Summa I q.14 a.12: Whether God Knows Infinite Things – Senses of 'In', Potency vs. Act, and Limits in Modern Physics

Orientation #

He opens straight on “Article Twelve” and closes by saying they stop here because the next thing is “the knowledge of future contingents and then enunciables.” The handout “Note for Book One, Reading Nine” (Physics I, Anaxagoras) is used in the digression on parts getting smaller without limit. Last time was a. 11 (God’s knowledge of singulars), next time a. 13 (future contingents).

The class, in order #

1. The three objections (“whether God is able to know”) #

Point: the infinite seems unknowable to God on three counts, each tied to the notion of the infinite in the Physics.

• Obj. 1. The infinite as such is unknown, since it is “that whose quantity, those taking it, one can always take something outside” (Physics III). Illustrated: bisect a line, you get two shorter lines you can bisect again; there is always a greater number. But Augustine (City of God XII): whatever is comprehended is limited by the grasp of the knower. The infinite cannot be made finite; therefore not comprehended by God.
• Obj. 2. If one says things infinite in themselves are limited to God’s knowledge: the infinite is what cannot be gone through, the finite what can (Physics III); the infinite cannot be gone through by finite or infinite (Physics VI). So it is not finite even to God’s infinite knowledge. Aside: Zeno used this so he “couldn’t get out the door.”
• Obj. 3. God’s knowledge is the measure of things known; to be measured is against the notion of the infinite.
• Aside on measure: Aristotle defines number as a multitude measured by one. In college the Oxford translation read “infinite number”; his teacher Kasurik [name uncertain in recording] said that is a contradiction and made him look up the Greek: “infinite” is there, “number” is not. Shakespeare says “countless and infinite”: counted, it would not be infinite. Kasurik did not really know Greek but knew philosophy, so knew the translator was wrong. Likewise Thomas sometimes corrects Moerbeke, e.g. Metaphysics VII on definition: a definition is never one name but a logos; Moerbeke renders ratio (the thought), but oratio (many words) fits better, and Thomas explains it as compositio nominum, the spoken or written definition. A student notes the form of the word oratio agrees with ratio.

2. Sed contra, immensus, and the Athanasian Creed (“adore unity in Trinity and Trinity in unity”) #

Point: Augustine says that though there is no number of infinite things, they are not incomprehensible to him whose knowledge is not number.

• Aside: reading the Catena Aurea on Matthew, Thomas quotes Chrysostom and Augustine most, even more explicitly in the commentary on John; Chrysostom is quoted from two works on Matthew.
• Church documents call God immensus: literally “not measured”, connected with infinity as an attribute; and mens (mind) comes from measuring, so measuring and numbering are very much acts of reason. A student: it is in the Athanasian Creed.
• The Creed’s “adore unity in Trinity and Trinity in unity” requires the different senses of “in” from Physics IV. Fundamental example: species in genus in one sense, genus in species in another. If A is in B and B in A in the same sense, A would be in itself, which cannot be. Likewise species is part of genus and genus part of species, in different senses of “part”. So: one nature in three persons (one sense) vs. three persons subsisting in one nature (another). A student asks which two senses: he says they attach to Physics IV senses, but extended, as when we say the nature is in the thing and the thing subsists in the nature.
• Aside: the Athanasian Creed divides the articles in two, the Nicene in three; theology follows the two, Trinity in the prima pars, Incarnation in the third part; something is said univocally of God and creatures, since “man” is said univocally of Christ and of us, “a condescension of his.”

3. “In the form of God” and “I’m in good shape” (“he was in the form of God”) #

Point: the odd sense in which a thing is in its form is a distant cousin of part-in-whole.

• Philippians: “he was in the form of God”; form means nature (Metaphysics V). Daily speech: “what shape are you in? I’m in good shape, in good health.” Yet health and shape are in me, as form in matter. Which sense of “in” is “I’m in health”?
• Argument: (1) parts are to whole as matter to form (Physics II); (2) matter is “that from which something comes to be, existing within it” (table from wood, wood is in it); (3) the whole comes to be from its parts and they are in it (chair from seat, back, legs; soldiers the matter of the army; man and woman the matter of marriage; we the parts of the church); so parts are like matter, whole like form. Hence as a part is in the whole, so we speak of matter as in the form: “I’m in good shape.” He calls it strange; strictly the health is more in the body than the body in health, but the proportional likeness holds.
• Student: is “the body in good health” like the wood informed by the shape, the form actualizing the matter? He accepts, then adds: “how did the wood get into the shape?” — we imagine matter getting into a shape as I get into my clothes, which is the first meaning of in, in place; “an obscure meaning.”

4. Respondeo: two knowledges, both of infinite things (“scientia visionis”) #

Point: God knows infinite things both of what is in act and of what is in potency.

