43. Porphyry's Isagoge and Aristotle's Categories

Subscribe in Podcast App | Download Transcript

Lecture Notes

Main Topics #

The Isagoge as a Distinction of Univocal Names #

• Porphyry’s Isagoge distinguishes five predicables: genus, difference, species, property, and accident
• These five represent a complete distinction of names said univocally of many things
• A univocal name is one said of many things with the same meaning in each case
• Example: “animal” said of dog and cat—both are living bodies with sensation

Univocal vs. Equivocal Names #

• Univocal names: Same meaning across all subjects (e.g., “animal” for all animals)
• Equivocal names: Different meanings across subjects (e.g., “bat” as flying mammal vs. sports equipment)
• Porphyry should have first distinguished univocal from equivocal names before subdividing univocal names into the five predicables
• Equivocal names can be further divided into:
  • Equivocal by chance (accidental homonymy)
  • Equivocal by reason (systematic homonymy)

The Five Predicables #

• Genus: That which is said of many differing in species, answering “what is it?”
• Difference: That which distinguishes within a genus
• Species: A combination of genus and difference
• Property: That which belongs to a thing through itself but is not part of its essence
• Accident: That which may or may not belong to a thing

The Categories Distinguished from the Isagoge #

• The categories are names said of individual substances in different ways, not univocal names of many things
• Thomas Aquinas divides the ten categories into three groups:
  1. Names said of individual substances as regards what they are → Substance
  2. Names said by reason of something existing in them, in addition to what they are → Quality, Quantity, Relation, etc.
  3. Names said by reason of something outside them → Where, When, Position, Possession, Action, Passion
• The categories and Isagoge are fundamentally different distinctions serving different logical purposes

Definition and the Logical Structure #

• A definition is speech (λόγος), not merely a name
• Definition must contain only the thing being defined and nothing else (a “tight fit”)
• Speech requires multiplicity—at least two parts that signify by themselves
• Definition makes something more distinct than a mere name

Substance and Accident in Relation to Definition #

• Substance can be defined by itself alone—it is a thing in itself
• Accident cannot be defined without bringing in that of which it is an accident—it is something of another
• This reflects a real distinction in things:
  • Substance has being in itself
  • Accident has being in another
• Definition may have two meanings:
  • Strict sense: contains only the thing being defined (substance)
  • Extended sense: contains the subject and what it is of that subject (accident)

Motion, Privation, and Degrees of Being #

• Motion is something of another (like accident), requiring reference to a subject
• Privation (e.g., blindness) requires reference to what is lacking (sight)
• Both motion and privation can be defined more distinctly than merely named, despite their dependence on another
• This shows that definition has degrees corresponding to different modes of being

Key Arguments #

Thomas Aquinas’s Disjunctive Argument (Summa Contra Gentiles) #

• Thomas proves no name is said univocally of God and creatures using a disjunctive syllogism:
  • Every name said univocally of many things must be either: genus, difference, species, property, or accident
  • Thomas eliminates each possibility for God and creatures
  • Therefore, no univocal predication obtains between God and creatures
• This argument relies on the completeness of Porphyry’s five predicables

The Problem of Definition and Being #

• If definition is limited to substance alone, accidents cannot be defined
• If accidents can be defined (as they can), then definition has two meanings
• This dual meaning of definition corresponds to a real distinction in things
• The inability to define something without reference to another reveals its metaphysical status

The Logical Basis for Metaphysical Distinctions #

• Differences in how things can be said (modi praedicandi) correspond to differences in being (modi essendi)
• The way the ten categories are distinguished—by how names are said of individual substances—reflects real differences in being
• Logic, proceeding by the way things are said, reveals metaphysical structure

Important Definitions #

Univoce (univocally) #

• A name said of many things with the same meaning in each case
• The meaning in mind is identical across all applications
• Example: “animal” said of dog and cat with the same meaning

Aequivoce (equivocally) #

• A name said of many things with different meanings
• Example: “bat” (flying mammal) vs. “bat” (sports equipment)

Praedicabilia (predicables) #

• Terms that can be predicated of (said of) many things
• The five predicables exhaust the ways a universal term can be said of many subjects
• Distinguished from the ten praedicamenta (predicaments/categories)

Ousia / Substantia (substance) #

• That which is not said of another subject
• That which answers the question “what is it?”
• In the Categories, Aristotle sometimes calls it “what it is” (ti esti)
• Substance is being in itself

Accidens (accident) #

• That which is said of another
• That which may or may not belong to a thing
• Accident is something of another—it has being in another

Logos (speech) #

• A composite utterance made of names
• More distinct than a single name
• Capable of signifying what a thing is

Examples & Illustrations #

Univocal Naming #

• Dog and cat are both called “animal” univocally
• Both are living bodies with sensation
• The same definition applies: a living body with sensation

