Porphyry's Five Predicables: Property, Accident, and Genus vs. Species as Relative Distinctions

Orientation #

He opens by recalling “the questions again here”: name said with one meaning of many things, divided into inside and outside the nature, and the inside subdivided into genus, species, difference (prev. lecture). He refers to “the bottom of page twelve” of the text in hand (handout “A Division of the Meno”, p. 2, and DHB Vol. II, The School of Plato, p. 2, verified as read from). At the end he says he will stop and “start with that question” next time: whether the highest genus is one or more than one. The next class continues the five predicables and the Poetics, Posterior Analytics, Summa contra Gentiles and Meno material.

The class, in order #

1. Property and accident: the names outside the nature (“either it follows upon the nature or it does not”) #

Point: names signifying something outside the nature divide completely into what follows upon the nature “like an effect follows upon a cause” (property, Greek idion) and what does not (accident, Greek symbebēkos, which “both in Greek and Latin has the word for happening”).

• Porphyry defines property “in the strictest and fullest sense”: belongs to only one species, to every member, and always. But the word can be used less fully “provided still there is connection with the nature.”
• Most properties lack a single name and need a speech. Textbook one-name example: man is risible [ASR: “visible”], subject to laughter—not his nature, but follows upon it: as animal he can make the sounds, as having reason he sees the absurdity.
• Two is half of four: strict property (only two, every two, always). Two is less than five: every two and always but not only two (four also), yet still classed a property because connected with the nature.
• Geometry’s standard example: triangle has interior angles equal to two right angles—every and always; and only, since a quadrilateral divides into two triangles and gets more right angles.
• Man is a logician: only man, but not every man and not always; still a property, since tied to his nature as animal with reason (vocal sounds plus reason).
• Green triangle, white man: no connection to being three-sided or to animal with reason—accident.
• Aside (a student’s joke): “the magician’s contribution to rational harmony.”

2. Why subdivide with a view to definition: two uses of property (“reason from the property back to the difference”) #

Point: the property has “a twofold relevance” to definition; the accident none.

1. If you know the property but not the difference, you can reason from property back to difference, as from effect to cause—the property is a middle term, “a beginning for reasoning towards the difference.”
2. You can use the property in place of the difference, giving an imperfect definition that still separates the thing. Dog and cat: “animal” (both), “four-footed animal” (both; separates from chicken or man), so finally “four-footed animal that barks / that meows.” Even if only dogs bark, “is he a dog because he barks, or does he bark because he’s a dog?” If the latter, barking is a property; ignorance of the essential difference makes us fall back on what “strikes my senses.” Aristotle sometimes calls this a periphrasis. Two as “a number half of four”: convertible with two, so it separates two from everything else.

• Nicomachean Ethics: Aristotle first speaks of human virtue as a praiseworthy quality and vice as blameworthy—“more the property than the difference”; it is praiseworthy because it is a virtue. Not until Book II does he bring out the real differences. From “what is praised” in eating and drinking (the right amount for oneself and circumstances) one reasons to “the reasonable middle.” So too the child knows what is frowned on or applauded before seeing intrinsic goodness.
• The accident is useless “both for defining even imperfectly something, and for investigating the essential differences.”
• Student: in “man is a rational animal”, are we using a property because we don’t know the specific difference? He: “in a way”—we are trying to get at what in the nature gives the ability called reason, so we tend to have just one difference there, “but it’s really a property.” Interesting that even in the Metaphysics Aristotle often calls man simply “a two-footed animal.”

3. The completeness of the five names, and their use (“See how complete that is”) #

Point: taken in reference to definition, the five names form something “very complete.”