1. God knows not only what is in act (scientia visionis) but what is in his own power or in creatures’ power (“all my sins of omission”). These are clearly infinite; so if he knows them he knows infinite things.
2. Some say the science of vision (of what is, was, will be) is not of infinite things, since they do not hold the world eternal or generation and motion lasting forever, multiplying individuals without end.
3. Nevertheless, considered diligently, even by the science of vision God knows infinite things: he knows the thoughts and affections of the heart, which are multiplied forever, since rational creatures remain without end (praising him in heaven again and again; cursing in hell).
4. The other knowledge [ed.: he does not name it; the recording is unclear here] is of infinite things, otherwise he would not comprehend his own power.

5. Why: knowledge follows the form that is its source (“do you know my brother Mark”) #

Point: the reach of a knower’s knowledge follows the form through which it knows.

• Sensible form in the sense: likeness of one individual, so only one individual known.
• Intelligible form of our understanding: likeness of the nature of the species, partaken by an infinity of particulars; through the form “man” we know in some way an infinity of men, as knowing what a square is I know all squares — but not as distinguished from each other, only as they come together in the species; not their individual principles.
• His sophistical argument: “Do you know my brother Mark?” “No.” “Do you know what a man is? a brother? that’s what Mark is, so you know him.” In some way yes, simply no. Once a young lady actually knew his son Marcus.
• The divine essence, through which God understands, is a sufficient likeness of all things that are or can be, in their common and their private principles, because it is the active power making them like itself. Whence God’s knowledge extends to infinite things even as distinct from each other.

6. Reply 1 begins: infinite belongs to quantity (“the notion of infinite belongs to quantity”) #

Point: the first meaning of “infinite” (Physics I) is quantitative; God is not infinite in that sense.

• Summa contra Gentiles order: infinity is the last thing on the substance of God, after simplicity (not a body, not continuous) and unity (no number of gods); so infinity must be said of God in a much different meaning. Scripture’s “wider, taller, you can’t escape me” is metaphor; Newton, dabbling in theology, made space the “sensorium of God”, making God continuous.
• “Infinite” negates “finite”; the first meaning of limit/end is the end of the continuous, e.g. the end of the table, as the first meaning of beginning is of the continuous.
• Why our words start there: De Anima III, the proper object of reason is the what-it-is of something sensed or imagined; I see the blackness of your robe only with the robe there (though the seeing is in my eye); I understand what a square is only imagining a square. So Boethius’s problem in the treatise on the Trinity: we cannot imagine God, so we think of him by negating material things or as their cause. On Memory: we do not think without the continuous and time; every sentence is past, present or future; “Before Abraham was, I am” seems ungrammatical because grammar follows our imagination-bound way of knowing.
• Metaphysics V moves “limit” gradually: of magnitude, of motion, purpose, then definition. “Only Aristotle could do that.”

7. Thomas orders the eight senses of “in” (“Aristotle doesn’t order for us there”) #

Point: Physics IV distinguishes eight senses of in without ordering them; Thomas orders them (a student asks: in the Physics IV commentary, not Metaphysics V, where the senses of limit are).

1. In place (we are in this room).
2. Part in whole. Boundary case: if you can cut the part out and put it back (false tooth, a piece cut from the table), it is there as in a place, not as a part; the senses are close.
3. Genus in species, and parts of the definition: still part in whole, less known to us.
4. Species in genus: katholou (universal) from the Greek for whole, “particular” from part, so universal to particular is like whole to part; but obscure, since the species is in the genus only in potency.
5. Form in matter: in potency, like 4; unlike 1–3, where something is actually in something.

• So 4 is more like 3 than 5 is, and more like 5 than 3 is (genus is actually in species; form is in matter only in potency). “It’s pretty.”
• Daily mistake: a clay sphere moulded into a cube — people say “the shape changed”, imagining the genus shape going from species to species; really the clay changed. A sick man’s “condition changes” — no, his body changes from one condition to another. They fall back on sense 4 when trying to speak of sense 5. A student: “this is the first time I’ve understood this.” He: it takes long to get the senses down, but “you get a lot of mileage out of them.”
• Anaxagoras imagines everything that comes out of matter actually in it and has to fit it in; Msgr Dionne: “he can’t move the word”; Thomas: words are picked up and placed on something else with a new meaning that keeps a likeness to the one before.

8. Falling back on an earlier sense: particles, marble, water (“every elementary particle is composed of all the rest”) #

Point: taking “in potency” for “actually in” (sense 2 for sense 5) reproduces Anaxagoras’s difficulties.

• Heisenberg cites the “well-known formula” that every elementary particle is composed of all the rest, because from any you can get the rest; but that gives particles within particles forever smaller, contrary to all electrons and all protons having the same mass, and the particles got out are sometimes larger than the original. Heisenberg himself rather compares energy to Aristotle’s matter, a potency that can take different forms.
• Michelangelo: the Pietà already in the marble — actual in his imagination (Weizsäcker: imagining makes a thing actual in imagination), not in the marble; “imagination is what deceives us.”
• Water: getting hydrogen and oxygen out does not by itself show they are actually there rather than in potency; two deadly chemicals make a table chemical [ed.: he does not settle the example]; from trees you get chairs, tables, doors without their being actually in trees. He does not say what the truth about water is.
• Handout, Physics I on Anaxagoras: if parts can get smaller without limit, the whole plant or animal could be any size, but experience shows kinds of plants within limits.
• Physics rediscovered limits in the 20th century: Planck’s smallest amount of energy (against Newtonian halving), Einstein’s maximum speed (1905), a minimum length, a universe limited in space and perhaps time. Weizsäcker’s story: an old physicist angry at the new limits with no scientific objection; his essay: the infinity of the universe came in at the Renaissance, when God was given up, as a substitute for the infinity of God, since the mind cannot be satisfied without something infinite.

