19. Reasoning, Definition, and the Categories of Being

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Lecture Notes

Main Topics #

Reasoning vs. Definition #

• Reasoning: Coming to know or guess a statement through other statements, by calculation (adding, subtracting, multiplying, dividing)
• Definition: Coming to know what you don’t know through what you do know; the art of understanding the simple unknown
• Both are ways of knowing through what is already known, though they differ in their operations
• Sometimes reasoning involves only probable premises, making the conclusion a “guess” rather than certain knowledge
• Not all reasoning is syllogistic; one can reason without necessary conclusions (e.g., “I had a bad meal last week, so it will be bad this week”)

Albert of Great’s Division of Logic #

• Logic divides into two arts: definition (art of the simple unknown) and reasoning (art of the complex known)
• Anticipated by Plato in the Meno: the dialogue explores how one can investigate what one doesn’t know
• The middle part of the Meno addresses what’s common to both: how can you come to know what you don’t know?

Relative Distinctions in Science #

• The same thing can be both genus and species, but in relation to different things
• Examples: double/half (mathematics), father/son (biology), cause/effect (metaphysics), mover/moved (physics)
• The same object can be both mover and moved in relation to different things (e.g., a book in a line being moved by one and moving another)

The Four Senses of “Before” and Their Application #

• Second sense: in being (one thing can exist without another)
• Third sense: in the discourse of reason (genus comes before species in how we naturally think)
• Fourth sense: in worth or value (some goods are better than others)
• Fifth sense (crowning sense): in causality (cause comes before effect)
• Application to genre and species: genus is prior to species in the third sense (discourse of reason), not the second

The Genus and Species Relationship #

• The genus is said of more things than the species
• The genus naturally comes first in our reasoning (students naturally begin with genus when defining: “A dog? Well, it’s an animal”)
• Question: Does every genus have a genus above it, or are there highest genera?
• Question: Is every species also a genus of something, or are there lowest species?

Lowest Species and Natural Kinds #

• Mathematical examples (clearest cases): Square, circle, seven have no subspecies; different squares are distinguished by accidental properties (size, color), not by species
• Natural examples (less clear): Whether dog or cat is a lowest species depends on whether differences create true species or merely accidental distinctions
• Biologists’ rule of thumb: Reproductive compatibility determines a species
• Man as lowest species: Race distinctions (white, black, etc.) are accidental to being human, not creating true species, because they don’t establish different kinds of reason
• True species must have differences that determine something intrinsic to the genus, not merely external properties

Application to Human Nature and Reason #

• If there were species of man in the strict sense, there would have to be different kinds of reason
• Different races do not have fundamentally different kinds of reason
• Heisenberg’s post-war reflections on international cooperation in physics disproved Nazi ideology about racial differences in intellect
• Philosophy is not essentially Greek, even though Greeks excelled in it; reason transcends any single language or culture
• Language differences (articles, verb forms) make some languages more suitable for certain philosophical expressions, but philosophy itself is not language-dependent

Language and Translation Issues #

• Greek articles mark distinctions that Latin cannot (e.g., “the evil one” vs. generic “evil”)
• The Our Father: Greek says “deliver us from the evil one” (τοῦ πονηροῦ with article), but Latin must render it as “from evil” (a malo)
• John’s Gospel: The Greek word πρός (pros, “toward”) in “the Word was toward God” carries relational significance crucial for understanding the Trinity
• Some languages lack a verb “to be,” making certain philosophical expressions difficult
• Medieval Latin added articles artificially (e.g., “L-Y”) to compensate for this deficiency

The Ten Categories #

• Aristotle’s enumeration: Ten highest genera
  1. Substance (primary; everything else depends on it) 2-10. Accidents: Quantity, Quality, Relation, Place, Time, Position, State, Action, Passion
• Thomas’s analytical approach: Rather than listing ten immediately, Thomas divides into two or three, then subdivides, arriving at the ten through a more transparent method
• Two main texts: Categories and Topics both list the same ten in the same order

