11. Substance, Equivocation, and the Division of Categories

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Lecture Notes

Main Topics #

The Division of Substance vs. Other Categories #

• Aristotle divides quantity into discrete and continuous species
• Aristotle divides quality into various species
• But: Aristotle does NOT divide substance into species like material vs. immaterial substance
• Why? Material and immaterial substances cannot share the same genus in the strict sense
  • Genus derives from matter; immaterial substances have no matter
  • Reason cannot easily separate what experience never separates
  • Knowledge of immaterial substances requires wisdom (metaphysics), not logic
  • Such a division is inappropriate for an introductory logical treatment

First Substance vs. Second Substance #

• First substance: Individual existing things (this man, this dog)
  • Neither said of another nor existing in another
  • Primary bearer of existence and predication
  • Most truly called “substance”
• Second substance: Species and genera (man, animal, living thing)
  • Said of first substances
  • Not existing in another, but said of another
  • Species more substance than genus (closer to first substance)
• This distinction differs from the anti-predicaments distinction of singular vs. universal
  • Anti-predicaments: establishes the distinction based on predicational properties
  • Categories, Chapter 5: adds order to the distinction
  • Pedagogical progression: see distinction first, then recognize the order

Equivocation by Reason vs. Equivocation by Chance #

• Equivocal by chance: Multiple meanings with no connection or order
• Equivocal by reason: Multiple meanings where an order exists among the senses
  • One meaning is primary or more known
  • Other meanings relate to the first through likeness or proportion
  • Example: substance as first substance (primary) vs. substance as second substance (derivative)
• The word “substance” applied to first and second substance is equivocal by reason, not univocal
  • Both are truly substance, but in ordered, non-identical ways
  • Not purely equivocal because there is real connection and order

Understanding Equivocal Words as Necessary #

• Critical question: Is it necessary to understand words equivocal by reason?
• Answer: Yes, because fundamental axioms and concepts rely on such words
  • Cannot understand axioms about whole and part without distinguishing their senses
  • Cannot grasp basic logical or metaphysical discourse without this skill
  • Modern philosophers fail to do this systematically
  • Example: Marx’s dialectical materialism never distinguishes the senses of “opposite” despite making it central

Key Arguments #

Why Substance Cannot Be Divided Like Quantity #

1. Genus is constituted from matter; difference from form
2. Material and immaterial substances do not share the same matter
3. Without shared matter, they do not share the same genus in the proper sense
4. Therefore, dividing substance into material/immaterial would be division by diverse ways of being, not division into species
5. This sophisticated distinction belongs to wisdom (metaphysics), not logic

The Whole-Part Paradox and How Equivocation Resolves It #

• Apparent contradiction: Animal is only part of what man is (man = rational animal + animality)
  • Yet animal is said of man, dog, cat, horse, elephant
  • So how can the part (animal) include more things than the whole (man)?
• Resolution through equivocation: “Whole” and “includes” have different meanings
  • Universal whole: Predicated of its parts (animal said of many things)
  • Composed whole: Put together from parts (man composed of animality + rationality)
  • In the universal sense: the whole is said of more than its parts
  • In the composed sense: the whole is more than one of its composing parts
  • Both statements are true when senses are distinguished

The Necessity of Distinguishing Senses Before Recognizing Order #

• Pedagogical principle: one must first perceive distinction before perceiving order
• Example: Singular vs. universal substance (distinction) comes before first vs. second substance (order)
• Understanding order requires prior grasp of what is being ordered
• This explains why Aristotle emphasizes distinction in the anti-predicaments, then adds order in the Categories

Important Definitions #

Key Greek and Latin Terms #

• Ὑσία (ousia): Substance; literally “what stands under”; connection to “understanding” (hypostasis as standing under in the mind)
• Λόγος (logos): Thought, definition, or rational principle
• Τὸ τί ἦν εἶναι (to ti ēn einai): “What it was to be”; essence or quiddity; what a thing is
• Ἐν ὑποκειμένῳ (en hypokeimenō): Existing in another as in a subject
• Κατὰ (kata): According to; used in phrases like “said of according to diverse ways of being”
• Divisio analogi: Division by diverse ways of being (analogical division), not into species

