Summa I, Q.11, Arts. 1–2: The One Convertible with Being, and How One and Many Are Opposed

Orientation #

He refers back to “question three that we read there on the simplicity of God”, the eight articles showing God is not composed in any way, and to the continuous as “divisible forever” as “we’ve seen before” (prev. lecture). He ends by announcing the break: the first two articles are about one in general, the last two about God being one and most one, which “we continue now or take a break now”. The previous class treated the aevum and the transcendentals, the next takes up aa. 3-4 on God being one and most one.

The class, in order #

1. The division of the four articles (“all things in general and the best things in particular”) #

Point: the order of q. 11 illustrates his maxim that, given the limits of the human mind, one either considers all things in general and the best things in particular, or lesser things in particular. Articles 1-2 are about the one convertible with being (the most general); 3-4 about the best thing (God one, God most one, maxime). The two “go together, strange as it may seem.”

2. Article 1, objections and sed contra (“whether one adds something over being”) #

He reads the three objections and the sed contra:

1. Whatever is in a determined genus adds to being, which “covers all ten genera” (substance, quantity, quality, relation…). One is the beginning of number, a species of quantity, so it is “not as universal” and must add something.
2. What divides something common adds to it; being is divided by one and many.
3. If one added nothing, “one being” would be a nugatio, a mere repetition. His example: “I am a man” vs. “I am one man”: are you adding something or not? Sed contra: Dionysius, last chapter of the Divine Names: nothing among existing things fails to partake of the one; that would not be if one contracted being.

3. Body of a. 1: one adds only a negation, and is convertible with being (“so it guards its own unity”) #

Point: one adds to being no thing but only the negation of division, a being of reason.

• Beings of reason are either negations or relations of reason; good and true (later) add a relation of reason, one adds “merely a negation”.
• “Convertible” glossed logically: A and B are convertible if every A is B and every B is A; e.g. a thing and its definition (triangle / plane figure contained by three straight lines).
• Thomas’s either-or argument that every being is one: (1) every being is simple or composed; (2) the simple is undivided in act and in ability (a point: you “can’t cut a point in half”); (3) the composed does not exist so long as its parts are divided, only once they compose it (the chair’s parts not put together: no chair); conclusion: the being of each thing consists in undivision.
• The sign added to the argument: each thing guards its unity as it guards its being (an army divided is destroyed as an army).
• Aristotle shows this in Metaphysics IV. Back to objection 1: it would hold only if the one that begins number were the same as the one convertible with being, “but they’re not the same one.”

4. Digression: ascending to the most universal, and the two ones (“whatever exists must be somewhere”) #

Point: it is hard for the mind to rise from the one tied to the continuous to the one convertible with being.

• Wisdom proceeds oppositely to natural philosophy in two ways: toward the immaterial (not toward matter), and from the less universal up to the more universal (not general to particular). Clearest in Metaphysics IX: first part treats only the act called motion and abilities relative to it, second part ascends to act universally, opening other senses of ability; likewise the study of substance begins with material substances and ascends to a notion valid for separated substances.
• Most people are stuck on the lower level: Physics IV on place quotes the common Greek opinion that whatever exists is somewhere; “go out on Main Street” and that is still the opinion. His grade-school question “Where is God?”: being somewhere is a property of bodies, so what-is is being identified with body. Physics I: after dividing his predecessors’ opinions on the causes of natural things, Aristotle says their consideration of what-is went the same way, since natural bodies are more fundamental than artificial. Only with Anaxagoras, Plato and Aristotle does the mind separate the ideas of being and substance from body.
• Same pattern in one and many: the one first in mind is tied to the continuous, its negated division being division of the continuous; the more universal one negates the division of being and not-being. “This problem” returns at the Trinity.

5. Reply to obj. 1: Pythagoras/Plato vs. Avicenna (“I’ve got your number”) #

Point: confusing the two ones led great thinkers into contrary errors.

• Pythagoras and Plato: seeing the one convertible with being adds nothing but signifies the substance of being as undivided, they took the one that begins number the same way; since number is composed of unities, numbers are the substances of all things (“I’ve got your number”: an old Pythagorean speaking).
• Avicenna, contrariwise: seeing that the one beginning number adds something (else number would not be a species of quantity), he held the convertible one adds something to the substance of being, as white adds to man.
• He stresses: these are “very great thinkers… So you gotta stop and realize how easy one can be deceived.”
• Refutation: each thing is one through its very substance; if through something added, that too is one and would need another, and so forever, with “no stand in the first.”
• Conclusion: the convertible one adds only a negation (nothing in reality); the one beginning number adds something in the genus of quantity. Student remark: Thomas uses res (“some thing”) for what the numerical one adds, marking it as real. He agrees: contracting being into substance, quantity etc. adds something real; the convertible one adds nothing real but does add a negation.

