40. Composition, Parts, and Divine Simplicity

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Lecture Notes

Main Topics #

Equivocation of ‘Composition’ and ‘Parts’ #

• The word ‘put together’ (compositio) originally applies to continuous quantities where parts have common boundaries and can exist independently
• This primary meaning is then extended analogously to other domains: matter-form, genus-difference, universal wholes
• Understanding this equivocation is crucial for defending metaphysical axioms from sophistic objections
• The term is equivocal ‘by reason’ (aequivocum a ratione)—not purely homonymous but sharing a proportional likeness across applications

Four Meanings of ‘Part’ in Aristotle’s Metaphysics V #

1. Quantitative parts (continuous or discrete): parts with common boundaries that can exist separately
2. Matter and form: not truly ‘put together’ in the first sense; form actualizes matter’s potentiality
3. Genus and difference: components of a definition, which are distinguished but not independently existing things
4. Universal whole and its particulars: said of many particulars, not composed from them

Composed Whole vs. Universal Whole #

• A composed whole is put together from parts that can exist independently (e.g., bricks in a wall, semicircles making a circle)
• A universal whole (like ‘animal’ said of man, dog, horse) is said of more than any one of its particulars but is not put together from them
• This distinction is critical: Aristotle teaches we know things confusedly before distinctly by examples of composed wholes, but he then makes a direct comparison (proportio) to the universal whole
• The axiom “the whole is greater than the part” applies differently to each type

Matter-Form Composition #

• Matter-form is unlike quantitative composition: the parts (matter and form) do not have common boundaries and cannot exist separately
• Yet we can say they are ‘put together’ in an analogous sense—they meet or coincide (like genus and difference in a definition)
• The crucial distinction: form actualizes matter’s potentiality; matter is the potential, form is the actualizing principle
• Example: removing form from matter (e.g., reason from man) leaves only the material principle (animal/beast), showing matter cannot exist actually without form

Numbers as Discrete Quantity #

• Numbers exemplify a middle ground between continuous and matter-form composition
• Composing parts of a number: Two and three are composing parts of five (we say “five is put together from two and three”)
• Subject parts of a number: Two is a subject part of even number (as man is a subject part of rational animal)
• The parts of numbers do not have common boundaries like continuous quantities, so they cannot be ‘put together’ like bricks or semicircles
• Instead, order actualizes the collection: the seventh one makes the collection be seven; the eighth one actualizes the potentiality of seven ones to become eight
• This is analogous to form actualizing matter: the ones are like matter (potential), the order/form is what makes them be one actualized whole

God’s Simplicity and Six Types of Composition #

Thomas’s Summa Theologiae I, Q.3 demonstrates God is not composed in six ways:

1. Not body (no quantitative composition)
2. Not composed of matter and form
3. Not composed of essence and existence (the third composition, analogous to matter-form)
4. Not composed of substance and accidents
5. Not composed of genus and difference
6. No universal whole composition (not three gods but one God)

The Problem of Universal Whole Composition in Trinitarian Theology #

• Muslims object to Christianity as polytheism because Christians speak of Father, Son, and Holy Spirit
• The error: treating the Trinity as if it were a universal whole with three parts (three particular gods)
• The truth: The Father, Son, and Holy Spirit are not distinguished by anything absolute but only towards each other (ad aliquid—a relational distinction)
• This is why Aristotle’s categories include Post-tee (relation/ad aliquid): something that exists not in itself but towards another
• Therefore, Father + Son + Holy Spirit are not more than the Father; their distinction is purely relational, not absolute or quantitative
• God cannot have parts even in the sense of universal wholes because God’s essence and existence are identical, allowing only one God

Key Arguments #

Against Equivocation in Philosophy #

• The Chaucer-Shakespeare example: “Chaucer came before Shakespeare” (in time) but “Shakespeare is before Chaucer” (in quality/greatness) seems to prove Chaucer is before himself—contradicting the axiom that nothing is before itself
  • Resolution: The word ‘before’ is equivocal; one must distinguish the senses to avoid sophistical conclusions
• The ‘part greater than whole’ sophism: Man = animal + reason; animal includes dog, cat, horse; therefore a part (animal) includes more than the whole (man)
  • Resolution: ‘Part’ is equivocal. When animal is a part of man, it means a composing part of the definition. When animal includes multiple species, it is a universal whole, which always extends to more particulars than any one of them. These are different senses of ‘whole’ and ‘part’

Numbers Actualize Potentiality #

• Seven ones are potentially eight; the eighth one actualizes this potentiality
• One cannot become eight in one step; strictu sensu, one can only become two, two can become three, etc.
• When we “add” seven and one to make eight, we are actualizing the potentiality, not merely calculating
• This parallels matter-form composition: matter is potential, form actualizes it
• The grandchildren analogy: The seventh grandchild made seven grandchildren (actualizing the potentiality). If an eighth comes, the eighth will actualize the potentiality to be eight. The seventh did not constitute the form of the other six; rather, the seventh actualized the whole collection’s being seven.

