Greek” — and the word number was not there; Aristotle said infinite multitude.
• Second reason: multitude existing in rerum natura is created; everything created falls under some intention of the creator, who does nothing in vain; so all created things are comprehended under a certain number. Application: God does not aim at an infinite multitude of the blessed; “there’s some number, and the number is completed. That’s it.”

3. Infinite multitude in potency (“division of magnitude”) #

Point: potential infinite multitude is possible because increase of multitude follows division of magnitude.

• Anaxagoras: “no smallest of the small” (true only of mathematical quantity) and “no largest of the large”; the connection is that as you divide and subdivide the line, the number of lines grows without limit — no largest number as no shortest line.
• Since the infinite is in potency in dividing the continuous (it proceeds to matter), by the same reason it is only in potency in adding multitude. Aristotle defines the continuous as what is divisible forever — an ability never fully actualized.
• Example: his ability to walk home — while walking home he has not walked home, and having walked home he is no longer walking; unlike wood’s ability to be a chair, which can be fully realized.
• Tie to infinity of the mind: the common way is via the universal, but another way is that through knowing one thing you can always know another, and so on, never completely actualized; in geometry “there’s going to be no end to this discovery.”

4. The replies (“reduced to act according to the way of its own being”) #

• Ad 1: what is in potency is reduced to act according to its own mode of being; a day is not actualized all at once but successively; so infinite multitude, after each multitude another can be taken, forever.
• Ad 2: species of figures get their infinity from infinity of number (trilateral, quadrilateral…); so they are not all actualized at once. Aside: “triangle” is named from angles; “trilateral” from sides “would probably make more sense.”
• Aside: Thomas says elsewhere that seeing God as he is we know all figures — hard to understand how in one thing we know many; like the idea of limits, knowing the circle as the limit of polygons, “trying to be like an angel, not quite getting there.”
• Ad 3: positing further things is not opposed to those posited, but positing an infinite multitude is opposed to every species of multitude.

5. Into q. 8: the infinite and being everywhere (“to the infinite, it seems to belong that it be everywhere”) #

Point: q. 8 attaches to God’s infinity, but God is not everywhere as a body fills everything (already excluded in a. 3), nor as space was thought to go on forever — “whatever Newton meant by the sensorium.”

6. Weizsäcker and the finite universe (“the discovery of limits”) #

Point: twentieth-century physics, against Newtonian physics, is characterized by limits; the resistance to a finite universe reveals the universe was made a substitute for God.

• Planck’s quantum hypothesis, December 1900: a smallest amount of energy that can be given or received, and only multiples of it; Einstein five years later (light), Bohr thirteen years later (atom); “quantum jumps.” His popular comparison: the penny — nothing less, nothing between one and two.
• 1905 special relativity: a limit on speed, the speed of light — a limit “in the direction of the large.” Neither limit existed in Newtonian physics.
• General relativity ten years later gave impetus to cosmology; the world seemed finite, against the Renaissance assumption of an infinite universe (Koyré, From the Closed World to the Infinite Universe, title as he gives it). Einstein was surprised; someone’s mathematics was wrong, and Einstein had to admit his own miscalculations. Big bang: finite in time too, “a great shock.”
• Quantum physicists went the other way: at least two Nobel laureates in elementary particles worked with a minimum length, about 10^-13 cm — a limit in nature, unlike mathematics.
• Weizsäcker’s story: an older physicist indignant at his lecture on limits; privately he had no objection to the theories, he “just couldn’t stand the idea” of a finite universe. Weizsäcker’s diagnosis: when they turned from the study of God, who is infinite, to the material world, the universe became a substitute for God; a finite thing cannot satisfy the mind, so the universe had to be infinite — and now science’s own methods find it limited: “a dead end. It points you back to God.”
• Joke: he and his wife call marriage a dead end — “there’s no way out”; a student: like Sartre, No Exit. He does not think Weizsäcker is a believer, but he sees the point.