The Division of What Is Said of Substances #

Things said of individual substances (like Socrates, Champion the horse, Moppet the cat) can be divided as follows:

By Reason of What They Are (Essential) #

• Said of the substance by reason of what it essentially is
• Examples: “Socrates is a man,” “Champion is a horse,” “Moppet is a cat”
• Progressively more general: man → animal → living body → body → substance
• Gives rise to the category of substance (the highest genus)

By Reason of Something in Them (Accidental - Internal) #

Things existing in the substance as modifications, further divided:

Absolutely (in itself, not toward another):

• Said by reason of something inherent in the substance
• Examples: healthy, sick, beautiful, ugly, big, little, wise
• Connected to matter and form: material substances have accidents because they are material

Toward Another (πρός τι / ad aliquid)

• Relational properties that define a thing by its relation to another
• Examples: father (toward son), double (toward half), mover (toward moved)
• These are subsisting relations

By Reason of Something Outside Them (Accidental - External) #

• Said of the substance by reason of something not inherent in it
• Example: “Socrates is clothed” (clothing is outside him, not in him)
• The Greek term is ἔξεσθαι (hexesthai), which Berquist translates as “outfitting”
• Eventually divided into six categories, though Thomas treats these more briefly

Quantity as Distinct from Substance #

• Key distinction: Quantity is something material substances have, but it is not what they are
• To be a man and to be five feet ten are not the same thing
• Being bigger than another man does not make you “more a man”
• Historical error: The Pythagoreans and Platonists confused quantity with substance; Descartes repeated this in modern philosophy
• Theological implication: Confusing quantity with substance contradicts the doctrine of transubstantiation
  • In the Eucharist, the substance of bread becomes the substance of Christ’s body
  • The accidents (quantity, sensible qualities) remain
  • If quantity were substance, the substance would remain, undermining transubstantiation

Truth and Theology #

• A philosophy is useful in theology because it is true, not true because it is useful
• Aristotelian philosophy is compatible with faith because it accurately describes reality
• Descartes’s philosophy is false not because it contradicts theology, but because it is false; the false contradicts the true
• The Euthyphro question applied to divine commandments: Are things good because God commands them, or does God command them because they are good?
  • Some commandments are good in themselves (honor father and mother, do not kill)
  • Some commandments are arbitrary but must be consistent (drive on right side of street)

Key Arguments #

The Infinite Regress Problem #

• If every genus had a genus above it, one would need to know infinitely many things before knowing anything
• This would make definition impossible
• Yet we clearly do come to know things through definition (e.g., odd/even numbers, geometric figures)
• Conclusion: There must be highest genera that are not species of anything

The Most Universal Names Argument #

• There are most universal names that cannot have anything more universal said of them: “being,” “thing,” “something”
• These names exhaust the possibilities (either think of the nature or don’t; either follows upon the nature or doesn’t)
• If every genus had a genus above it, there would always be a name said of more things
• Conclusion: There must be highest genera

The Equivocity of Being #

• “Being” and “thing” are not said univocally of all things
• A man and a dog are “things” in the same way (both substances)
• A man and his health are not “things” in the same way
• This distinction is not merely nominal but reflects real metaphysical differences
• Conclusion: There must be multiple highest genera, not one

Important Definitions #

Reasoning (λογισμός / ratiocinium) #

• Coming to know or guess a statement through other statements
• Operates by calculating: adding, subtracting, multiplying, dividing
• May involve only probable premises, yielding probable conclusions
• Not always syllogistic; conclusion may not follow necessarily even if premises are certain

Definition (ὅρος / definitio) #

• Coming to know what one doesn’t know through what one does know
• The art of understanding the simple unknown
• Naturally proceeds from genus to species in human cognition

Substance (οὐσία / substantia) #

• That which is said of individual substances by reason of what they are
• The highest genus; what exists in itself, not in another
• All other categories depend on substance for their being
• Examples: individual man, individual horse; universally: man, animal, living body, body

Accident (συμβεβηκός / accidens) #

• That which is said of individual substances by reason of something other than what they are
• Either something existing in them (quality, quantity, relation) or something outside them
• Cannot exist independently; requires a substance as subject