The Importance of Understanding Word Meanings #

• Aristotle is praised as the first and almost the last man to fully understand the words he uses everywhere
• Without knowing the multiple meanings of common words (whole, part, composed, before, after), one cannot defend axioms or understand metaphysics and theology
• This is a prerequisite for wisdom: “If you know the meanings of the words you use, you are wise. If you don’t know the meanings of the words you use, then you’re not wise.”

Important Definitions #

Compositio (composition/putting together): The joining of parts; equivocal term applied primarily to continuous quantities (where parts have common boundaries and can exist separately) but extended analogously to matter-form, genus-difference, and other domains.

Quantitative whole: A whole composed of parts that have common boundaries and can exist independently; can be either continuous (with common point, line, or surface) or discrete (with no common boundary, like numbers).

Composed whole (totum compositum): A whole put together from parts; differs from universal whole in that it is made up of its parts rather than said of them.

Universal whole (totum universale): A whole said of many particulars but not put together from them; always extends to more instances than any single particular (e.g., ‘animal’ is said of man, dog, horse, etc.).

Post-tee (Latin: ad aliquid; Greek: προς τι): A relational quality or category; something that exists not absolutely in itself but towards or in relation to another thing. Applied to Father-Son distinction in Trinity.

Order (ordo): In the context of numbers and form, that which actualizes a collection of potential units into a unified whole; analogous to form actualizing matter.

Ability and act (potentia et actus): Matter is potential (able to be), form is the actualizing principle; used to explain both matter-form composition and number composition.

Examples & Illustrations #

Continuous Quantity: Chalk and Shape #

• The chalk and its shape are really distinct (can change shape without changing chalk)
• But they cannot exist separately (cannot put shape here and chalk there)
• Therefore, they are distinct but not independent parts

Discrete Quantity: The Brick Wall #

• Bricks are put together by cement; each brick can exist independently
• This exemplifies the primary meaning of ‘put together’
• Contrasts with matter-form, which cannot be separated even though they are distinct

Numbers as Neither Fully Quantitative nor Matter-Form #

• Two and three are parts of five; five = two + three
• But the ones cannot be put together like bricks (no common boundary)
• Instead, order/form actualizes the collection, like form actualizes matter
• Adding ones to seven makes eight by actualizing potentiality, not merely calculating

The Grandchildren Analogy (Extended) #

• Berquist has seven grandchildren; the seventh grandchild made them seven
• The first grandchild (Kate) was special but did not make seven
• The seventh actualized the potentiality of becoming seven
• Similarly, when an eighth child arrives, that child actualizes the potentiality to be eight
• The point: order and the actualizing principle (the last one, the form) make the collection one unified whole

The Foursome and Cards Game #

• Three people need a fourth person to play cards or golf
• When the fourth arrives, that person makes it “a foursome”
• The fourth does not constitute the form of the other three but actualizes the being-four of the whole group

Letters and Words (CAT, ACT, TAC) #

• The letters C, A, T can form different words depending on order
• Order is like form; the letters are like matter
• This shows discrete composition is not like quantitative parts put side-by-side but like matter-form
• What makes them be one word is the order, not material contact

Islamic Misunderstanding of Trinity #

• Muslims see “Father, Son, Holy Spirit” and think: three gods = polytheism
• This treats Father, Son, and Holy Spirit as three absolute, independent beings (three particular gods)
• But they are distinguished only relationally—each defined by its relation to the others, not by absolute qualities
• Therefore, they do not form a universal whole with three parts

Questions Addressed #

How can God be said to have ’no composition’ when there are real distinctions in God? #

Resolution: Because ‘composition’ is equivocal. God has no composition in the primary sense (quantitative parts with common boundaries). The other senses of composition (matter-form, essence-existence, genus-difference, substance-accidents, universal whole) are all denied by understanding them analogously rather than univocally. Each is shown to be inapplicable to God for different reasons.

What is the relationship between continuous composition and matter-form composition? #

Resolution: They are both called ‘composition’ by analogy. In continuous composition, parts have common boundaries and can exist separately. In matter-form, parts have no common boundary and cannot exist separately. Yet both involve a joining of principles. Matter-form is closer to definition (genus-difference) than to quantitative joining because form actualizes potential, not merely contacts matter.

How do numbers exemplify composition? #

Resolution: Numbers are discrete quantities; their parts (ones) do not have common boundaries like continuous quantities. Yet they are still ‘put together’ because order actualizes the collection into a unified whole, similar to how form actualizes matter. The seventh one makes seven; the eighth one actualizes the potentiality to be eight.

Why is the Trinity not polytheism? #

Resolution: Because the Father, Son, and Holy Spirit are not distinguished by absolute properties but only towards each other (relational distinctions). They are not three particulars under one universal (universal whole composition) nor three independent substances. Their distinction is purely relational (ad aliquid), so Father + Son + Holy Spirit = one God, not three gods.

How can we avoid sophistical arguments about wholes and parts? #

Resolution: By understanding the multiple meanings of ‘whole,’ ‘part,’ and ‘composed’ in Aristotle’s Metaphysics V. Sophistical arguments mix these senses equivocally. Once distinctions are clear, apparent contradictions dissolve.