• Species: name of what is defined. Genus: name that begins the definition. Difference: name that completes a perfect definition. Property: useful for completing an imperfect definition or for investigating. Accident: useless for naming and defining (“nowhere in geometry would green appear”).
• Porphyry: also useful for dividing (a genus into species by differences, or by properties if you lack differences) and for demonstration—in “the logic of the third act” one shows a property belongs to a species through its nature (genus and differences), e.g. the triangle’s interior angles. Also useful for understanding Aristotle’s Categories (taken up later).
• Thomas, Summa contra Gentiles Bk. I, chapter that no name is said univocally of God and creatures: among many arguments, an either-or—every name said univocally is genus, species, difference, property or accident; he eliminates each; concludes none. So he goes “all the way back to” the Isagoge in the highest part of our knowledge. (He notes some names are said of God and creatures “univocally by reason.”)
• Albert the Great paraphrased it; Cajetan (sent to Luther) commented on it; Mohammedans and Greek philosophers used it—though Porphyry was “violently anti-Christian,” his books burned by the Christian emperor; Augustine (City of God, “if I remember right”) speculates whether it was pride.
• It “grows out of what you can see people doing naturally”: ask students “what is a dog?"—“an animal”; “what is love?"—“an emotion” (but so is anger, fear), so they must add differences.
• Full title: Isagoge to Aristotle’s Categories; Ammonius made it the introduction to the whole of philosophy, because philosophy is “the three Ds”: define, divide, demonstrate. Many philosophers don’t know it.

4. Genus of genus; genus and species as names or as things (“What’s the genus of genus? Name”) #

Point: the definitions of the five names share the genus “name” (said with one meaning) and differ by differences (of many things / other in kind / signifying what it is).

• The word genus (and species) is “equivocal by reason”: sometimes the name of a general kind, sometimes the general kind itself. Dividing a genus into species divides a kind into kinds, not a name into names. Names are distinguished here because a definition is composed of names and we ask for it with a name. “Genus” and “difference” for a name equivocal by reason is a looser use; the five names are first taken strictly.

5. Footnote: logic vs grammar (“green triangle and equilateral triangle”) #

Point: grammar sees no difference where logic sees “an enormous difference.”

• Both phrases: noun plus adjective. Logically: triangle is genus or species; green an accident; equilateral a species-making difference. Triangle = plane figure contained by three straight lines; green is no way of being three-sided, but equilateral, isosceles, scalene are three ways the three sides can be. “Red, white and blue might sound patriotic.”
• Genus/species more by a noun; difference (and accident) by an adjective, since the difference signifies how it is what it is.

6. One genus, many differences; grammatical vs logical order (“the desire for good things and the ability to achieve them”) #

Point: a definition has only one genus (else “you wouldn’t be talking about one thing”) but usually more than one difference.

• Meno’s definition of virtue: “the desire for good things and the ability to achieve them”—two genera. One can desire without ability, or have ability without desire (money: a gun gives ability without desire; another has desire without the gun; anecdote of the philosopher who showed he could make money if he wanted to). This is his “first criticism,” distinct from Socrates'.
• Aristotle’s tragedy: one genus (imitation/likeness), many differences—“serious” shared with epic, “acted out” shared with comedy, both together separate from both.
• Second logic/grammar difference: English puts adjective before noun, so the difference comes first grammatically. “Genus is the first word” means first in our understanding: unless you understood quadrilateral you wouldn’t see why equilateral and right-angled are its differences; unless you understood triangle you wouldn’t see why scalene, isosceles, equilateral are differences and red, white, blue are not; unless you saw tragedy, comedy, epic as likeness you wouldn’t see their sources of difference. “A square is an equilateral and right-angled quadrilateral”—quadrilateral is last in speech, first in understanding. Latin/Greek could say animal rationale; English cannot say “animal rational” but can use a phrase, “animal with reason.” Similarly his definition of name began with “sound,” then vocal, signifying by custom, no part signifying by itself. Students asked “what is a dog?” say “animal” first, never “four-footed.”

7. The same name both genus and species: absolute vs relative distinction (“Can the same name be both a genus and a species?”) #

Point: yes—because genus/species is a relative distinction, “towards another,” not absolute, “in itself.”

