40. Unity, Division, and God's Supreme Oneness

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Lecture Notes

Main Topics #

The Distinction Between “Many” and “One” #

• Every privation or lack does not entirely take away being; it presupposes a subject
• The distinction between a thing not seeing and being blind: blindness is a privation (absence of the power to see in a subject naturally apt to see), not mere negation
• Privation implies a subject capable of the perfection it lacks; negation does not
• Therefore, every privation of being is founded in some being
• This principle applies equally to being, one, and goodness (which are convertible with being)

Homogeneous vs. Heterogeneous Wholes #

• Homogeneous whole: composed of parts having the same form as the whole (e.g., water composed of water)
• Heterogeneous whole: parts lack the form of the whole (e.g., a house is not composed of houses; a man is not composed of men)
• Multitude is a heterogeneous whole, composed of units
• Units constitute multitude not insofar as they are not multitude, but insofar as they are beings (just as bricks constitute a brick wall insofar as they are bodies, not insofar as they are not brick walls)

The Ambiguity of “Many” #

• “Many” has two meanings:
  1. Absolutely: opposed to one (even two things are “many” in this sense)
  2. Implying excess: opposed to few (two things are not “many” in this sense)
• Following Aristotle’s rule in the Topics: if a term has multiple opposites, it has multiple meanings
• Example: “liberal” opposed to “stingy,” “conservative,” and “servile” indicates that “liberal” has multiple meanings
• Consequence for definitions: when defining genus as “a name of many things, other in kind,” the word “many” means “more than one” (opposed to one), not “many as opposed to few”

The Order of Understanding #

Berquist presents a crucial epistemological sequence:

1. Being - first grasped by the intellect
2. Division/Distinction - understanding that this being is not that being
3. One - understood as undivided being
4. Multitude - understood as a collection of ones

This order reflects how our minds ascend from composed to simple, contrary to geometry’s progression from simple to composed. The mind knows simple things through composed things (e.g., Euclid’s definition of point as “that which has no part” is known by successive negations from body: body has length, width, and depth; surface loses depth; line loses width; point loses all three dimensions).

Why Division Is Understood Before One #

• Division is understood from the negation of being itself
• One is undivided being; therefore, one cannot be understood without first understanding division (what division negates)
• However, multitude presupposes one, since multitude is a collection of ones
• Thus, the order of understanding places being first, then division, then one, then multitude

Three Demonstrations of Divine Unity #

1. From Divine Simplicity

• What makes something “this something” (an individual) cannot be communicated to many
• In creatures, what makes Socrates human (humanity) can be shared, but what makes him this man cannot be
• In God, His nature is identical with His being: God is His nature
• Therefore, it is by the same thing that God is God and that He is this God
• Hence, there cannot be many gods

2. From Divine Infinity of Perfection

• God comprehends in Himself the whole perfection of being
• If there were many gods, they would necessarily differ
• Any difference would mean one lacks a perfection the other possesses
• If this were merely a privation, that god would not be simply perfect
• If it were a perfection, the other would lack it
• Therefore, there cannot be many gods
• The ancient philosophers were “coerced by truth itself” to posit only one infinite beginning

3. From the Unity of the World Order

• All things are ordered to one another
• Diverse things come together in one order only through one ordering principle
• One is the cause of unity through itself (per se)
• Many cannot cause something one except accidentally, insofar as they are themselves in some way one
• What is first must be through itself, not by accident, and therefore most perfect
• Therefore, the first principle ordering all things must be one only, which is God

God Is Most Supremely One (Maxime Unus) #

The Two Conditions for Supreme Unity

• For something to be supremely one, it must be: (1) most being, and (2) most undivided
• God satisfies both conditions:
  • Most being: God is not a being having some determined essence; He is to-be-itself subsisting (ipsum esse subsistens): “I am who I am”
  • Most undivided: God is simple in every way—neither divided in act nor divisible in potency, in any way whatsoever
• Therefore, God is supremely one

