Aquinas on the Trinity (Summa I, q.30 a.3): Numbers in God, the Transcendental 'Many' and Two Kinds of 'One'

Orientation #

He says article 3 is “where we left off, I believe”; the third and fourth articles are “a little bit of wordy things,” and he stops “before we do the fourth article” for a break. The previous class treated why there are exactly three persons (q. 30 a. 1–2) and the next treats a. 4, whether “person” is common to the three.

The class, in order #

1. Thinking and believing in words (“can you think without words”) #

Point: after the prayer he asks whether we can think or pray without words in this life; he grants “to some extent” but insists that what we believe is said in words and we must know how we use them.

• Angels, and Thomas as a separated soul, think and pray without words; but our Lord, asked how to pray (Luke), gives words — the Our Father; Benedict XVI on this in Jesus of Nazareth; the psalm “May the words of my mouth and the thought of my heart…” begins with the words.
• Logic directs our thinking with words (not words alone), and does not direct any wordless thinking; if I can’t say what I think, do I know what I’m thinking?
• Example from the creed: “I believe in God the Father Almighty, Creator of heaven and earth” vs. “the Word was made flesh.” Both believed, but not the same way of speaking: only the Son became man (the Father and Holy Spirit did not); but “Father Almighty, Creator” does not mean the Father alone — these are common to the three and appropriated to the Father, for reasons Thomas gives later. Likewise charity diffused “by the Holy Spirit,” the overshadowing of the Virgin: the Incarnation is a work of the whole Trinity, appropriated to the Spirit. Thomas even has an article on whether one should appropriate, since it can be misunderstood.
• So “if we think or believe without words, I’m not sure that we do much.”

2. The three objections (“numerical terms lay down something in God”) #

Point: he reads the objections, which argue that number posits something in God.

1. The divine unity is his essence; every number is unity repeated (“three ones”); so every numerical term signifies the essence and posits something. He flags it as “dangerous” — you don’t have three natures.
2. Whatever is said of God and creatures belongs more eminently to God; “three men on this side of the table” posits something in us; so even more in God.
3. If numerical terms only remove (plurality removes unity, unity removes plurality) there is a circle in reason, confounding the intellect and making nothing certain.

• Aside: his old teacher Schaefer [ed.: name uncertain in recording]: the business of the teacher is to confuse the issue — at the beginning, so you stop and think; that is what Thomas is doing.

3. Sed contra: Hilary and Ambrose (“we do not place quantity in God”) #

Point: the authorities say number is brought in to remove, not to place.

• Hilary, De Trinitate bk. 4 (after Augustine, perhaps the most quoted work in the treatise on the Trinity): the profession of consortium (the three) sustains the understanding of singularity and solitude, “whatever that means exactly.”
• Ambrose, On Faith: “one God” excludes a plurality of gods, “for we do not place quantity in God.”
• He has been reading Euclid bks. 7–9 on numbers; number is one of the two species of quantity in the categories.
• Dilemma he leaves standing before the body: if numerical terms place something in God, I have quantity in God; if they place nothing, “there’s no Trinity.” He notes Thomas will reply to this sed contra, which he does not usually do.

4. The Master and the Sentences (“the magister in the sentences”) #

Point: “the Master” is antonomasia for Peter Lombard, who held that numerical terms do not place but only negate; “others say the contrary.”

• The Sentences, after the Bible, a key text for centuries; to become a doctor in theology one commented on it (Albert, Thomas, Bonaventure). Mainly Augustine’s texts gathered and ordered, with problems resolved; Thomas comments on and divides the text, then adds questions. He meant to redo the commentary, struck out on his own in the Summa, “perhaps in a little better order.”

5. Division vs. distinction (“all plurality follows upon some division”) #

Point: before accepting Thomas’s first premise he distinguishes the words.

• Compare beginning vs. cause: often used interchangeably, but in Metaphysics bk. 5 Aristotle notes beginning is more general — every cause is a beginning, not every beginning a cause (the point is the beginning of the line, not its cause).
• Likewise: every division is a distinction, not every distinction a division. Division, strictly, is the distinction of the parts of some whole (composed, universal, potestative); distinction is broader — “things are distinct when one is not the other.”
• Boundary case: Thomas says a real distinction of Father, Son, Spirit, but never a division of God, since that would imply parts. So here “division” is a synonym for distinction.
• Aside: his shock reading St. Basil calling the Father the aitia of the Son (arche = beginning, aitia = cause); Thomas would say Basil doesn’t mean it wrongly but isn’t using the words in the best way.

6. Material vs. formal distinction (“the division of the continuous”) #

Point: Thomas’s “fundamental” twofold division.