Substantive Definitions #

• First substance: Individual thing that exists in itself, neither said of nor existing in another; the primary subject of predication
• Second substance: Species or genus said of first substances; universal substance
• Equivocal by reason (ὁμώνυμα λέγεται, homonuma legetai): Name shared by multiple things where meanings are ordered and connected through similarity or proportion
• Universal whole: A universal predicated of multiple particulars (e.g., animal said of man, dog, cat)
• Composed whole: A composite made from parts (e.g., man from rationality and animality)

Examples & Illustrations #

The Man-Animal Example #

• Mother objected to calling man “an animal”
• Clarification: “Man is not just an animal; he’s an animal that has reason”
• Response: “That’s better, Duane”
• Illustrates that while man is said of animal, man is more than animal alone
• Shows how equivocation resolves apparent contradiction: animal is part of man’s definition but predicated of things beyond man

Guardian Angel Example #

• Question: “Where would you put your guardian angel?”
• The very question uses “where,” placing it in a genus (space/place)
• Illustrates how we necessarily use categories and their primary sense (place) even when extending analogically
• Leads to Thomas’s ordering of the eight senses of “in” (ἐν, en)

The University Building Joke #

• A person shows another three university buildings: building A, building B, building C
• The second person asks, “Now where is the university?”
• Answer: “It’s in all these buildings”
• Illustrates that the whole can be “in” the parts in an analogical sense
• The whole is to parts as form is to matter

Translator vs. Trader Wordplay #

• Berquist paraphrases Plato: “Until philosophers are kings or kings are philosophers, you will have bad government”
• Adapts it: “Until philosophers are translators or translators are philosophers, you will have [bad translations]”
• Emphasizes importance of philosophical precision in translation and interpretation

Notable Quotes #

“Reason has difficulty separating things that are never separated in its experience.” — Berquist, explaining why early philosophers identified substance with body

“You have to see a distinction before you can see an order.” — Berquist, on the pedagogical progression in Aristotle

“Things seen are a glimpse of what is not seen.” — Hank Seager (cited by Berquist), on analogical knowledge

“Too late have I come to know thee, thou ancient beauty.” — Saint Augustine, Confessions (cited by Berquist, likely Book 10, regarding beauty as object of knowledge)

Questions Addressed #

Why doesn’t Aristotle divide substance into species like he divides quantity? #

• Because material and immaterial substances do not share the same genus (matter is constitutive of genus)
• Knowledge of immaterial substances requires wisdom/metaphysics, not logic alone
• It would be inappropriate for an introductory logical work
• Instead, Aristotle divides substance by diverse ways of being, not into species

Is the distinction between first and second substance a division of genus into species? #

• No — Thomas clarifies this is a “divisio analogi” (analogical division)
• Nothing is contained under second substance that is not in first substance
• Rather, it divides by diverse ways of being (modes of existence)
• First substance signifies nature as individually subsisting
• Second substance signifies nature of genus absolutely/universally

How can animal be “part” of man yet be “predicated of” things man is not? #

• Requires distinguishing two senses of “whole”:
  • Universal whole: The species/genus is said of more things (animal said of man, dog, cat)
  • Composed whole: The composite is more than one of its parts (man more than animality alone)
• Both statements are true under their respective senses
• Failure to distinguish leads to apparent contradiction known to sophists

Is calling both first and second substance by the name “substance” purely equivocal? #

• No — it is equivocal by reason with ordered senses
• First substance is primary; second substance is derivative
• Species is more substance than genus
• There is a real connection and order among the meanings
• This illustrates why understanding equivocation by reason is essential to logic

Key Methodological Points #

• Pedagogical order matters: Aristotle presents distinction before order, beginning with the anti-predicaments
• Equivocation is not defect but necessity: Modern philosophers fail by ignoring equivocal words by reason, leading to confusion
• Proportionality structures analogical thinking: The likeness of ratios (whole to parts as form to matter) is how we extend terms across domains
• Experience shapes metaphysical understanding: We cannot easily separate what experience never separates (substance from body) until we have reason to do so