• Man vs woman (absolute) against father vs son (the same man, toward different people; “I am the son of Reno Victor Berquist and the father of Paul Berquist”). Odd vs even (absolute) against double vs half (four is both). Quadrilateral: species of rectilineal plane figure alongside triangle, pentagon; genus of square, rhombus, oblong. Relative does not mean subjective or imprecise.
• “Once you see this, then arise the ultimate questions”, at either end of the series:
  • Is every son a father? No. Is every father a son? Adam is a father but not a son (a student: “son of God”—but not with a father as we have). Hard to know at one end, easier at the other.
  • Cause and effect: same thing can be both; is every cause an effect? Eventually the answer is no—there is a cause that is not an effect; maybe an effect that is not a cause. “The most ultimate question.”
  • Whole and part: Worcester County in Massachusetts in New England in the United States. Is there a part not a whole? a whole not a part? Twentieth-century physics: Planck’s quantum hypothesis (Dec. 1900, ~30 years to develop) and Einstein’s special (1905) and general (1915) relativity; the quantum physicists went down from atoms to elementary particles, splitting them, seeking a part that is not a whole (indivisible; for a while a “minimum length”); general relativity led to cosmology and the universe appearing finite, contrary to the moderns since the Renaissance (Aristotle held it limited, the first Greeks infinite)—a shock Einstein himself did not fully realize; if finite, there is a whole that is not a part. He does not assert either conclusion.
  • Mother and daughter: daughters who are not mothers; a mother not a daughter—Eve.
  • Series need not be closed at either end. Straight lines: the continuous is divisible forever (Physics, “Natural Hearing,” Bk. VI) and lines can always be extended, so no line is half without being double or double without being half—open at both ends. Numbers: the one is indivisible (unless “a crazy modern”), so three is a half that is not a double, but no number is double without being half—closed at one end.
  • Reasoning: a conclusion can be a premise of the next argument (Euclid), a relative distinction; but not every premise is a conclusion, “in that case you’d never know anything.”
• Applied: quadrilateral is both. Does every genus have a genus above it (rectilineal plane figure, plane figure, figure…)? Does every species have species below it, or is there a lowest species (a species not a genus) and a highest genus (a genus not a species)? “This is where Aristotle comes on the scene with the Categories”—the Isagoge is for lesser minds; Aristotle takes the hardest case.

8. Lowest species: the logician explains, the sciences determine (“Is triangle a lowest species?”) #

Point: the logician defines lowest species but leaves to each science which names are lowest species.

• Square: lowest species (no kinds). Oblong: not—different shapes; perhaps an oblong with sides two to one is lowest. Triangle: not; scalene, isosceles still vary in shape; equilateral triangle is lowest (bigger/smaller is not a difference in the figure). Circle: lowest. Man: if races had different kinds of reason, man would be a genus; if those are accidental differences, man is a lowest species—“not as easy to see” as the circle. Student raises male and female; he: “a very difficult subject.”
• Definition: a name said with one meaning of many individuals not other in kind, signifying what it is—“this circle, this circle, this circle” called circle for the same reason. Species was earlier defined in comparison to genus; lowest species has a unique relation to what is below.
• Comparison: genus, difference and lowest species share “name said with one meaning of many”; genus and lowest species signify what, difference how; genus and difference are said of many other in kind, lowest species only of many individuals. So each needs two marks, “just like you need one difference” but here both.
• Distribution: Euclid says circle, equilateral triangle, square are lowest; mathematician says odd and even are not but seven is, prime and composite are both genera and species; biologist/natural philosopher decides man and dog; poetic science decides comedy—his own view: good-natured comedy and satire are different forms, the former superior since it expels melancholy while satire makes a misanthrope (Swift; Shakespeare’s three good-natured comedies more enjoyable than his two satires; a black satire, Troilus [ed.: “Crasyd” in recording, likely Troilus and Cressida, inferred]).

9. Highest genus: the logician is master (“Is there a genus that is not a species?”) #

Point: not every genus has a genus above it—shown two ways—but whether the highest genus is one or many is the next question.

1. You must know the genus before the species (quadrilateral before square, not vice versa). If every genus had one above, you would have to know infinitely many to know anything, presuppose infinite definitions before any definition, and could not even begin to define; you “couldn’t even say you don’t know anything.”
2. Not in the text, “why not? That should be”: there would always be a more universal word than any you have, but there are most universal names—something, thing, being (nothing is something that isn’t something, or a thing not a thing).

