Porphyry's Five Predicables: Difference, Species, Property and Accident

Orientation #

He carries on from genus (“the genus of square we saw was quadrilateral”) and closes by proposing to “start to look at the categories next time,” handing out a review sheet called “First distinctions and definitions in logic.” The previous class began Porphyry’s five predicables with genus; the next takes up the opening of Aristotle’s Categories.

The class, in order #

1. Two descriptions of difference (“what the species has in addition to the genus”) #

Point: difference is made known two ways, and each description points to one of its two jobs.

• (a) Difference is what the species has in addition to the genus: square is a quadrilateral (genus) plus equal sides plus right angles. Points to its role in completing a definition the genus only began.
• (b) Difference is what separates species under the same genus: equilateral separates square from oblong (right-angled does not); right-angled separates square from rhombus and rhomboid (which have acute and obtuse angles). Points to its role in dividing a genus into its species.
• Porphyry’s proemium to Chrysaorius: knowing the five is useful not only for the Categories but for definition and division (and demonstration). Division of a genus into species is among the most important in science: quadrilateral into its species; habit into virtue and vice; virtue into its species.
• Etymology: Greek dia + phora, “carry apart” (pherō / Latin fero); carrying apart = separating, so the word expresses description (b), not (a).

2. Difference is said of many, and signifies how (“how it is what it is”) #

Point: like genus, difference is a name said with one meaning of things other in kind, but of fewer, and it signifies not what but how.

• Said of many, but usually not as many as the genus: quadrilateral is said of more than equilateral; equilateral is said of square and rhombus (“many” means only more than one).
• A difference may fit one species only (rational for man), but the old logic books define man as mortal rational animal, since they (Platonists) held there are immortal rational animals; modern books take “rational animal.” Usually you need a combination of differences: equilateral (square, rhombus) and right-angled (square, oblong) together fit square alone.
• What it signifies: not what it is but how it is what it is — an essential how, not “how are you today.” Quadrilateral says four sides; the difference says how those sides are: equal or not, meeting at right, obtuse or acute angles.
• Latin quale / qualis, Greek poion; Aristotle defines quality in the Categories in terms of “how.” Grammatically we tend to a noun for the genus, an adjective for the difference (said later, §7).
• Aside: “species” gives English “specific.”

3. Aside: Aristotle’s order in the Categories (“takes up relation or towards something next”) #

Point: Aristotle enumerates substance, quantity, quality, relation but treats substance, quantity, relation, quality — and there is a reason.

1. The enumeration follows the order of being: substance underlies all; quantity before quality because some qualities (colour) presuppose surface; both before relation because relations are based on quantities or qualities.
2. But some qualities are said to be of another just as relatives are: “I am the son of Reno Victor Berquist”; “knowledge is knowledge of the known”; likewise love. Is knowledge a relation or a quality? (Class: a quality.)
3. So Aristotle must first clear up the relativa secundum dici (what is merely said to be of another) from what whose whole being is towards another. Boundary case: half — “how much is half?” cannot be answered absolutely (“I’ll give you half of my money” — how much? depends on the pocket); its whole being is towards another. Knowledge is not like that.
4. Hence relation is treated before quality; Aristotle “likes to proceed from the senses,” i.e. from the words.

• Asides: his father named after Major Marcus Reno, who escaped Custer’s last stand; Marcus Berquist got the name.

4. Porphyry’s order: enumerating vs. treating the five (“look before and after”) #

Point: Porphyry enumerates genus, difference, species, property, accident, but treats genus, species, difference, property, accident; this is not a mistake but two orders.

• Order of being: can there be a quadrilateral without a square? Yes. An equilateral quadrilateral without a square? Yes (rhombus). A square without equilateral? No. So genus and difference are before species, and genus before difference (a quadrilateral without equilateral, not the reverse). Property and accident come after because they are outside the nature; property before accident because it is connected with the nature.
• Order of knowing: genus and species are known together like relatives or opposites — species is defined by simply turning the definition of genus around (“what is placed under a genus, and of which the genus is said in answer to what it is”). Both descriptions of difference are given through genus and species. So in knowledge genus and species precede difference.
• In defining, the order differs again: first find the genus, then add differences.
• “It’s very subtle, but I really admire Porphyry” for enumerating in one order and treating in the other. Shakespeare: we are taught to “look before and after,” not descend to the beast.
• Aside: Augustine has some pity for Porphyry — why did he not become a Christian? probably anti-Christian; still, everyone reads him.