Highest Genus #

• A genus that has no genus above it
• A name said of more things than any other name
• Not every genus is a highest genus; lower genera are both genera and species

Lowest Species #

• A species that is not a genus of anything else
• Has no subspecies distinct by essential differences
• Not every species is a lowest species; higher species are both species and genera
• In mathematics: square, circle, seven
• In nature: possibly man (if racial distinctions are accidental)

Relative Distinction (distinctio secundum rationem / προς τι) #

• A distinction that holds only in relation to something else
• The same thing can be both relata (both mover and moved, both father and child) in relation to different things
• Examples: double/half, cause/effect, mover/moved, predicate/subject

Equivocal by Reason (ἀναλογικῶς / analogice) #

• A term having multiple meanings that are related through a common reference point
• Being is equivocal by reason because its meanings (substance, quantity, quality, etc.) all relate back to substance as primary
• Contrasts with purely equivocal terms (like “bank”) which share no common reference

Examples & Illustrations #

Reasoning About a Party #

• How many people will attend? About 25 (uncertain)
• How much will each person drink? About 4 beers (uncertain)
• Calculation: 4 × 25 = 100 beers
• The conclusion is rigorously calculated, but the premises are only probable, so the conclusion remains a “guess”
• Shows that even correct mathematical operations on uncertain premises yield uncertain results

Non-Syllogistic Reasoning #

• “I had a lousy meal at Restaurant X last week, so I shouldn’t go there this week”
• The person may be certain about the past fact, but the conclusion doesn’t follow necessarily
• One bad meal doesn’t guarantee another bad meal
• This is reasoning, but not necessarily valid reasoning

Defining a Dog #

• When asked to define a dog, students naturally start: “Well, it’s an animal…”
• This shows the genus comes first in the order of our reasoning
• Then they would add the specific difference: “an animal that…”

Mathematical Lowest Species #

• Square: There are different squares (large, small, red, blue), but these are accidental distinctions
• Different squares don’t create subspecies because color and size don’t determine the essential nature of being square
• A square is fundamentally defined by having four equal sides and four right angles; this admits no subspeciation
• Similarly: circle (no types of circles, only circles of different sizes or colors) and seven (seven things of different kinds, but not different kinds of seven)

Man as Lowest Species #

• The question: Are white men, black men, and other racial groups different species of man?
• Answer: No, because they don’t have fundamentally different kinds of reason
• Reason is what defines humanity (man = rational animal)
• Racial differences affect appearance (accidental properties), not reason (essential property)
• This refutes racial pseudoscience and Nazi ideology about “master races”

Heisenberg on Reason Transcending Culture #

• Heisenberg recalled his student days in Copenhagen under Niels Bohr
• Scientists from all nations and cultures studied together
• Japanese physicists not only learned physics from Westerners but made original contributions
• This demonstrates that reason is not culturally or racially limited
• Philosophy and science belong to humanity as such, not to any particular people

Philosophy and Language #

• Heidegger said “philosophy speaks Greek” — a compliment to Greek contributions
• But philosophy is not by definition Greek or English
• Some languages have more explicit grammar (more parts of speech, articles) making them more suitable for philosophical discourse
• Latin lacks articles; medieval philosophers artificially added them (e.g., “L-Y”)
• This may be the origin of French articles (le, la)
• Despite linguistic variations, philosophy remains universal

The Lord’s Prayer Translation Issue #

• Greek: ἀλλὰ ῥῦσαι ἡμᾶς ἀπὸ τοῦ πονηροῦ (“deliver us from THE evil one” — masculine with article)
• Latin: et libera nos a malo (“and deliver us from evil” — neuter without article)
• The Greek article (ὁ, ἡ, τό) is absent in Latin, so translators render it as generic “evil” rather than “the evil one”
• This matters: the evil one (the devil) is more specific than evil as an abstraction
• Shows how language structure affects philosophical and theological precision

