21. The Ten Categories and the Five Predicables

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Lecture Notes

Main Topics #

The Ten Categories and Highest Genera #

• The ten categories represent the highest genera—fundamental divisions distinguishing how something can be said of individual substances
• Substance is the first and most fundamental category; the remaining nine (quantity, quality, relation, where, when, position, outfitting, acting upon, undergoing) are all said of or exist in individual substances
• Categories cannot be strictly defined since they have no genus above them; they are known through their species
• The word “being” is equivocal by reason, which explains why multiple highest genera exist

Substance: The First Category #

• Division of substance begins with material substance (encountered first in experience) versus immaterial
• Material divides into living and non-living
• Living divides into plant and animal
• Animal divides into beast and man
• Example: Socrates → man (species) → animal (genus) → living body → material substance → substance (highest genus)

Quantity: Discrete and Continuous #

• Discrete Quantity: Parts do not meet at a common boundary (e.g., numbers: 3 and 4 parts of 7 do not meet anywhere)
• Continuous Quantity: Parts meet at a common boundary
• Logical Definition of continuous: “a quantity whose parts meet at a common boundary”
  • Line: left and right sides meet at a point
  • Surface: parts meet at a line
  • Piece of chalk: parts meet at a plane
  • Time: past and future meet at the present moment (now)
• Natural Philosophy Definition of continuous: “that which is divisible forever”
• Discrete quantity (number) is not divisible forever; the unit cannot be further divided
• Main kinds of continuous quantity: line (one dimension), surface (two dimensions), body (three dimensions)
• The distinction is foundational to mathematics: arithmetic concerns discrete quantity; geometry concerns continuous quantities
• Euclid’s Elements reflects this: books 1-6 are plane geometry (line and surface), books 11-13 are solid geometry

The Immateriality of Intellect #

• Critical Argument: Our thoughts are discrete (like numbers), not continuous, even when thinking about continuous material things
• Principle: “Whatever is received is received according to the nature, the condition of the receiver”
• Conclusion: Since we receive continuous things (bodies) in a non-continuous way (discrete thoughts), the intellect must be immaterial
• This is one of the first arguments in Aristotle’s De Anima for the immateriality of universal reason
• The brain is not the organ of thought but related to it in some other way

Quality: Four Species #

Aristotle divides quality into four species:

1. Disposition/Habit (ἕξις, hexis): A firm disposition (e.g., virtue, vice)
2. Natural Ability/Inability (δύναμις, dynamis): Capacity to act (e.g., ability to digest, see, reason)
3. Sense Qualities (ποιόν, poion): Sensible properties (e.g., color, taste, temperature)
4. Figure/Shape (σχῆμα, schema): Spatial form

• Virtue and vice fall under the category of habit/disposition
• Moral virtue is not a natural ability, passion, or sense quality, but a disposition to act rightly
• Example: Temperance is not the ability to be hungry but a disposition to desire things moderately and reasonably
• Thomas Aquinas uses this framework in the Summa Theologiae, Prima Secundae when discussing moral theology

Relation (Towards Something) #

• Relations are based on something more fundamental
• Relations based on quantity: taller than, shorter than, equal to (presuppose quantity/size)
• Relations based on acting upon and undergoing: father-son, mother-son, teacher-student, mover-moved (presuppose qualities and actions)
• Teacher-student relation requires the teacher to act upon the student; mover-moved requires actual motion

The Remaining Six Categories #

Aristotle enumerates but does not extensively analyze:

• Where (place): Being in a room, being in Massachusetts
• When (time): Being this week, being this month
• Position (κεῖσθαι, keisthai): Arrangement of parts (standing, sitting)
• Outfitting (ἔχειν, exein): Things fitted on a person but not part of them (clothing, armor)
• Acting upon (ποιεῖν, poiein): Active relation
• Undergoing (πάσχειν, paschein): Passive relation

Key Arguments #

Why Highest Genera Must Exist #

• If every genus had a genus above it, infinite regress would follow
• Infinite regress prevents knowledge
• Therefore, highest genera must exist
• Multiple highest genera exist because “being” and “thing” are equivocal by reason

The Discrete Structure of Thought #

• Premise 1: All material things are continuous (divisible forever)
• Premise 2: Our thoughts are discrete, like numbers, not divisible forever
• Premise 3: When we think about continuous things, our thoughts remain discrete
• Conclusion: The nature of the receiver (intellect) must be immaterial, not the nature of what is received

Important Definitions #

• Substance (οὐσία, ousia): That which does not exist in another; individual things like Socrates, a horse, a cat
• Category (κατηγορία, kategoria): One of the ten highest genera; ways something can be said of individual substances
• Discrete Quantity (διακριτόν, diakriton): Quantity whose parts do not meet at a common boundary (e.g., number)
• Continuous Quantity (συνεχές, synechés): Quantity whose parts meet at a common boundary (e.g., line, surface, body)
• Disposition/Habit (ἕξις, hexis): A firm quality that inclines one to act in a certain way
• Natural Ability (δύναμις, dynamis): A capacity or power to perform certain actions
• Relation (πρός τι, pros ti): A way of being towards another thing

Examples & Illustrations #

Quantity Examples #

• A line: left and right sides meet at a point
• A surface: parts meet at a line
• A circle: diameter divides it into parts meeting at a line
• A piece of chalk: breaking it creates two parts meeting at a plane
• Time: past and future meet at the present moment (now)
• Number: 3 and 4 (parts of 7) do not meet anywhere

Quality Examples #

• Virtue and vice are habits/dispositions
• The ability to digest is a natural ability
• Red, blue, and green are sense qualities
• Being square or circular is figure/shape
• Temperance regarding food, drink, and sex

Relation Examples #

• “I am taller than you” (based on quantity)
• Father and son (based on acting upon and undergoing)
• Teacher and student (presupposes the teacher’s action upon the student)
• Mover and moved (presupposes actual motion)

Notable Quotes #

“Whatever is received is received according to the nature, the condition of the receiver. So it’s a sign that the reason is not a body, that it knows bodies, the continuous, in a non-bodily way, a non-continuous way.”

“If every genus had a genus before it, you’d have to know an infinity of things before you could know anything.”

“In a demonstration, you tend to prove a property of a species… The conclusion of a demonstration is stating the property of the species.”

Questions Addressed #

On the Structure of Categories #

• Q: How do we know where individual things like “Socrates” fit in the scheme of categories?
• A: By progressively dividing the highest genus (substance) through intermediate genera and differences until arriving at the species (man) that answers what he is

On Discrete vs. Continuous Quantity #

• Q: What is the difference between how discrete and continuous quantities are divisible?
• A: Continuous quantities are divisible forever (each part can be divided again into parts meeting at a boundary); discrete quantities (numbers) are not divisible forever—the unit cannot be further divided

On the Immateriality of Intellect #

• Q: Why is the fact that our thoughts are discrete rather than continuous a sign that reason is not material?
• A: Because all material things are continuous, yet we receive continuous things in a non-continuous way; this must be due to the nature of the receiver (intellect), not the nature of what is received (material bodies)

On the Status of Quality #

• Q: Under which species of quality do moral virtues fall?
• A: Under disposition/habit, not natural ability, passion, or sense quality—virtue is a firm disposition to act rightly