6. Reply to obj. 2: one in one way, many in another (“nothing prevents that which is in one way divided”) #

Point: what is divided one way may be undivided another, and being is divided by one simply and many secundum quid.

• Divided in number, undivided in species (you and I one in species; you and the dog one in genus).
• One simply and many secundum quid: undivided in essence though divided in what lies outside the nature (one in subject, many in accidents: he is one subject but a geometer, white, healthy “more or less”); or undivided in act, divided in potency (one as a whole, many in parts).
• Conversely many simply, one secundum quid: divided in essence but undivided in notion or in origin/cause (many in number, one in species or origin).
• Multitude falls under being only by falling in some way under one. Dionysius’ list: many in parts one in whole; in accidents one in subject; in number one in species; in species one in genus; in “going forward” one in source.
• Heraclitus: wise to agree, listening not to me but to reason, that all things are one — but some simply, some in some way. His examples: twelve grandchildren, one family, one in their source (“you are responsible for all this”); citizens one in a country, not simply; an army dispersed is a crowd, no longer an army.
• Student: is “one in source” about the Trinity? No: it is like the family, or acts of intellect and will one in their source, the soul.
• “There’s that distinction again that we meet so often in philosophy” (simply / secundum quid).

7. Reply to obj. 3: not a nugatio, since one adds a negation in meaning (“This man is blind”) #

Point: “one being” is no repetition because one adds “undivided” secundum rationem, though a negation is nothing real.

• “This man is blind” adds nothing to the man; it is really something taken away, whereas “the man is healthy” adds something real. The mind takes the negation as a kind of being: “being as true”, Metaphysics V.
• Aside: number arises from the division of the continuous, and since the continuous is divisible forever, number goes on forever.

8. Article 2: objections, sed contra, body (“as the measure is to the measured”) #

Point: one is opposed to many, but the two ones are opposed to multitude in two different ways.

• Preliminary: understanding these most universal names requires seeing how they differ from each other (one adds “undivided” to being) and also their opposites: good/bad, true/false, one/many, “opposed in different ways”.
• Objections: (1) no opposite is said of its opposite, but every multitude is in some way one; (2) nothing is constituted from its opposite (“sickness making up health”), but one constitutes multitude; (3) one thing has one opposite (black/white, healthy/sick), and few is opposed to many; (4) if one is opposed to many as privation to habit, one would be posterior to and defined through multitude, yet multitude is defined by one: a circle in definition, “which is inconvenient”.
• Sed contra: things whose definitions are opposed are opposed; one’s notion is indivision, multitude’s contains division.
• Body: the one beginning number is opposed to multitude (number) as measure to measured, one being the first measure, number “a multitude measured by one” (Metaphysics X; the idea of measure is later carried over to other ones). The one convertible with being is opposed to multitude by privation, undivided to divided. “A very interesting distinction.”
• Aside: one may attach the consideration of God’s unity to God as measure of all things, or to simplicity, “very close together”. He notes the body is short and the detail is in the replies.

9. Reply to obj. 1: privation does not take away being entirely (“no privation takes away entirely being”) #

Point: opposites are not said of opposites, because one holds simply and the other secundum quid.

• Privation is a negation in a subject (the Philosopher): the cup does not see, but is not blind; everything in the room sees or does not see, but not everything sees or is blind. Blindness is non-being of the ability to see in a subject apt by nature to see: it takes away some being, not the subject.
• Because being is most common, the lack of being is founded in some being (the blind man exists), which does not happen with special forms (sight, whiteness): the blind man does not see.
• So too for one and good: privation of good founded in something good (the devil’s nature is good, his will disordered); removal of unity founded in something one; hence multitude is something one, the bad something good, non-being a certain being.
• But not simply: being as ability vs. act; substance vs. accidental being. “Am I or am I not?” I am, simply; I am not a pianist, in some way; I cannot both be and not be simply. The devil is bad simply, good in some way (“if it wasn’t so good; he would not have been tempted to make himself God”). Many are one in some way (their order), simply many; “not one and many in the same way.”

10. Reply to obj. 2: homogeneous and heterogeneous wholes (“no part of the house is a house”) #

Point: units constitute multitude by what they have of being, not by their indivision.

