17. The Five Predicables: Genus, Species, Difference, Property, Accident

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Lecture Notes

Main Topics #

The Five Predicables: Exhaustive Division of Names #

Names said with one meaning of many things are divided into two categories:

Names signifying something INSIDE the nature:

• Genus: Said of many things other in kind, signifying what it is in a general way
• Species: A particular kind under a genus; the lowest species is said of many individuals (not other in kind), signifying what it is
• Difference: Said of many things other in kind, signifying how they are what they are (not what it is)

Names signifying something OUTSIDE the nature:

• Property (ἴδιον/idiosum): Connected to and follows upon nature as an effect; belongs to one species, to every member, and always
• Accident (συμβεβηκός/bebekos): Not connected to nature; something that “happens” to a thing

The Utility of Property vs. Accident in Definition #

Though definition concerns what a thing is, the five predicables are studied because:

1. Property has two-fold relevance to definition:

   • One can reason from property back to difference (from effect to cause)
   • One can use property in place of difference for an imperfect definition when the true difference is unknown

2. Accident is useless for both defining and investigating essential differences

Example: “Man is capable of laughter” uses a property (following from being rational), not the essential difference. “A triangle is green” uses an accident with no connection to triangularity.

Absolute vs. Relative Distinctions #

Two fundamentally different kinds of distinction:

Absolute distinction: A distinction in itself; the same thing cannot be both

• Example: Man/woman, odd/even numbers
• The distinction is intrinsic

Relative distinction: A distinction toward another; the same thing can be both in relation to different things

• Examples: Father/son (same man to different people), double/half (4 is both double of 2 and half of 8), whole/part, cause/effect
• The distinction is extrinsic and relational

Critical application: The distinction between genus and species is a relative distinction, not absolute. Therefore, the same name can be both a genus and a species:

• Quadrilateral is a species relative to rectilineal plane figure
• Quadrilateral is a genus relative to square, rhombus, oblong

This is not subjective or imprecise—it is exact and certain.

Ultimate Questions from Relative Distinctions #

Once one recognizes relative distinctions, profound questions arise:

On causality and series:

• Is every son also a father? Is there a father who is not a son? (Adam as potential example)
• Is every cause an effect? Is there a cause that is not an effect?
• Is every premise a conclusion? (If so, infinite knowledge would be required)

On composition:

• Is every part a whole? Is every whole a part?
• Is there a whole that is not a part? (Leads to cosmology—study of the universe as a finite whole)
• Is there a part that is not a whole? (Leads to atomic physics—search for indivisible particles)

On logic itself:

• Does every genus have a genus above it? Or is there a highest genus?
• Does every species have a species below it? Or is there a lowest species?

The Necessity of a Highest Genus and Lowest Species #

There must be a highest genus—one that is not a species of anything else. If every genus had a genus above it, infinite knowledge would be required to know anything.

There must be a lowest species—one that has no species below it and is not itself a genus.

Definition of lowest species: A name said with one meaning of many individuals (not other in kind), signifying what it is.

• Example: Circle is a lowest species (all circles have the same essential shape)
• Example: Square is a lowest species (all squares have the same shape)
• Counterexample: Isosceles triangle is NOT a lowest species (isosceles triangles vary in shape—some acute, some obtuse)

Grammar vs. Logic: Two Different Orders #

The grammatical order of words in English often reverses the logical order:

• Grammatically, “a rational animal” places the adjective (rational) before the noun (animal)
• Logically, the genus (animal) comes first in our understanding; the difference (rational) comes second
• A child asked “What is a dog?” answers “animal” first, then adds “four-footed” as a difference
• In Latin or Greek, one can express logical order more flexibly; in English, grammatical conventions may obscure logical priority

The logical order depends on understanding—one must understand the genus before grasping why certain things count as differences of it.

Key Arguments #

The Completeness of the Five Predicables #

The five predicables exhaust all possible names said with one meaning of many things:

1. A name either signifies something inside the nature or outside it
2. If inside the nature:
   • Either what the thing is (genus/species)
   • Or how it is what it is (difference)
3. If outside the nature:
   • Either connected to nature and following upon it (property)
   • Or not connected to nature (accident)

This division is complete and exhaustive with no overlap.

Why Property Is Useful for Definition Despite Being Outside the Nature #

Though accidents are useless for definition, properties are useful because:

• A property is connected to and follows upon the nature
• The property can serve as a “starting point” for reasoning back to the essential difference
• When one does not yet know the true specific difference, a property can substitute for an imperfect definition
• Example: “Man is a magician” (property) can lead investigation to the essential difference: rational animal
• The property thus functions as a sign pointing toward the interior nature

Why Multiple Differences Are Necessary #

A single difference is often insufficient because:

• In geometry: Equilateral alone doesn’t define square (rhombus is equilateral but not square)
• Right-angled alone doesn’t define square (oblong is right-angled but not square)
• Only the combination “equilateral AND right-angled quadrilateral” is convertible with square
• This reflects how humans know things: from confused (external accidents) to distinct (internal essences)
• Each difference removes some confusion, getting closer to the complete specification

Relative Distinctions and Series #

When a distinction is relative (not absolute), one can ask whether the series is infinite or has endpoints:

• Physics example: Quantum theory investigates whether there is a part that is not a whole (indivisible particles)
• Cosmology example: General relativity suggests the universe is finite, implying a whole that is not a part of anything
• Arithmetic example: In numbers, there exists a number that is “half” but not “double” (e.g., 3 is half of 6 but double of 1.5 if fractions allowed; but considering only integers, 3 is half of 6 but not double of any integer). However, in straight lines (continuous magnitudes), one can always extend further in both directions
• Genealogy example: There may be sons who are not fathers, but Adam (if he existed) would be a father who is not a son

Important Definitions #

Genus (γένος/genus) #

A name said with one meaning of many things other in kind, signifying what it is in a general way.