Response to Objection: Privation Admits No Degrees

• Objection: privation does not admit of more or less, so God cannot be “more one” than other things
• Response: while privation itself admits no degrees, that which is opposed to privation (undividedness) does
• According as something is more divided, divisible, or not divisible at all, it is said to be less one, more one, or supremely one

Response to Objection: Point and Unit Are Indivisible

• Objection: a point and a mathematical unit are indivisible in act and in potency, and thus should be most one
• Response: the point and the unit (beginning of number) are not supremely beings (maxime entia) because they exist only in a subject or as accidents
• Neither exists as the subject itself; the subject is not supremely one due to the diversity of accident and subject
• Therefore, neither point nor unit is supremely one

Important Definitions #

Privation (Privatio) #

• The absence of a form or quality in a subject capable of having it
• Distinguished from mere negation: blindness (privation in a seeing creature) vs. not seeing (a cup does not see but is not blind)
• Presupposes a subject and a natural aptitude for what is lacking
• Removes some being but not the subject itself

Negation #

• A pure absence without any implication of a subject or capacity
• The negation of division that constitutes “one” is a negation, not a privation
• Negations can be known by our intellect even though they add nothing real to a thing

Secundum Quid vs. Simpliciter #

• Simpliciter (simply): in an absolute, unqualified sense (I am a man)
• Secundum Quid (in some way): in a qualified, partial sense (I am not a pianist)
• The same thing cannot both be and not be in the same respect: what is good simpliciter may be bad secundum quid, and vice versa
• The devil is bad simpliciter but good secundum quid (his nature)

Mathematical One vs. Transcendental One #

• Mathematical one: the beginning of number, something in the genus of quantity; adds a real thing to being
• Transcendental one: convertible with being itself; adds only the negation of division, not a real thing
• The transcendental one is a being of reason (ens rationis)—a mental construct without existence outside the mind

Examples & Illustrations #

Blindness vs. Not Seeing #

• Everything in the room either sees or does not see (negation always applies)
• Not everything in the room is either seeing or blind (blindness requires a subject naturally apt to see)
• Blindness is the non-being of the ability to see in a subject apt to see by nature

Successive Negations in Geometry #

• Body: has length, width, and depth
• Surface: has length and width, but not depth (one negation)
• Line: has length only (two negations)
• Point: has none of these dimensions (three negations)
• We know the simple point through composed bodies by successive negations

The Devil and Mixed Predicates #

• The devil is bad simpliciter (in his will, which has a disorder)
• The devil is good secundum quid (his nature is something good)
• If his nature were not good, he would not have been tempted to make himself God
• This illustrates that even in evil things, good (being) is foundational

Bricks and the Brick Wall #

• A brick is not a brick wall
• A brick wall is composed of what are not brick walls (bricks)
• Yet bricks constitute a brick wall through what they are (bodies), not through what they are not (walls)
• This shows multitude is composed from units; units do not constitute multitude qua non-multitude but qua units

Questions Addressed #

Can One Be Opposed to Multitude? #

Objection: Every multitude is in some way one; therefore, one and multitude are not truly opposed.

Resolution:

• No privation or complete lack takes away all being
• Though blindness is a lack, the blind thing still exists
• The multitude has unity (is undivided in itself); this unity is founded in being
• One is opposed to multitude as undivided is opposed to divided
• Multitude’s unity is secondary; the dividing is primary
• Therefore, one and multitude are not opposed in the sense that multitude is entirely bereft of unity

Does One Constitute Multitude? #

Objection: Nothing opposed is constituted from its opposite; but one constitutes multitude; therefore, one is not opposed to multitude.