9. Replies 1–3 finished (“to know part after part”) #

• Reply 1: to the notion of quantity belongs an order of parts; to know the infinite as infinite is to know part after part, like counting to the end of numbers, impossible since something always remains outside. God does not know thus, not discursively (Shakespeare: “discourse”; counting is a discourse), but all at once, the opposite of before and after; so nothing prevents his knowing infinite things.
• Reply 2: transition implies succession of parts, so the infinite cannot be gone through by finite or infinite; but for comprehension “equalness” suffices — nothing of the thing is outside the grasper. So what is infinite in itself is finite to God’s knowledge as comprehended, not as gone through one by one; even eternity would not suffice for that. Aside: the Categories has a chapter on before and after, then on simul.
• Reply 3: Plato in the Laws rejects Protagoras’s “man is the measure of all things” for “God is the measure”; this divides the Greeks from the moderns and humanists (cf. Benedict XVI’s recent addresses on “technically facile people”). He thinks Thomas should have had a question on God as measure attached to God’s unity, since measure is a property of the one. God’s knowledge is a measure but not a quantitative measure; each thing has the truth of its nature as it imitates the divine knowledge, as an artefact agrees with art. Even granting things infinite in act (an infinity of men, infinite air — which Thomas does not hold), they would have a determinate, finite kind of being and so be measurable by God’s knowledge.
• Psalm: he knows my thoughts before I have them; past, present, future thoughts all actual to God at once, not waiting for the next.

His words #

• Natural Hearing; his name for the Physics [ed.: Physics]
• infinite; “that whose quantity, those taking it, one can always take something outside”; what cannot be gone through
• number; a multitude measured by one; “infinite number” a contradiction
• logos / ratio / oratio; definition as many words, compositio nominum
• immensus; not measured; mens from measuring
• ability [ed.: potency]; “in the ability of the creatures”
• scientia visionis; knowledge of vision; of what is, was, or will be
• understandable form [ed.: intelligible species]; likeness of the nature of the species
• private principles; the principles peculiar to each individual
• limit / end; first meaning the end of the continuous
• katholou; universal, from the Greek for whole; particular from part
• discursive; Shakespeare’s “discourse”; counting as discourse
• equalness; what suffices for comprehension
• “move the word” (Msgr Dionne); carrying a word to a later meaning

Texts #

Read in class:

• Thomas Aquinas, Summa Theologiae I, q. 14, a. 12 (whole article, objections through replies)
• Handout “Note for Book One, Reading Nine” (Aquinas on Physics I, Anaxagoras), used in segment 8
• Augustine, City of God XII (in objection 1 and sed contra)

Mentioned:

• Aristotle, Physics III (definition of infinite), Physics VI (infinite not gone through), Physics I (infinite belongs to quantity; Anaxagoras), Physics IV (eight senses of in), Physics II (parts to whole as matter to form)
• Aristotle, Metaphysics (“Wisdom”) V (limit; form as nature), VII (definition as logos)
• Aristotle, De Anima III; On Memory and Reminiscence; Categories (before/after, simul)
• Thomas Aquinas, Summa contra Gentiles (order: simplicity, unity, infinity) (inferred: Book I)
• Thomas Aquinas, Catena Aurea on Matthew; commentary on John
• Boethius, treatise on the Trinity
• Plato, Laws; Athanasian and Nicene Creeds; Philippians (“in the form of God”); a Psalm (knows my thoughts before I have them)
• Heisenberg on elementary particles; Weizsäcker; Newton; Benedict XVI’s addresses; printed volume DHB Vol. III p. 375 (per verified sources)

His questions #

• How can you grasp something that always has something outside of what you have? Comprehension needs equalness, not going through; God knows all at once.
• How would you translate immensus? Not measured.
• What two senses of “in” are in “unity in Trinity and Trinity in unity”? Nature in the persons, persons subsisting in the nature; extended senses of Physics IV.
• “I’m in good shape”: what sense of in is that? A distant cousin of part in whole, since parts are to whole as matter to form.
• Do you know my brother Mark? In some way yes (you know what a man, a brother is), simply no — not as distinguished.
• The clay sphere moulded into a cube: what has changed, the clay or its shape? The clay; saying “the shape changed” falls back on species-in-genus.
• Does getting hydrogen and oxygen out of water show they are actually in it? No; they may be there only in ability. Left open what the truth is.
• Has the sick man’s condition changed, or his body? His body, from one condition to another.