4. Porphyry's Isagoge and Aristotle's Categories: Genus, Species, and Highest Genera

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Lecture Notes

Main Topics #

Porphyry’s Definition of Species #

• Asymmetry in definition: Genus and difference are defined by what is said of them (what is below), but species is defined by what it is said of (what is above—the genus)
• Reason for asymmetry: Below a species there may be only individuals (if it’s the lowest species, like ‘man’ or ‘circle’), or there may be further species (like virtue having courage, temperance, and justice below it)
• Same thing as both genus and species: Virtue is a species of habit but a genus of courage, temperance, and justice; similarly, a man can be both father and son, but not to the same person

The Infinite Regress Problem and Highest Genera #

• The question: Does every genus have a genus above it? Does every species have species below it?
• Infinite regress argument: If every genus had a genus above it, one would need to know infinitely many genera to know anything; therefore, one could never begin to know what anything is
• Parallel with statements: If every statement required proof by other statements, no statement could ever be known; therefore, there must be some statements known through themselves (first principles)
• Conclusion: There must be either one highest genus or multiple highest genera; there cannot be infinite regress

Names Said of All Things (Transcendentals) #

• Being as universal name: ‘Being’ is said of everything that is in any way whatsoever; no non-being can exist
• The crucial question: Is ‘being’ said univocally (with one meaning) or equivocally (with multiple meanings)?
• Equivocation of being: Demonstrated through examples:
  • Duane Berquist and the shape of Duane Berquist are not two things in the same way as Berquist and Father Michael
  • Duane Berquist and his health are not the same thing, nor are they two things like two separate persons
  • ‘Cease to be’ means something different when applied to substantial existence versus being physically in a room
  • Being seated is ‘something,’ but not in the same way a person is ‘something’

Why Being Cannot Be a Genus #

• First argument: A genus is not part of the definition of its differences, but every difference must ‘be’; therefore, being cannot be a genus (it would appear twice in the definition)
• Second argument: Being is not said univocally of all things (as demonstrated above); a genus must be said univocally of its species
• Conclusion: There must be multiple highest genera, not one supreme genus of all reality

Aristotle’s Categories Chapter 1: Three Types of Names #

1. Homonyma (Equivocal Names)

• Definition: Things sharing only the name in common; the λόγος (logos—meaning, definition) of what it is differs
• Example: ‘Ζῷον’ (zōon—animal) said of a man and of a painting or statue of a man; Lafayette’s experience seeing statues of Washington versus the living Washington
• Significance: Names said of the highest genera will be equivocal
• Equivocal by chance vs. by reason: If a name were equivocal by chance, it would not be said of everything; but if a name is said of all things, there must be some connection among the meanings, making it equivocal by reason

2. Synonyma (Univocal Names)

• Definition: Things sharing both the name and the λόγος (logos) of what it is
• Example: ‘Ζῷον’ (zōon—animal) said of man and of cattle (βοῦς—bous, ox); the same definition applies to both
• Etymology note: Greek ‘ζῷον’ derives from ’life’ (ζωή—zōē); Latin ‘animal’ derives from ‘soul’ (anima)
• Significance: The highest genera are said univocally of their species

3. Paronyma (Denominative Names)

• Definition: Names derived from another name but differing in grammatical ending
• Examples: ‘Grammatical’ (from ‘grammar’); ‘courageous’ (from ‘courage’); ‘just’ (from ‘justice’)
• Mechanism: Something in one genus (e.g., quality) can be said denominatively of something in another genus (substance)
• Key insight: We say ‘Berquist is healthy’ or ‘Berquist is just’ (denominative) rather than ‘Berquist is health’ or ‘Berquist is justice’
• Further examples: ‘Mozart is a musician’ (not ‘Mozart is music’); ‘Mary is holy’ (denominative from ‘holiness’); ‘Berquist is a logician’ (denominative from ’logic’)
• Significance: Shows how Aristotle proceeds methodically through the order of names in discourse and in knowledge

Key Arguments #

The Infinite Regress Argument (Necessity of Highest Genera) #

1. If every genus had a genus above it, there would be infinitely many genera to know before knowing anything
2. To know anything, one would have to know infinitely many things first
3. Therefore, one could never begin to know anything
4. But we do know some things
5. Therefore, not every genus has a genus above it—there must be highest genera

Why Being Cannot Be a Single Highest Genus #

1. There is at least one name said of all things (‘being,’ ‘something’)
2. If this name were said univocally, there would be one highest genus
3. But ‘being’ is not said univocally (proven by examples showing different modes of being)
4. If equivocal by chance, it would not be said of everything
5. Therefore, it is equivocal by reason
6. Therefore, there are multiple highest genera (the ten categories of Aristotle)

