39. Composition, Parts, and God's Simplicity

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Lecture Notes

Main Topics #

The Equivocity of Composition and Parts #

• The word compositio (composition) originally means ‘placing together’ or ‘putting together’ (from Latin componere)
• This primary meaning derives from continuous quantities where parts can exist independently and are brought together with common boundaries
• The term is then carried over analogically to other types of wholes that lack these characteristics
• Understanding this equivocity is critical for avoiding sophistic arguments and theological confusion

The Continuous vs. Discrete Distinction #

Continuous Quantities:

• Parts have common boundaries that coincide when put together
• Example: Two semicircles form a circle; two triangles form a parallelogram
• These parts can exist independently as individual substances

Discrete Quantities (Numbers):

• Parts do not have common boundaries
• Two ones cannot be ‘put together’ the way two semicircles are
• Yet they are not composition in the strict sense of independent parts brought together
• Numbers display a different kind of unity based on order

Four Types of Composition in Creatures (from Summa Theologiae, Question 3) #

Thomas Aquinas identifies six articles negating different types of composition found in creatures:

1. Quantitative Composition - God is not a body with quantitative parts
2. Matter-Form Composition - God has no composition of materia and forma
3. Nature-Individual Composition - God’s nature and individual existence are identical
4. Substance-Existence Composition - God’s substance and existence are identical
5. Genus-Difference Composition - God is not in any genus and has no differences
6. Substance-Accident Composition - God has no accidents

Article 7 shows universally that God has no composition; Article 8 shows God does not enter into composition with anything else.

The Problem of Number and Order #

• When we say “five is composed of two and three,” we use composed in a fundamentally different sense than “a circle is composed of two semicircles”
• Numbers cannot have common boundaries like continuous quantities
• Yet they possess a kind of order that actualizes potential
• Seven ones are able to become eight through the addition of one
• The form of a number appears to be the order itself, not any individual unit
• This mirrors the matter-form relationship: the ones are like materia (matter); the order is like forma (form)

Ability and Act in Numbers #

• In the strict sense, you are able to be something only when you are one step away from it
• Example: Two is able to be three; three is able to be four; but two is not strictly able to be four
• In reasoning: A student can strictly know C only after knowing B, not from knowing A alone
• The added one actualizes what was potential in the previous number
• This structure—ability being made actual by the addition of form to matter—applies to all natures

The Analogy of Numbers to Natures (following Plato and Aristotle) #

From Aristotle’s Metaphysics, Book VIII:

• Just as adding or subtracting one from a number gives a different number, adding or subtracting properties gives a different nature
• Body = one; Body + Life = two (plant); Body + Life + Sensation = three (animal); Body + Life + Sensation + Reason = four (man)
• Remove reason from man → you have an animal, not a man
• This shows that natures are structured with hierarchical order and composition

Key Arguments #

The Sophistical Argument About Parts and Wholes #

The Puzzle:

• “Animal is a part of man’s definition” (animal is a composing part)
• “Animal includes man, dog, cat, horse” (animal as universal whole)
• Conclusion (sophistic): “A part includes more than the whole”

The Resolution: The argument equivocates on pars (part) and totum (whole). Two distinct senses are conflated:

• Composing part (definitional): Animal is a genus composing the definition of man
• Universal whole: Animal as a universal is said of all animals, hence includes more individuals than any one species

These are fundamentally different relationships and cannot generate a contradiction.

Why Letters and Order Matter #

• The letters C, A, T form different words depending on order: CAT, ACT, TAC
• The letters are identical; the order makes them different
• Order functions as form, actualizing the potential of the letters
• This demonstrates that composition is not merely “putting together parts” but involves the ordering principle

God’s Simplicity and Composition #

• God differs absolutely from creatures in having no composition whatsoever
• Creatures have multiple types of composition; God has none
• God’s essence and existence are identical (not composed of substance and existence)
• Therefore, God cannot have parts in any sense

Important Definitions #

Compositio (Composition) #

Primary meaning: Placing together things that can exist independently and have common boundaries (continuous quantities)

Extended meaning: Any kind of whole made up of parts, including:

• Matter-form wholes
• Genus-difference wholes (definitions)
• Discrete quantities (numbers)
• Universal wholes

Key principle: The word is equivocal and must be understood differently depending on context. Failing to recognize this leads to sophistic arguments.

Pars (Part) #

• A part is always something imperfect
• The whole is always more perfect than any of its parts
• Types include quantitative parts, composing parts (in definitions), and subject parts (particulars of universals)

Totum (Whole) #

• Composed whole: Made up of parts that are brought together
• Universal whole: Said of its parts rather than composed from them

Ordo (Order) #

• In numbers and definitions, order functions like form
• The order of elements makes a difference in what the whole is
• Order actualizes the potential of the elements

Examples & Illustrations #

The Word ‘Cat’ #

Letters C, A, T can be arranged as:

• CAT (the animal)
• ACT (the action)
• TAC (abbreviation)

The same letters in different order produce different wholes. The order is the form that actualizes the potential of the letters.

Continuous vs. Discrete Assembly #

Continuous: Two semicircles put together form one circle because their boundaries coincide at the diameter

Discrete: Two ones cannot be put together the way two semicircles are because they have no boundaries. They remain “two ones,” never becoming “one two.”

The Grill Assembly Problem #

• Unassembled grill arrives with many parts and assembly directions
• Parts can exist independently before assembly
• Putting them together produces a new whole
• This illustrates the primary meaning of composition (continuous, with common boundaries)

The Foursome Example #

• Three people need a fourth to make a foursome
• The fourth person “makes” them four
• This illustrates how adding one actualizes the potential of the previous number

Rectangle Perimeter vs. Area #

Historical example: Old “crooked geometers” would sell land by perimeter, not area

The principle: A rectangle with dimensions 5×5 has perimeter 20 and area 25. A 2×10 rectangle has perimeter 24 but area only 20. More fence (perimeter) can enclose less land (area). This shows we are easily deceived about common sensibles (size, shape) when not directly perceiving them.

Notable Quotes #

“The word ‘part’ is always something imperfect, and that’s an extremely important thing to see.”

“If you don’t know the meanings of the words you use, then you’re not wise.”

“Aristotle is really the first man to fully understand the words he uses everywhere.”

“Rubber is able to be a rubber ball—you have to add a form of a certain kind to it, and then it becomes actually a rubber ball.”

Questions Addressed #

How can we defend God’s simplicity against the charge that creatures are composed? #

God’s absolute simplicity means God has no composition whatsoever, unlike creatures which have multiple types. God’s essence and existence are identical; in creatures they are distinct. This is the fundamental difference.

How can the Trinity be one God if there are three persons? #

The Father, Son, and Holy Spirit are distinguished only relationally (ad aliquid = “towards another”), not absolutely. Their distinction is not in themselves but in their relations to each other. Therefore, they do not constitute three parts or three gods, but one God with three relational distinctions. (This protects against the Muslim misinterpretation of Christianity as teaching three gods.)

What is the difference between putting together continuous quantities and matter-form composition? #

In continuous quantities, parts exist independently and are brought together with common boundaries. In matter-form composition, matter cannot exist without form, and form cannot actualize any matter—only matter of a specific type. Matter and form cannot be “put together” the way continuous parts are; rather, form actualizes the potential inherent in matter.