• “Now the next step is key here.” Does a name said of everything make one genus of everything? Only if said with one meaning. Aristotle showed these most universal names are not said univocally (“not said equally of everything”), so there cannot be one highest genus—how to distinguish the many is the business of the Categories. He stops here for next time.

10. Closing aside: the thirst for truth (“the first condition for the saving encounter with Christ”) #

Point: a quotation from the July–August L’Osservatore Romano: awakening in others “that thirst for truth, which is the first condition for the saving encounter with Christ.”

• He connects it to humility and recognizing sinfulness: Teresa of Avila’s “humility is the truth” is a predicatio per causam—humility is not truth but its cause is truth (God chiefly responsible for one’s good, oneself for one’s evil). People today have no desire to know the truth about the moral law or their own condition; the broader thirst for truth about the afterlife and universe leads a man toward Christ.

His words #

• inside / outside the nature; the first division of names said with one meaning of many things.
• property (idion); a name for what follows upon the nature “like an effect follows upon a cause”; strict sense: only one species, every member, always.
• accident (symbebēkos); what does not follow upon the nature; “the word for happening.”
• risible; subject to laughter [ASR “visible”].
• periphrasis; Aristotle’s name for a speech using property in place of difference.
• “equivocal by reason”; his phrase for a word with related meanings (genus as name / as kind).
• species-making difference [ed.: specific difference].
• “the three Ds”; define, divide, demonstrate.
• “the logic of the third act”; where demonstration is treated.
• absolute vs relative distinction; “in itself” vs “towards another.”
• lowest species; a name said with one meaning of many individuals not other in kind, signifying what it is [ed.: infima species].
• highest genus; a genus with no genus above it.
• Natural Hearing [ed.: Physics].
• most universal names; being, thing, something.
• predicatio per causam; predicating the cause of the effect (“humility is the truth”).

Texts #

Read in class

• Porphyry, Isagoge (the text in hand, “bottom of page twelve”): property and accident; usefulness of the five names; same name genus and species.
• Handout “A Division of the Meno”, p. 2 / DHB Vol. II, The School of Plato, p. 2 (verified).
• L’Osservatore Romano, July–August issue (quotation read aloud).

Mentioned

• Aristotle, Nicomachean Ethics, Bk. I (virtue as praiseworthy quality) and Bk. II.
• Aristotle, Metaphysics (man as two-footed animal).
• Aristotle, Categories.
• Aristotle, Poetics (definition of tragedy).
• Aristotle, Physics Bk. VI (the continuous).
• Thomas Aquinas, Summa contra Gentiles Bk. I, chapter on no name said univocally of God and creatures.
• Albert the Great, paraphrase of the Isagoge; Cajetan, commentary on the Isagoge; Ammonius.
• Augustine, City of God (on Porphyry; “if I remember right”).
• Plato, Meno (Meno’s definition of virtue).
• Euclid, Elements.
• Shakespeare’s comedies and satires; Swift; Teresa of Avila.

His questions #

• Why subdivide names outside the nature when you are interested in definition? Because the property can be a middle term for reasoning to the difference and can stand in for it in an imperfect definition; the accident is useless for both.
• Is he a dog because he barks, or does he bark because he’s a dog? If the latter, barking is a property, used in the definition only because we are ignorant of the essential difference.
• What is the genus of genus? Name (said with one meaning).
• Can there be more than one genus in a definition? No—you would be talking about two things (Meno’s virtue); but usually more than one difference.
• When we say the genus is the first word in the definition, what does that mean? First in our understanding, not in grammatical order.
• Can the same name be both a genus and a species? Yes; the distinction is relative, like father and son or double and half.
• Is every cause an effect? Eventually no—there is a cause that is not an effect.
• Is man a lowest species? Depends whether racial differences are different kinds of reason or accidents; left to the natural philosopher.
• Does every genus have a genus above it? No—else infinite knowledge before any knowledge, and there are most universal names.
• Is the highest genus one or more than one? More than one, since the most universal names are not said univocally—left for next time.