• Material distinction: according to the division of the continuous. Physics bk. 6: the continuous is divisible forever, hence number can increase forever (recall Anaxagoras: no smallest of the small, no greatest of the great). Many chairs of exactly the same kind because there is enough wood; many identical windows because enough glass. Found only in material things having quantity; the philosopher says number in this sense arises from division of the continuous. Fitting that Euclid does geometry (bks. 1–6) before number (7–9): quantity is more sensible.
• Formal distinction: by opposed or diverse forms; on it follows a multitude not in any one genus but among the transcendentibus — the most universal terms transcending the ten categories: being, thing, one, something, true, good — “according as being is divided through the one and the many.” Metaphysics bk. 4: wisdom is about being as being and the one and the many; both are its subject (being in bks. 6–9, the one and many in bk. 10). Such multitude is found only in immaterial things: his teacher Kossorek [ed.: name uncertain]: after death you won’t be counting angels, each is a totally different kind — you need “the same kind of thing” before you count (how many dogs, cats, men, trees).
• How Thomas uses it for the persons: the distinction can’t be material (God immaterial), so formal; formal distinction is by opposites; of Aristotle’s four opposites in the Categories three are eliminated — not contradictories (being/unbeing, “I am who am”), not privation (unbeing too), not contraries (one lacks what the other has) — leaving only relatives, father and son. Hence the interest of John 1: “the Word was towards God,” where “God” stands for the Father.

7. Two wrong solutions (“not considering except the multitude which is a species”) #

Point: both prior positions saw only the multitude that is discrete quantity — the multitude we know first and only at first.

• Categories: quantity divided into discrete (parts don’t meet) and continuous (parts meet at a common boundary); discrete into number and speech (“kind of strange division”).
• (a) Some, seeing that discrete quantity has no place in God, said numerical terms only negate.
• (b) Others said: as scientia is placed in God by its difference (knowing causes), not its genus (quality — he corrects a slip: not quantity); so number by its proper notion, not its genus quantity. He explains the principle Father Boulet “hammered into us”: when names are carried to God the genus often drops and the difference is kept; Porphyry’s Isagoge, genus is to difference as matter to form; matter is in ability, form in act, God pure act; Physics bk. 1, form is “something godlike.”

8. Thomas’s own answer: transcendental multitude (“as they come into divine predication”) #

Point: numerical terms said of God are not taken from number (a species of quantity) — that would be metaphorical, like length and width (cf. the early Summa objection that God is a body, “wider than the skies”) — but from multitude “according as it is transcending.”

• Wisdom proceeds in a way contrary to natural science: the proemium of the Physics goes from general to particular and towards matter; wisdom goes towards the immaterial and from less universal to more universal. Clearest case: Metaphysics bk. 9, act and ability first in movable things, then ascending to act even in what doesn’t move; similarly from material substance to substance in general for separated substances. So too we must rise from number to transcendental multitude.
• Aristotle’s proemium to wisdom: the most universal is furthest from sense, hence “perhaps” most difficult; students who call philosophy “so abstract” mean “so universal.” Aside: “predicament” (Latin for category) — being stuck in a genus.
• The argument as read: transcendental multitude relates to the many as the one convertible with being relates to being. That one (as said “when we treated of the unity of God”) adds nothing positive over being but only negation of division — even formal division; so “one” said of anything signifies that thing undivided (“one man” signifies the substance of man, undivided — “unguillotined”). Because it adds only a negation, not something real (unlike white to man), it is convertible with being. Multitude thus taken signifies the things with indivision about each. Number, and the one that begins number, add an accident over being.
• History: Euclid, defining the one, hadn’t separated the one that begins number from the one convertible with being; the confusion goes back to Plato, who thus thought natures were numbers; even Avicenna confused them — though Thomas follows Avicenna on the transcendentals (De Veritate opening) and on two of the four relations of reason. Aristotle separated the two by diverging from Plato: the one beginning number belongs to arithmetic and quantity; the one convertible with being to Metaphysics bk. 10 and to the Trinity.
• Conclusion: numerical terms signify the things they are said of and add only a negation; “the Master said the truth.” “The essence is one” = undivided essence; “the person is one” = undivided person; “the persons are many” = those persons with indivision about each, since multitude is constituted from units.
• Student asks to backtrack on why number adds an accident: it adds the idea of measure — best definition, “the multitude measured by the one.” Student: no measure in the transcendental? He: only in a kind of analogous way.