7. Substitutes for theology (“not really philosophy class”) #

Point: modern philosophers, having given up theology after exposure to it (unlike the Greeks, never exposed), seek in philosophy a substitute for theology.

• Aside on a newsletter calling this “our philosophical class”: as a philosopher he does not know there is a Trinity or that God became man; the order here imitates God’s knowledge, so it is not a philosophy class. Student: “you should sue them.”
• Hegel’s philosophy of history as a secularized City of God; his system a “perverse imitation” of the Trinity, ending with thought becoming flesh.
• “Feitich” [ed.: likely Feuerbach; possibly Fichte] “is something like that”: the natural world as substitute for God, which requires it to be infinite.
• Communism as salvation: Whittaker Chambers (Witness), from Columbia, either become a communist or commit suicide — his brother committed suicide, he became a communist; Alger Hiss; Lenin and others taking new names, “preserving the body” — “a deep imitation of Christianity.”
• Student: Thomas’s commentary on Job, end of chapter 6, gives four things that end disputation, one being when someone has no reason against your argument but does not want to hear it — that is the old physicist’s “visceral reaction.”
• Return: the substitute need not have God’s kind of infinity, but the average mind does not see that. The Greeks, “coerced by the truth” (Thomas), thought the beginning of things infinite, but quantitatively; so Thomas contrasts that infinity with God’s, and hence must ask what ubique means — not spread out like space, nor like the Manichaeans’ God as a light extended through space.

8. The prologue of q. 8 (“four things are sought”) #

• Melissus or the like: being is infinite, quantitatively, hence everywhere — “how close this is to the way the mind works.”
• The four articles: whether God is in all things; whether everywhere; whether everywhere by essence, presence and power (“a breakdown of the second”); whether to be everywhere is proper to God. He stresses that in omnibus rebus and ubique are not exactly the same for Thomas — separate articles.

9. q. 8 a. 1, objections and sed contra (“it seems that God is not in all things”) #

• Obj. 1: what is above all things is not in all things; Psalm 120 (as he cites it): the Lord raised above all nations, above the heavens. “To be in is said in many ways.”
• Obj. 2: what is in something is contained by it (“only the first sense of being in” — the four walls of this room); God contains things, we are “in God’s hand”; Augustine, Eighty-three Questions: all things are in him rather than he in them.
• Obj. 3: the more powerful the agent, the farther its action reaches; God, most powerful, need not be in things.
• Obj. 4: demons are things, but God is not in demons — no fellowship of light with darkness, 2 Cor 6:14.
• Sed contra: where something acts, there it is; Isaiah 26:12, all our doings you do in us. Aside: does God cooperate with the sinner? Whatever of goodness in the sinner’s act is from God; the defect is from the sinner.

10. The body of the article (“as an agent is present to that in which it acts”) #

Point: God is in all things not as part of their nature nor as accident, but as an agent is present to what it acts on.

1. Every agent must be joined to that in which it immediately acts and touch it by its power; Physics VII proves mover and moved are together.
2. God is ipsum esse, being by nature, so created being is his proper effect, as being ignited is fire’s proper effect.
3. He causes this not only at the start but as long as things are conserved, as light is caused in air by the sun so long as the air stays illuminated.
4. So as long as things have being God is present to them, in the way they have being.
5. But being is what is most intimate and most profoundly within each thing, formal with respect to all that is in the thing, the actuality of everything. Conclusion: God is in all things, and intimately. The saints: he is closer to you than you are to yourself (Teresa of Avila’s interior castle — going in to God); why? because he is the cause of being, always, and nothing can be without him — “that would be a contradiction.” “Just not the most obvious sense of being in”: we fall back on the earlier senses and misunderstand.