Resolution:

• Multitude is a heterogeneous whole (parts lack the form of the whole)
• Multitude is composed from units, but not insofar as they are post-multitude (not insofar as they exclude multitude)
• Rather, units constitute multitude insofar as they are beings
• Just as bricks constitute a brick wall through being bodies, not through being non-walls
• The parts do not constitute the whole through their negation but through their positive reality

Is “Many” Ambiguous? #

Objection: If “many” has multiple opposites (opposed to one in one sense, opposed to few in another), then “many” has multiple meanings.

Resolution:

• Following Aristotle’s rule in the Topics: a term with multiple opposites has multiple meanings
• “Many” as opposed to one means “more than one” (applicable even to two)
• “Many” as opposed to few implies an excess (two is not “many” in this sense)
• In defining genus as a predicable of many things other in kind, “many” means the former sense (more than one)
• Therefore, a genus can have as few as two species (e.g., quantity divided into discrete and continuous)

Why Can God Be Said to Be “One” If One Implies Privation? #

Objection: One implies a negation of division, which is a privation; all privation is an imperfection; therefore, God cannot be one.

Resolution:

• The one convertible with being is not the mathematical one (beginning of number), which does have quantity
• The transcendental one is metaphysical and depends not on matter according to its very being
• Although God has no privation, we know God through privation or removal (negation) according to the mode of our understanding
• Nothing prevents things being said privatively of God (e.g., incorporeal, infinite, above all)
• One adds to being only the negation of division, which is a being of reason, not a real imperfection
• The word “privation” moves from a strict sense (an imperfection) to a lesser sense (a mere negation) by dropping out parts of its meaning
• When applied to God, we retain the sense of undivided being without the sense of imperfection

Is God More One Than Other Things? #

Objection: Privation admits no degrees of more or less; therefore, God is not more one than other things.

Resolution:

• While privation itself does not admit degrees, that which is opposed to privation (undividedness) does
• According as something is more divided, more divisible, or not divisible at all, it is said to be less one, more one, or supremely one
• God is supremely undivided and supremely being; therefore, supremely one

Objection: The point and the mathematical unit are indivisible in act and potency; if one is said to be more one insofar as more indivisible, God is not more one than these.

Resolution:

• The point and unit are not supremely beings (maxime entia) because they do not have being except in a subject or as accidents
• A subject is not supremely one due to the diversity between accident and subject
• Neither point nor unit is supremely one

Objection: What is essentially good is most of all good; what is essentially one is most of all one; but every being is one through its very nature; therefore, every being is most of all one.

Resolution:

• The argument conflates simple oneness with supreme oneness
• The conclusion that every being is one through its very nature is true
• But not every being is supremely one; supreme oneness requires supreme being and supreme undividedness
• Only God, who is supreme being (ipsum esse subsistens) and absolutely simple, is supremely one

Notable Quotes #

“Thomas, in that sense, was a very humble student of Aristotle. He wasn’t afraid to learn from Aristotle or from St. Augustine.” — Berquist, on Thomas’s intellectual humility

“One is not opposed to the multitude [in the sense that] every multitude is in some way one.” — Thomas Aquinas, cited approvingly by Berquist

“Many is taken in two ways. In one way, absolutely, and thus it is opposed to the one. In another way, insofar as it implies a certain excess. And thus it is opposed to the few.” — Thomas Aquinas, Summa Theologiae I, Q. 11, A. 2, ad tertium

“That by which some singular is a this something in no way is communicable to many.” — Thomas Aquinas, Summa Theologiae I, Q. 11, A. 3

“I am who I am.” — God to Moses (Exodus 3:14), cited as expressing divine being

“Hear, Israel, the Lord your God is one.” — Deuteronomy 6:4, cited as the fundamental text for divine unity

“Among all things which are said to be one, the unity of the divine Trinity holds the high point.” — Thomas Aquinas, citing Bernard of Clairvaux, Summa Theologiae I, Q. 11, A. 4

“You can’t avoid that distinction between simply and not simply.” — Berquist, emphasizing the importance of the simpliciter/secundum quid distinction