20. God Not in a Genus: Article 5 on Divine Simplicity

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Lecture Notes

Main Topics #

The Structure of Article 5 #

• Part of the systematic elimination of six kinds of composition in God
• Follows articles eliminating: quantitative composition, matter-form, essence-individual, essence-existence
• This article eliminates composition of genus and difference
• Directly related to showing God is not in any genus and therefore has no definition

Two Ways of Being in a Genus #

1. Simply and Properly (simpliciter et proprie): As a species contained under the genus
   • Example: Dog is in the genus Animal
2. By Reduction (per reductionem): As a principle or privation of the genus
   • Example: Soul (principle of substance), Point (beginning of continuous quantity), One (beginning of discrete quantity)
   • Example: Blindness (privation of the quality vision)

The Distinction Between Points and Ones #

• Similarity: Both are indivisible and beginnings
• Key Difference in Ratios:
  • One can have to a number the same ratio that a number has to a number: 1:2 = 2:4 = 3:6
  • A point cannot have to a line the same ratio that a line has to a line
  • Therefore, one is closer to being a number than a point is to being a quantity
• Mathematical Evidence: Line is not composed of points, but number is composed of ones
• Euclid’s Theorem: In the theorem about numbers in the least ratio, Euclid must extend the word ’number’ to include one—an analogous (not purely equivocal) use

Key Arguments #

First Argument: Species Constituted from Genus and Difference #

• Species is constituted from genus and difference
• The “wherefore” of difference always stands to the “wherefore” of genus as act to potency
• Porphyry notes: genus is to difference as matter is to form
• Examples of act-potency relationship in genus-difference:
  • Animal (sensitive nature) to Rational (intellectual nature): intellectual is to sensitive as act to potency
  • Each case of genus and difference manifests this relationship
• Conclusion: Since God is pure act with no potency, He cannot be a species in any genus

Second Argument: Being Cannot Be a Genus #

• God’s being is His essence (proven in Article 4)
• If God were in some genus, that genus would have to be Being
• But Aristotle shows in Book III of the Metaphysics that being cannot be a genus
• Reason: Every genus has differences outside the nature of the genus, but no difference can be found outside being
• Non-being cannot be a difference (difference must be something)
• Conclusion: God is not in the genus of substance or any other genus

Third Argument: Being vs. Existence in Genera #

• All things in one genus share the nature/essence of that genus (predicated as “what it is”)
• But they differ in their being/existence: the being of man ≠ the being of horse, the being of this man ≠ the being of that man
• Principle: Whatever things are in a genus must differ in their existence while sharing a common nature
• In God: existence and nature are identical (no difference)
• Conclusion: God is not in a genus as a species

On God Not Being in a Genus by Reduction #

• The beginning that is reduced to a genus does not extend beyond that genus
  • Point: beginning only of continuous quantity
  • One: beginning only of discrete quantity (number)
• God is the beginning of all being (as will be shown below)
• Conclusion: God is not in a genus even by reduction as a principle

Important Definitions #

Genus (γένος / genus) #

• From Logic: “The name predicated of many things differing in kind, or in species, in answer to the question ‘what is it?’”
• Signifies the essence or nature of a thing
• In Aristotle’s framework, substance is the first and primary genus

Species (εἶδος / species) #

• A particular kind of thing placed under a genus
• The genus is predicated of the species in answer to the question “what is it?”
• Examples: Dog under Animal; Virtue under Habit; Justice under Virtue

Difference (διαφορά / differentia) #

• The distinguishing feature that determines how a genus is divided into species
• Always stands to genus as act to potency
• Cannot be predicated in answer to “what is it?” but rather indicates how the thing is

Substance (οὐσία / substantia) #

• First sense (Aristotle’s proper usage): An essence to which belongs the property of existing in itself, not in another
• Distinguished from accident, which exists in another
• In the notion of substance: a distinction between the thing (its nature) and its being
• God cannot be in the genus of substance because God’s nature and existence are identical

Predicament (praedicamentum) #

• Latin for the ten highest genera (categories of Aristotle)
• From the English development: “predicament” now means a difficult situation from which there is no escape
• Philosophical parallel: Once something is in a genus (predicament), it cannot escape to another category
• Example: Man (substance) cannot become a quality instead