Clothing as External Accident #

• I am clothed: clothing is said of me, but it exists outside me, not in me like health
• Unlike quality (wisdom) or quantity (size) which inhere in the subject, clothing is purely external
• Yet I am still correctly said to be clothed
• This exemplifies accidents that are extrinsic to the substance

Man’s Hand as Tool of Tools #

• Animals are given specific tools by nature: claws, horns, stingers, wings
• Man is not given these specific tools; instead, he has a hand
• The hand can use an infinity of different tools: shovel, axe, rake, knife, fork, spoon, screwdriver, key, car, fire extinguisher
• Because there is no limit to what man can do, there is no limit to the tools he might need
• The hand corresponds to reason, which is unlimited (like the mind described in Anaxagoras’s fragment)
• Aristotle correctly notes that man has a hand because he is most intelligent, not that he is intelligent because he has a hand
• Just as the hand enables use of infinite tools, reason enables infinite knowing

Man’s Lack of Natural Clothing #

• Man is not given by nature the fur or natural covering that other animals have
• Additionally, man desires variety in clothing (women’s fashion especially; men tend to wear the same clothes repeatedly)
• Clothing is therefore an extrinsic accident — said of man but existing outside him
• This reflects man’s rational nature and capacity for self-determination

Questions Addressed #

What is the relationship between reasoning and definition? #

• Both are ways of coming to know through what is already known
• Definition operates on the simple unknown (what a thing is)
• Reasoning operates on the complex known (whether a proposition is true)
• Reasoning sometimes yields only probable conclusions; definition seeks essential understanding

Does every genus have a genus above it? #

• No. If it did, one would face infinite regress, making knowledge impossible
• There must be highest genera that are not species of anything
• Examples: substance (highest genus of essence), and the other categories

Is being said univocally or equivocally of all things? #

• Equivocally by reason (analogice)
• Being means something fundamentally different when said of substance versus accident
• A man and his health are not “beings” in the same sense; substance is primary being
• This equivocity is why there cannot be a single highest genus of being

Are there lowest species in nature? #

• Possibly: Man may be a lowest species (no true subspecies based on reason)
• Ambiguity in biology: Whether dog, cat, or species is lowest depends on reproductive capability
• Clear in mathematics: Square, circle, seven have no subspecies
• For something to be a true species, differences must be intrinsic to the genus, not accidental

How do substance and accident differ metaphysically? #

• Substance exists in itself; accident exists in another
• This is not merely logical but reflects real modes of being
• All accidents depend on substance for their existence
• Substance is primary being; everything else depends on it

How does this relate to transubstantiation? #

• If quantity were identical to substance (Cartesian error), the substance would not change in the Eucharist
• Because quantity is distinct from substance, the substance can change while accidents remain
• The bread’s substance becomes Christ’s body; the quantity (appearance, taste, texture) remains as accident
• Aristotelian metaphysics alone preserves the coherence of Eucharistic doctrine

Notable Quotes #

“The genus is always said of more than the species, so if every genus had a genus before it, there’d always be a name said of more than any word or name.”

“Coming to know or guess — why do I say guess? Because sometimes when we add, subtract, multiply, or divide numbers correctly, we’re not always sure of the numbers we’re adding.”

“Either think of the nature or not think of the nature. If it follows upon the nature or doesn’t follow upon the nature, it’s got to be one or the other.”

“Students naturally begin with the genus before the species — you ask them ‘What’s a dog?’ and they say ‘Well, it’s an animal.’”

“There are no different kinds of square. There are different kinds of quadrilateral, but not different kinds of square.”

“If there were species of men in the strict sense, it would have to be different kinds of reason. Does the white man really have a different kind of reason?”

“Philosophy speaks Greek — that’s a compliment to the Greeks. But philosophy is not by definition Greek.”

“Being is not true because it’s useful in theology, but it’s useful in theology because it is true.”

“If your quantity was your substance, then when your quantity changed, you no longer have the same substance. So you never grew up.”

“Nature has given man a hand — the tool of tools — which corresponds to reason, which is unlimited.”

“Instead of having every tool, man has a hand that can use an infinity of different tools. There’s no end to the tools that man might require.”