9. Replies to the objections (“more common than substance and than relation”) #

• Ad 1: one, being transcendental, is more common than substance and relation, likewise multitude; so it can stand in God for substance or for relation according to what it is joined to, adding only a negation of (formal, not continuous) division. His parallel: “Are Father, Son, Spirit one thing?” — sophism: if one thing, not really distinct. Solution: “thing” first means substance, secondarily accidents — man and dog in a room: two things; dog leaves: man and his shape, health, knowledge of Euclid; nose and ear two things, nose and its shape? (“fatten your nose”). Taking “thing” absolutely they are one thing; as relation, three things; no contradiction. Aristotle: the commonest error is mixing senses of one word — as the whole article mixes two senses of “one” and “multitude.”
• Ad 2: not the same thing said of both. “Wise” of Socrates and God: same notion, fuller in God. “Three” of the three men at the table (quantity, “you got a lot of flesh”) and of the persons: not the same three. Created multitude is not carried over (transumitur); only the transcendent one, adding just “each is undivided.” If quantitative number were said of God properly it would belong more to him, but it isn’t said properly at all.
• Aside: never discuss the Trinity without the text in front of you (as the German poet says of a work of art).
• Ad 3: one does not remove multitude but division, which is prior by reason to both one and multitude; multitude does not remove unity but division about each of its units. Back-reference to the treatment of divine unity, where the apparent circle (one negates many, many made of ones) was solved: division first in thought, then one, then many.
• Reply to the sed contra: the authorities don’t prove enough — plurality excludes solitude, unity excludes many gods, but it doesn’t follow that only this is signified: whiteness excludes blackness, yet “whiteness” doesn’t signify only the exclusion of blackness.

10. “The Father and I are one” (“show us the Father”) #

Point: closing example of how carefully one must speak. Philip in John: “Show us the Father”; Christ: the Father and I are one. Sophism: so the Father is the Son — Sabellius, denying the distinction of persons. Counter: a father is not his son (he is not his sons Marcus or Paul, nor his father Victor Berquist), so Father and Son are not one. Resolution reached with a student: one in essence — no real distinction between the Father and God or the Son and God, so the Father is the same God the Son is; but “is the Father the Son?” — no, true in us and in God. Break before article 4.

His words #

• appropriated: common attributes assigned to one person (Father: Creator, Almighty; Spirit: charity, overshadowing), unlike “the Word was made flesh,” which is proper to the Son.
• confuse the issue: what the teacher does at the beginning (the objections).
• antonomasia: “the Master” for Peter Lombard.
• beginning / cause: every cause a beginning, not conversely (point and line).
• division / distinction: division = distinction of parts of a whole; distinction = “one is not the other”; in the Trinity, distinction not division.
• material distinction: by division of the continuous; formal distinction: by opposed or diverse forms.
• Natural Hearing [ed.: Physics]; Wisdom [ed.: Metaphysics]; ability [ed.: potency]; unbeing [ed.: non-being].
• transcendentibus / transcendentals: being, thing, one, something, true, good — beyond the ten categories.
• predicament: category; being “stuck” in a genus.
• divine predication: being said of God.
• transumitur: carried across (of the created multitude, not carried to God).
• one convertible with being: undivided being, adds only negation; one, beginning of number: adds an accident (measure).
• number: “multitude measured by the one.”
• thing (res): first substance, secondarily accident/relation.

Texts #

Read in class

• Thomas Aquinas, ST I, q. 30, a. 3 (objections, sed contra, body, replies, reply to the sed contra) — verified source.
• Hilary, De Trinitate bk. 4; Ambrose, De fide (via the sed contra).

Mentioned

• Peter Lombard, Sentences; commentaries by Albert, Thomas, Bonaventure.
• Aristotle, Metaphysics bk. 4 (subject of wisdom), bk. 5 (beginning/cause), bk. 9 (act and ability), bk. 10 (one and many); proemium of the Metaphysics.
• Aristotle, Physics bk. 1 (form godlike), bk. 6 (continuous divisible forever), proemium.
• Aristotle, Categories (quantity; four opposites); Porphyry, Isagoge.
• Euclid, Elements bks. 1–6, 7–9; definition of the one.
• Thomas, De Veritate (opening, transcendentals); ST I on the unity of God, and the early objection that God is a body.
• St. Basil (aitia of the Son); Avicenna; Plato; Anaxagoras; Sabellius.
• Luke (teach us to pray); John 1:1, 14; John 14 (Philip); Benedict XVI, Jesus of Nazareth; the psalm on words of my mouth.
• Flagged by text-matching but not evident in the transcript: SCG IV ch. 15; handout “Second Road in our Knowledge” p. 5; DHB vol. III p. 295.

His questions #

• Can you think, or pray, without words in this life? To some extent, but what we believe is said in words and we must know how we use them.
• Are “the Father Almighty, Creator” and “the Word was made flesh” the same way of speaking? No: only the Son became man; creation and omnipotence are common, appropriated to the Father.
• Do numerical terms place something in God or only negate? Taken from transcendental multitude, they signify the things and add only a negation of division.
• Is all plurality from division — and is division the same as distinction? Every division is a distinction, not conversely; here “division” means distinction.
• Is the distinction of the persons material or formal, and by which opposites? Formal, by relatives only.
• What does number add over being? An accident: the idea of measure (multitude measured by the one); only analogously in the transcendental.
• Are the Father, Son and Holy Spirit one thing? One thing as “thing” names the absolute nature; three things as it names relation.
• Is God the Father God the Son? No; but Father and Son are one in essence.