Examples & Illustrations #

The Soul in the Genus of Substance #

• Question: Is the soul a substance, or a part of a substance, or a principle of a substance?
• Answer: The soul is a principle of a substance
• Nevertheless: The soul is reduced back to the genus substance (even though not “simply and properly” a substance)
• Distinction: A principle differs from a species but shares in the genus through reduction

Blindness and Privation #

• Blindness is a privation of sight
• Reduced to the genus Quality (as the lack of a quality)
• Not “simply and properly” a quality but by reduction as a privation

Point as Beginning of Continuous Quantity #

• Point is the beginning of a line
• A line is a species of continuous quantity
• Is the point itself a quantity? No
• Yet it is reduced to the genus of quantity as its principle
• Unlike quantity, a point has no parts

The One and Number #

• Is one itself a number? No
• Yet one can have to two the same ratio that two has to four (1:2 = 2:4)
• This shows one is closer to number than a point is to quantity
• In contrast: A point cannot have to a line the same ratio that a line has to a line
• Therefore: One is more like a number (as a beginning) than point is like quantity

Shakespeare’s Understanding of One and Number #

• The Phoenix and the Turtle: “Love has made the lover and the loved one”
• “Therefore it’s murdered number”
• Shakespeare’s insight: Understands that one is not itself a number
• Personal example: “I don’t have a number of wives, as I tell my students. Or a number of heads. I have a number of arms, a number of legs, because two is the first number.”

Triangle in General vs. Particular Triangles #

• Universal concept of triangle: open to equilateral, scalene, and isosceles
• The universal is not actually any one of these but is able to be all of them
• Analogy: Like wood that can be made into a chair, table, or door
• Wood is not actually any of these until it receives its form
• Problem with Locke and Anaxagoras: Both struggle with the notion that genus must contain all its differences virtually
• Anaxagoras: puts everything in matter, causing logical problems
• Locke: makes the universal idea of triangle all or none of the particular triangles

Implications for Theology #

Why God Has No Definition #

• Definition is composed of genus and difference
• God is not in any genus
• God has no differences
• Therefore: God has no definition (definitio)
• Consequence: There is no demonstration (demonstratio) of God (in the Aristotelian sense)
  • Because the middle term in a demonstration is a definition
  • And definition depends on understanding what genus a thing belongs to

The Reply to the First Objection #

• Objection: Substance means “existing by itself” (ens per se), which belongs most to God; therefore God is in the genus substance
• Thomas’s Reply: The term “substance” signifies not only existing by itself, but rather an essence to which it belongs to exist in this way
  • That is, a thing whose nature is such that it has this kind of being (in itself, not in another)
  • But being itself cannot be a genus
  • Therefore, God is not in the genus of substance

The Key Distinction in Substance #

• In creatures: There is a distinction between the nature of a thing and the existence it has
• In God: Nature and existence are identical
• Conclusion: The notion of substance as a category requires this distinction; since God lacks it, God is not in any genus
• In the Summa Contra Gentiles: More explicitly developed—substance is “a thing whose nature belongs to it not to exist in another”

Questions Addressed #

Why doesn’t Thomas have a separate question eliminating God as a universal whole? #

• In the discussion of wholes (composed vs. universal), the question arises why Thomas doesn’t explicitly ask about God and universal wholes
• Answer: This is implicitly addressed in the question on God’s unity (where it is shown there is only one God, not many gods)
• Thus both kinds of wholes are eliminated: no composed whole (Article 3-4), and no universal whole (shown when proving God is one)

How does understanding the Isagoge relate to this article? #

• Central to the lecture: Understanding Article 5 requires knowledge of:
  • What genus is
  • What species is
  • What difference is
  • Porphyry’s distinctions (the predicables)
• Berquist laments: “Most philosophers I run into now have not read the Isagogi. And some of them have not even heard of it.”
• Without the Isagogi: One cannot understand why God is not in a genus
• The name: Isagogi is Greek (Εἰσαγωγή) meaning “introduction” (Latin: introductio)
• The text is an introduction to the Categories of Aristotle but useful for understanding predication universally