Important Definitions #

• Genus: A name said with one meaning of many things other in kind (ἕτερα τὸ εἶδος—hetera to eidos), signifying what it is (τὸ τί ἐστιν—to ti estin)
• Species: What is placed under a genus and of which the genus is said in answer to ‘what is it?’
• Difference (διαφορά—diaphora): That which distinguishes members of a genus from one another; said of things ‘how they are,’ not ‘what they are’
• Homonyma (ὁμώνυμα): Things equivocally named; the name only is common, but the λόγος (logos) differs
• Synonyma (συνώνυμα): Things univocally named; both the name and the λόγος (logos) of what it is are the same
• Paronyma (παρώνυμα): Denominative names; names derived from another name but differing in ending
• Equivocal by reason (καθ’ ὑπεροχήν—kath’ hyperochēn, or by analogy): A name with multiple meanings where there is a connection or order among the meanings, typically ordered toward one primary meaning
• Equivocal by chance: A name with multiple meanings due to mere coincidence with no necessary connection
• Transcendentals (’the set of alls’): Names said of all things whatsoever (being, something, one, true, good, etc.)
• Logos (λόγος): The meaning, definition, or rational account of what something is

Examples & Illustrations #

Mathematical Examples #

• Circle as lowest species: Different circles do not differ in kind (shape); they differ only in size—they are merely individual instances
• Quadrilateral as non-lowest species: Has species below it—square, oblong (rectangle), rhombus, rhomboid, trapezium
• Isosceles triangle: There are many shaped isosceles triangles, unlike circles which all have the same shape
• New England: A whole compared to Massachusetts, but a part compared to the United States (demonstrating that the same thing can be both whole and part)

Biological and Conceptual Examples #

• Habit: Genus of virtue and vice
• Virtue: Species of habit, but genus of courage, temperance, and justice
• Dog: Open question for zoologists whether it is a lowest species or has species below it (e.g., different breeds)
• Father and son: The same man can be both, but not in relation to the same person (just as virtue is both genus and species)

Physical Examples #

• Einstein’s finite universe: A whole that is not a part of anything greater (infinite regress avoided in the upward direction)
• Elementary particles: Seeking a part that is not a whole (infinite regress avoided in the downward direction); Heisenberg said he never thought this would go on forever
• Water and hydrogen: Water was thought to be fundamental; hydrogen was discovered as more fundamental; electrons and protons discovered below hydrogen
• The four elements: Thales thought water was the beginning; then hydrogen was discovered; then subatomic particles

Everyday Examples #

• Lafayette and Washington: Lafayette saw statues of Washington—the statue is not Washington in the same sense as the living man he knew
• Richard (the name): Several people named Richard; the name applied by chance to multiple people, not because of any essential connection
• Being seated vs. ceasing to be: ‘Cease to be’ means something different when applied to leaving a room versus substantial death
• Health and knowledge: One does not ‘be’ health or ‘be’ geometry; rather, one ‘has’ health or ‘has’ knowledge; hence ‘healthy’ or ’learned’ are denominative

Notable Quotes #

“If every genus had a genus above it, how many genera would you have to know to know anything? You’d have to know infinitely many. So could you know what anything is? You couldn’t begin to know what anything is.”

“Can there be something that is not a being? Being means what is, and can be said of anything that is in any way whatsoever. So can there be something that is not a being? No.”

“If a name is equivocal by chance, how many things do you think it’d be said of everything? No. But if the name is said of all, there must be some connection among the meanings. It must be a name equivocal by reason.”

“Is Duane Berquist and the Shape of Duane Berquist one thing or two things? Or is Duane Berquist and the Health of Duane Berquist the same thing? But is Duane Berquist and the Health of Duane Berquist two things like Berquist and Father Michael?”

“Wonder is the beginning of philosophy. There is no other beginning of philosophy than wonder.”

Questions Addressed #

Q: Why doesn’t Porphyry define species by what is below it? A: Because below a species there might be only individuals (if it is a lowest species), or there might be other species. The definition would not be uniform.

Q: Can the same thing be both a genus and a species? A: Yes, with respect to different things—just as a man can be both father and son, but not to the same person. Virtue is a species of habit but a genus of courage, temperance, and justice.

Q: Does every genus have a genus above it? Does infinite regress occur? A: No. If every genus had a genus above it, infinite regress would make knowledge impossible. There must be highest genera.

Q: Is there one highest genus of all things? A: No, because ‘being’ (the name said of all) is not univocal but equivocal by reason, indicating multiple highest genera—the ten categories.

Q: Why can’t being be a genus? A: (1) A genus cannot be part of the definition of its differences, but every difference must ‘be’; (2) Being is not said univocally of all things, and a genus must be said univocally of its species.

Q: How can something in one category be said of something in another? A: Denominatively—we say someone ‘is healthy’ (from ‘health’) or ‘is just’ (from ‘justice’), using a name derived from an accident to describe a substance.

Q: What is the significance of ’equivocal by reason’ versus ’equivocal by chance’? A: If a name is equivocal by chance, it would never be said of all things; but if it is said of all things (like ‘being’), there must be some rational connection (proportion or analogy) among the meanings, making it equivocal by reason.

Q: Why does Aristotle discuss these three types of names at the beginning of the Categories? A: To prepare students to understand how the highest genera (the ten categories) are said of things below them—univocally within each category, but equivocally by reason across all categories.