11. The replies, and the senses of “in” (“if you knock my tooth out”) #

• Ad 1: God is above all things by the excellence of his nature, in all things as causing their being — not above in the same way he is in.
• Ad 2 draws on Thomas’s order of senses of “in” from Physics IV: first, in a place (in the room); second, part in a whole — Thomas shows the closeness by saying a part loosened from the whole is in it as in a place: a knocked-out tooth put back, or false teeth, are in the mouth as in a place, not as parts; third, species in genus. The reply: bodily things are in something as in what contains them, but spiritual things contain that in which they are, as the soul contains the body — when the soul leaves, the body falls apart, so the soul holds it together (though in another sense, form in matter, one might say the body contains the soul). So God is in things as containing them; all things are said to be in God only by a likeness of bodily things. Also the seventh sense of “in”: “I’ve got you in my power,” and “it’s out of my hands.”
• Ad 3: no agent, however powerful, reaches something distant except through intermediaries; it belongs to God’s maximum power to act immediately in all things, so nothing is distant from him. Things are said distant from God through unlikeness of nature or of grace, as he is above by the excellence of his nature (back to ad 1).
• Ad 4: in demons there is the nature, from God, and the deformity of guilt, not from him; so it should not be conceded absolutely that God is in demons insofar as they are demons, but with the addition, insofar as they are things whose staying in existence depends on God. In things naming an undeformed nature it can be said absolutely.
• Aside: “Hail Mary, full of grace, the Lord is with thee” — “with,” not “in.”

His words #

• ability — his rendering [ed.: potency]; “in ability” for in potentia.
• ninth book of wisdom — [ed.: Metaphysics IX].
• multitude per se vs per accidens — required for something to be vs. merely happening to be so.
• in rerum natura — “in reality, in the real world.”
• number — a multitude measured by one; “infinite number” a contradiction in terms.
• continuous — that which is able to be divided forever.
• ubique / in omnibus rebus — everywhere / in all things, not exactly the same.
• sensorium — Newton’s term, “whatever Newton meant.”
• quantum — a smallest amount of energy given or received; his penny comparison.
• “coerced by the truth” — Thomas on the Greeks positing an infinite beginning.
• to be in — said in many ways; senses of Physics IV: place, part in whole, species in genus, …, seventh: in one’s power.
• proper effect — as being ignited to fire; created esse to God.

Texts #

Read in class

• Thomas Aquinas, Summa Theologiae I, q. 7, a. 4 (whole article).
• Thomas Aquinas, Summa Theologiae I, q. 8, prologue and a. 1 (whole article). Mentioned
• Aristotle, Metaphysics IX (“ninth book of wisdom”), abilities never fully actualized.
• Aristotle, Physics VII, mover and moved together; Physics IV, senses of “in.”
• Wisdom 11:21; Psalm 120 (as cited); 2 Corinthians 6:14; Isaiah 26:12.
• Augustine, Eighty-three Questions.
• Weizsäcker, The World View of Physics; Koyré, From the Closed Universe to the Infinite Universe (as he gives it).
• Thomas Aquinas, commentary on Job, end of ch. 6 (student’s reference).
• Whittaker Chambers, Witness; Sartre, No Exit; Teresa of Avila, interior castle.
• Hegel, philosophy of history and system; Augustine, City of God.

His questions #

• What’s the connection between “no smallest of the small” and “no largest of the large”? The number of lines always grows as you divide, so no largest number as no shortest line.
• Is the continuous an ability that can ever be fully actualized? No — like walking home, which ceases once completed.
• Does God aim at an infinite multitude of the blessed? No; some number, and the number is completed.
• Why is God closer to you than you are to yourself? Because he is the cause of being, always, and nothing can be without him.
• Is God in the demons? Not absolutely, insofar as they are demons; yes insofar as they are things.
• Does God cooperate with the sinner? Whatever goodness is in the act is from God; the defect from the sinner.
• What does it mean that God is ubique? Not spread out like space or like the Manichaean light; left to be worked out in the coming articles.