Equivocal Naming #

• “Bat” as flying mammal vs. “bat” as sports equipment—completely different meanings
• “They weren’t batting very good last night” vs. “there are bats in the church”—different meanings of the same word

The Two Semicircles #

• Two semicircles meet at the diameter (the common boundary of a circle)
• Illustrates how the continuous is divisible and how spatial extension allows for multiplicity

Definition vs. Mere Naming #

• To say “point” is merely a name
• To say “the point is the limit of a line” or “the end of a line” is a definition
• The definition is more distinct because it brings in the relation to another (the line)

Motion as Something of Another #

• Walking is not motion itself; it is always something other than walking that walks
• Motion cannot be defined without reference to a subject in motion
• This is why modern philosophers (Descartes, Locke) who cannot define motion have missed its true nature

Multiple Individuals of the Same Kind #

• Many windows of exactly the same kind exist because of the matter (glass) and its extended quantity
• Many chairs of the same kind exist because of the matter (wood or metal) and its divisible quantity
• Because quantity is divisible, one individual can be here and another there

Angels and Inequality #

• No two angels are of exactly the same kind
• Unlike material substances, which can be multiplied by matter and quantity, immaterial substances are each unique
• Angels love each other more because of their inequality, not despite it
• The common good is better served by inequality than equality

Notable Quotes #

“When you say the dog is an animal, and you say the cat is an animal, I mean, I have the same meaning of animal in mind, a living body with sensation. I call it a dog an animal because it’s a living body with sensation. I call it a cat an animal for the same reason, exactly.”

“The Isagoge is about names said of many things univocally, okay? Meaning a name said of many things with the same meaning in mind in each case.”

“Either there is definition only of substance, because substance is not something of another, right? Or if you want to admit that there is in some way a definition of health, right? It brings in something other than health. Then you’re changing the meaning of definition.”

“A definition should contain only the thing being defined and nothing else, right?… So it should include only the thing being defined and nothing else. That’s a tight fit.”

“If a substance is not material, that doesn’t have length and width and depth, then the basis for there being many individuals of the same kind disappears.”

Questions Addressed #

Should Porphyry Have Structured the Isagoge Differently? #

• Question: Should Porphyry first distinguish univocal from equivocal names before subdividing univocal names?
• Answer: Yes. Monsignor Dian agreed that the logical structure would be more complete if Porphyry had first divided all names into univocal and equivocal, then subdivided univocal names into the five predicables, and also provided a subdivisions of equivocal names (equivocal by chance and equivocal by reason).

How Are the Isagoge and Categories Related? #

• Question: What is the relationship between Porphyry’s five predicables and Aristotle’s ten categories?
• Answer: Both distinguish names, but in fundamentally different ways. The Isagoge concerns univocal names said of many things. The Categories concern names said of individual substances in different ways. The distinction in the Categories proceeds from how something can be said of individual substances (modi praedicandi), which reflects different ways of being (modi essendi).

Can Accidents Be Defined? #

• Question: If definition requires that a definition contain only the thing being defined, how can accidents be defined when they necessarily involve reference to a subject?
• Answer: Accidents cannot be defined in the strict sense (as substance can be). However, accidents can be defined in a broader sense by specifying what they are of their subject. Definition thus has two meanings, corresponding to the two ways things exist: substances exist in themselves, while accidents exist in another.

Why Could Modern Philosophers Not Define Motion? #

• Question: Why did Descartes and Locke claim that motion cannot be defined?
• Answer: Because they failed to understand that motion is something of another (a type of accident). Once one recognizes that motion is always a motion of something, one can say what it is of something else and thereby give a definition more distinct than the mere name “motion.” Their failure reflects a deeper failure to understand substance and accident.

How Can a Point Be Defined if It Has No Parts? #

• Question: How can a point be defined when a definition requires multiplicity of parts, but a point has no parts?
• Answer: A point can be defined not by its own internal parts, but by its relation to another: as the limit or end of a line. Because the point is something of another (the line), one can bring in that relation and achieve the multiplicity needed for a definition.

Connections to Other Topics #

Logic as a Gateway to Metaphysics #

• Understanding univocal and equivocal naming is essential for understanding being
• The way things are said (modi praedicandi) leads to understanding the ways things are (modi essendi)
• Logic and natural philosophy are the two great sciences that lead us by the hand toward wisdom (metaphysics)

The Metaphysical Significance of the Categories #

• The ten categories are not merely logical conveniences; they reflect real distinctions in being
• Understanding how substance differs from accident through the lens of definition and predication prepares the way for understanding matter and form in natural philosophy

Natural Theology #

• Thomas Aquinas’s argument that no name is said univocally of God and creatures depends on the completeness of Porphyry’s five predicables
• Failure to understand univocal predication impairs the ability to make proper theological distinctions