16. Porphyry's Five Names: Genus, Species, and Difference

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Lecture Notes

Main Topics #

• Porphyry’s Isagoge: An introduction to Aristotle’s Categories, useful for understanding definition, division, and demonstration
• Names Said of Many Things: The fundamental distinction between univocal names (one meaning) and equivocal names (multiple meanings)
• Genus: A name said univocally of many things other in kind, signifying what a thing is in a general way
• Species: A particular kind under a genus; the name of what is being defined
• Difference (Διαφορά/differentia): A name said univocally of many things other in kind, signifying how they are what they are
• Relative vs. Absolute Distinctions: How the same name can function as both genus and species depending on context
• Definition and Precision: How combinations of common names create unique definitions

Key Arguments #

The Problem of Common Names in Definition #

• A definition must separate a thing from everything else, yet definitions use names that are common to many things
• Solution: A combination of common names, each shared with other things, can uniquely define something—just as longitude and latitude together pinpoint a unique location
• Example: “equilateral and right-angled quadrilateral” uses two names common to multiple things but together fits only the square

Univocal Predication and Convertibility #

• A name is said univocally when it is said with one meaning of many things (the same reason applies to all instances)
• A definition must be convertible with what is defined: every instance of the thing must fit the definition, and everything fitting the definition must be an instance of that thing
• Example: If “something to sit on” is given as the definition of chair, it is not convertible because benches and saddles also fit this definition

Genus: The Fundamental Name #

• The genus represents confused knowledge because it is shared with many other kinds
• Example: “animal” is the genus of dog, cat, horse, dolphin (other in kind)
• It is the foundation upon which differences are added to complete a definition
• The genus does not distinguish one species from another

Species and the Relative Distinction #

• Species is defined relatively, not absolutely—the same name can be a species in relation to a genus above it and a genus in relation to things below it
• Example: “quadrilateral” is a species of “rectilineal plane figure” but a genus of “square,” “oblong,” “rhombus”
• Species is always the name of what is being defined

Difference: Separating and Completing #

• The difference signifies how they are what they are (not what they is)
• It serves two functions: (1) completes the definition by stating what the species has in addition to the genus, and (2) separates one species from another under the same genus
• Example: In quadrilaterals, “equilateral” and “right-angled” are differences. Equilateral separates square and rhombus from oblong and rhomboid. Right-angled separates square and oblong from rhombus and rhomboid. Together they define only the square.
• The same difference that defines a species also divides a genus into species

The Question of Lowest Species #

• A lowest species (infima species) is a species that is not itself a genus—it has no species below it
• Not every species necessarily has a species below it
• Example: “equilateral triangle” appears to be a lowest species (all equilateral triangles have the same shape)
• Example: “isosceles triangle” may not be a lowest species (different angle configurations are possible)
• Example: “square” is a lowest species, but “oblong” may not be (different proportions create different shapes)

Important Definitions #

• Univocal (univocē): A name said with one meaning of many things; the same reason applies to each instance
• Equivocal by Chance (aequivoca casu): A name applied to different things for no particular reason (e.g., “bat” for a baseball bat and a flying mammal)
• Equivocal by Reason (aequivoca secundum analogiam): A name applied to different things for a reason based on similarity or connection; often important in philosophy
• Convertible (convertibilia): Two terms are convertible when every instance of one is an instance of the other (A and B are convertible if every A is B and every B is A)
• Genus (γένος/genus): A name said univocally of many things other in kind, signifying what it is in a general way
• Species (εἶδος/species): A particular kind under a genus; the name of what is being defined (relative distinction)
• Difference (διαφορά/differentia): A name said univocally of many things other in kind, signifying how they are what they are

Examples & Illustrations #

Mathematical Examples #

• Quadrilateral: Genus for square, oblong, rhombus, rhomboid, trapezium

  • “Equilateral” separates square and rhombus from others
  • “Right-angled” separates square and oblong from others
  • Combination of both separates only the square
  • Etymology note: The rhombus has an ‘S’ in it, reminding us it is like a square (but slanted)

• Triangle: Genus for equilateral, isosceles, and scalene

  • Equilateral triangle is a lowest species
  • Isosceles and scalene are not lowest species

• Longitude and Latitude: An analogy for how common names combine to create precision

  • Longitude alone is shared by infinitely many points
  • Latitude alone is shared by infinitely many points
  • Together they pinpoint one unique location
  • Similarly, differences common to many species can combine to define one species uniquely

Logical Examples #

• Definition of Chair: “Something to sit on” is not convertible because benches and saddles are also things to sit on. A proper definition must add further differences to make it convertible.
• Animal and Dog: “Animal” is the genus; “dog” is a species under it. “Dog” is a name said univocally of many things other in kind (different dogs).
• Tragedy: A combination of names shared with epic and comedy
  • Shared with epic: represents serious actions of great men
  • Shared with comedy: acted out rather than narrated
  • Unique combination: serious action, complete, of magnitude, acted out

Questions Addressed #

How can a definition use common names yet define something uniquely? #

• Resolution: The combination of common names creates precision. Each name in isolation is common to many things, but their combination is unique to the thing defined. Longitude and latitude illustrate this: each is common to many points, but together they identify one location.

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

• Resolution: Yes, because the distinction is relative, not absolute. “Quadrilateral” is a species in relation to “rectilineal plane figure” but a genus in relation to “square.” This is analogous to how one person can be both a father and a son in different relations.

Why does the genus represent confused knowledge? #

• Resolution: The genus is shared with many other kinds, so it does not distinguish one kind from others. Understanding something as merely “animal” does not tell you whether it is a dog, cat, or horse. The differences must be added to reach distinct knowledge.

What is the role of difference in definition versus division? #

• Resolution: The difference serves both functions simultaneously: it completes the definition of a species (by stating what that species has in addition to the genus) and divides the genus into species (by separating one species from another). These are not two separate uses but one use with two effects.