• Homogeneous whole: parts have the whole’s form (each part of water is water); such is the continuous. Heterogeneous whole: no part has the form of the whole (no part of a house is a house, no part of a man a man: “my arm or my leg, even my soul is not a man”); such is multitude.
• Bricks make a brick wall out of what is not a brick wall, but insofar as they are bricks, not insofar as they are not a wall. Aside: “next time you make some cake, brother”: a cake out of what is not a cake.

11. Reply to obj. 3: two meanings of “many” (“many is taken in two ways”) #

Point: many absolutely is opposed to one; many as implying excess is opposed to few; two are many in the first way, not the second.

• Rule from Aristotle’s Topics: more than one opposite means more than one meaning. “Liberal” opposed to stingy, to conservative, to servile, so several meanings.
• Application: in “a genus is a name said of many things other in kind”, many means more than one (a genus may have only two species: quantity into discrete and continuous), not many-as-opposed-to-few.
• Socrates in the Protagoras reasons from “one opposite each”: folly opposed to both wisdom and temperance, so they must be the same (the drunk acts foolishly).

12. Reply to obj. 4: the order being, division, one, many (“being, division, one, many”) #

Point: division precedes one in our way of understanding, not simply; one is in the definition of multitude, not the reverse, so no circle.

• We grasp simple things through composed (De Anima III). Stock example: Euclid’s point, “that of which there is no part”, or beginning of a line; body known affirmatively with length, width, depth; surface one negation, line two, point three (“position only”). Our reason’s object is something sensed or imagined, hence composed; the non-composed is known by negation, as q. 3’s eight articles showed God not composed in any way. Geometry interestingly goes the other way, simple to composed, “appropriate in geometry”.
• Avoiding the circle: divided things get the notion of multitude only by attributing unity to each; and division falls in understanding from the negation of being. So: first being; second this being is not that (division, distinction); third one, undivided being; fourth multitude. Student asks to draw out the third: one is being with division negated; multitude needs many ones, divided from one another yet each undivided.
• Aristotle was the first to understand the most universal things, which includes their distinction and order; “get your thoughts in order.”
• Aside: the dinner where De Koninck said praise Thomas, not me, and the Cardinal said praise Aristotle; Thomas a humble student of Aristotle and Augustine; Cajetan: he inherited the mind of the Church Fathers through reverence.

His words #

• all things in general and the best things in particular; his maxim on the basic choice in human thinking
• convertible; every A is B and every B is A
• undivided in act and in ability [ed.: potency]
• being of reason; negation or relation of reason
• Wisdom [ed.: Metaphysics]; Natural Hearing [ed.: Physics]
• nugatio, nugatoria; a mere repetition
• res; “some thing”, the real addition of the numerical one
• simply / secundum quid (in some way)
• being as true; the mind taking a negation as a kind of being
• multitude measured by one; his definition of number
• privation; negation in a subject apt by nature
• homogeneous / heterogeneous whole
• many as more than one vs. many as excess
• book on places [ed.: Topics]
• Common Doctor’s order: being, division, one, many

Texts #

Read in class

• Thomas, Summa Theologiae I, q. 11, a. 1 (objections, sed contra, body, replies)
• Thomas, Summa Theologiae I, q. 11, a. 2 (objections, sed contra, body, replies)
• Dionysius, Divine Names, last chapter (via Thomas)
• Heraclitus fragment on agreeing that all things are one (quoted)

Mentioned

• Aristotle, Metaphysics IV (being and one convertible), IX (act and ability), X (measure), V (being as true)
• Aristotle, Physics IV (place), I (predecessors)
• Aristotle, Categories (ten genera)
• Aristotle, Topics (one word, several opposites)
• Aristotle, De Anima III (simple known through composed)
• Plato, Protagoras (Socrates on virtues and one opposite)
• Euclid, definition of point (inferred: Elements I, def. 1)
• Thomas, Summa Theologiae I, q. 3 (simplicity of God)
• Cajetan on Thomas and the Fathers

His questions #

• “I am a man. I am one man. Are you adding something or not?” Yes in meaning (undivided), but nothing real: a negation.
• Convertible in logic means what? Every A is B and every B is A, as a thing and its definition.
• Is everything in this room either seeing or blind? No; everything sees or does not see, but blindness requires a subject apt to see.
• “Am I or am I not?” I am, simply; I am not a pianist, in some way.
• Is “one in their source” referring to the Trinity? (student) No; like a family, or acts of intellect and will one in the soul.
• What is a brick wall made out of? What is not a brick wall, but insofar as they are bricks.
• What does “many” mean in the definition of genus? More than one, opposed to one, not to few.
• How do we come to the third, one, after being and division? (student) One is being with division negated; multitude then needs many such ones.