• Example: Animal (genus of dog, cat, horse)
• Contrast: Said of things different in kind, not merely different individuals

Species (εἶδος/species) #

When compared to a genus above it: A name of a particular kind under a genus, signifying what it is more specifically.

When at the lowest level: A name said with one meaning of many individuals (not other in kind), signifying what it is.

• Example: Dog (lowest species, said of this dog and that dog, not other in kind)
• Example: Quadrilateral (species relative to rectilineal figure; genus relative to square)

Difference (διαφορά/differentia) #

A name said with one meaning of many things other in kind, signifying how they are what they are (the manner of being, not the essence itself).

• Example: Rational (difference of man from other animals)
• Contrast: Signifies mode or quality, not the fundamental nature

Property (ἴδιον/idiosum) #

A name signifying something outside the nature but connected to it and following upon it.

In the strictest sense: Belongs to one species only, to every member of that species, and always.

• Example: “Capable of laughter” (proper to man)
• Example: “Interior angles equal to two right angles” (proper to triangle)
• Example: “Half of four” (proper to the number two)

In a looser sense: Any name connected to nature even if not uniquely and always.

• Example: “Man is a magician” (connected to rationality, though not all men are magicians)

Accident (συμβεβηκός/bebekos) #

A name signifying something outside the nature and not connected to it; something that “happens” to a thing.

• Example: “Triangle is green” (color has nothing to do with triangularity)
• Example: “Man is white” (whiteness unrelated to being rational)
• Property: Useless for defining or investigating the essential nature

Examples & Illustrations #

Quadrilateral and Its Species #

• Genus: Quadrilateral (plane figure with four straight sides)
• Difference: Equilateral (all sides equal), Right-angled (all angles right angles)
• Species:
  • Square = Equilateral AND right-angled quadrilateral
  • Rhombus = Equilateral but not right-angled
  • Oblong = Right-angled but not equilateral
  • Trapezium = Neither equilateral nor right-angled

Note: Neither equilateral nor right-angled alone is convertible with square; both together are necessary and sufficient.

Triangle Species and Lowest Species #

• Genus: Triangle
• Species: Equilateral, Isosceles, Scalene
• Lowest species:
  • Equilateral triangle (all equilateral triangles have the same shape; cannot be divided into further kinds)
  • NOT isosceles triangle (isosceles triangles vary in shape—some acute-angled, some obtuse-angled)

Properties of Mathematical Objects #

• Number 2: “Half of four” (1/2 of 4 = 2; a property expressing a relation that follows from being two)
• Triangle: “Interior angles equal to two right angles” (180°; belongs to every triangle, always, and only to triangles)
• Number 3: Half of six (3 is half of 6) but not double of anything in integers

Properties in Natural Philosophy #

• Man: “Capable of laughter” (proper to man because he is rational and can perceive absurdity)
• Dog and Cat: “Barks” (dog), “Meows” (cat)—properties from which one might reason to differences when the true specific differences are unknown

Accidents in Nature #

• Triangle: Being green or red (no connection to the nature of triangularity)
• Man: Being white or black (no connection to being a rational animal)

Notable Quotes #

“Because he’s an animal, he can make the sounds of laughter. But because he has reason, he can see the absurdity of something that makes him laugh.” — Explaining why “capable of laughter” is a property proper to man

“If he barks because he’s a dog, then barks is really like a property following upon his nature as a dog. But because I’m too ignorant to see the essential difference between the dog and the cat, by the barking and the meowing you know strike my senses, rather than be completely ignorant of the difference, I say that one is a four-foot animal that barks.” — On using properties as temporary substitutes for unknown specific differences

“Can you see any connection between the nature of the triangle and being green? Or is that something that actually happens?” — Distinguishing property from accident

“The accident is useless, right, both for defining even imperfectly something and for investigating the essential differences.” — The complete uselessness of accidents in logical inquiry

Questions Addressed #

Can the same name be both a genus and a species? #

Answer: Yes, when understood as relative distinctions. Quadrilateral is a species relative to rectilineal plane figure but a genus relative to square. This is not subjective—it is a precise logical relationship. The distinction between them is relative, not absolute.

Why do we study the five predicables even though definition concerns what a thing is? #

Answer: Because property, though outside the nature, is connected to it and can serve two purposes:

1. Property can be the middle term for reasoning from effect back to cause (investigating the difference)
2. Property can substitute for the unknown difference in an imperfect definition

Accidents are studied to show they are useless for these purposes and thus must be excluded from definition.

Why is the distinction between genus and species not absolute? #

Answer: Because the same thing can be a genus in one context and a species in another. This mirrors other relative distinctions: father and son, double and half, cause and effect. The relation depends on what the name is compared to, not on intrinsic properties of the name itself.

Is there a highest genus and a lowest species? #

Answer: Yes to both. If every genus had a genus above it, infinite knowledge would be required to know anything. If every species had species below it, infinite division would be required. There must be endpoints: a most general name that is not a species of anything, and ultimate particulars that are not genera of anything.

Why are multiple differences necessary in a single definition? #

Answer: Because a single difference is often not sufficient to specify a thing uniquely. In geometry, equilateral alone (rhombus) and right-angled alone (oblong) do not specify square. Only their combination is convertible with square. This reflects how humans progress from confused to distinct knowledge, each difference removing ambiguity.

How does Thomas Aquinas use the five predicables? #

Answer: In Summa Contra Gentiles I, Aquinas argues that no name is said univocally of God and creatures. He uses the five predicables to show that any univocal name must be either a genus, species, difference, property, or accident of both God and creatures—and then eliminates each possibility individually, concluding that all names of God and creatures are equivocal by reason.