5. Property and accident (“belongs to only one species, to every member, and always”) #

Point: the first three refer to the nature (what, generally or specifically, and how it is what it is); property and accident are outside the nature, differing in that property follows upon or is connected with it and accident is not.

• Triangle: interior angles equal two right angles follows from what a triangle is (property). Three green triangles: green says nothing about or connected with the nature (accident).
• Accident as opposed to substance (what exists in another) can be a property; accident as opposed to property cannot. (Back-reference to “the despair of Father Delac.”)
• Porphyry’s definition of property in the fullest sense, three marks: (1) belongs to only one species, (2) to every member, (3) always. Example: two (a species of number) is half of four and a third of six — only two is half of four, every two, always; a property without a name, expressed by a phrase.
• Dropping a mark: “less than ten” belongs to every two, always, but not only to two — still called a property, not by chance, because it is connected with what two is; “not as much so.” “Every square is green? always? only squares?” — no on the third; clearly an accident.
• This is another way a name becomes equivocal by reason: by dropping out part of its meaning, generalizing it.

6. Digression: names generalized by dropping meaning (“undergoing, right? It’s not an acting upon”) #

Point: Aristotle’s “undergoing” in On the Soul and the word “road” show how a meaning is carried over by dropping part of it.

• Grammatically “to see” is active, but seeing is the colour acting on the eye, not the eye on colour (eclipses blind; loud bands deafen). So sensing is an undergoing, a being acted upon.
• The Greek word for undergoing is “suffering”: its first meaning connotes harm (“he’s undergone a lot in life”). You notice being acted upon when a pin is stuck in you or you bump into something, not when colour acts on you all day. Drop the harm: hearing Mozart perfects the ear (all knowledge is good; knowledge of a better thing is better), yet is still bodily. Then understanding is an undergoing: drop even the body, still acted upon by the agent [intellect], the phantasms.
• Hodos, road: his son Paul says a road “has cars and trucks on it”; drop the cars and the cement or asphalt, keep the before-and-after, and “road” becomes equivocal by reason — three roads in the mind (natural road, common road of reason, private road of each reasoned-out knowledge); Thomas: virtue is the road to happiness, vice to misery; sensing before memory before experience before universal knowledge; Aristotle calls philosophy methodos. Thomas on the proemium to On the Soul: Aristotle renders the student desirous, teachable and attentive — teachable by showing the distinction and order, the road to follow.
• Aside: Warren Burr’s joke that adults are like cement, all mixed up and set.

7. Property carried over; the accident again; the proemium’s three uses (“useful for definition and division and demonstration”) #

• “Property” can be carried over to what has two or even one of the three marks, so long as connected with the nature, making the word equivocal by reason. Example: the soul’s immortality is connected with its nature (as Aristotle shows) but not only to man — for Homer men are “the mortals,” the gods “the immortals”; the Divine Mercy chaplet calls God “the immortal one”; Athanasius means immortal (a-thanatos). Student: once resurrected we are immortal in the body.
• Accident: green, not connected with the nature yet said of many (triangle, circle, square).
• Return to the proemium: what you define is a species, beginning with the genus and completed by the differences; every science divides some genus (animals into two-footed and four-footed, feathered and non-feathered); in demonstration you prove a property of a species through its nature, i.e. genus and difference (extend a side of the triangle, draw a parallel, two right angles). “That’s in a nutshell what Porphyry’s doing in the Isagoge.” Later Greek commentators call it the Book of the Five Names and the Categories the Book of the Ten Names — “modern logicians never do that, never be so concrete.”

8. Why species is not defined by what is below it (“did the great Porphyry know what he was doing”) #

Point: genus and difference are defined by what they are said of; species only by what is above it — an apparent inconsistency that turns out to be deliberate.

• Aside on wonder: “Twinkle, twinkle… how I wonder what you are”; wonder asks what and why, the questions of definition and demonstration; Plato and Aristotle, “the chief philosophers,” say wonder is the archē of philosophy and there is no other. His niece Sophia’s answer to “what is wisdom?”: “the knowledge of God” — an amphiboly, the knowledge by which we know God and the knowledge God most has.
• Argument: (1) every species is under a genus said of it in answer to what it is; (2) but what is under a species is either individuals or another species — habit is a genus of virtue and vice, virtue a species with courage, temperance, justice under it; (3) only the lowest species has individuals immediately under it (circle is perhaps a lowest species: circles differ in size, not kind); quadrilateral is a species of rectilineal plane figure and a genus of Euclid’s square, oblong, rhombus, rhomboid, trapezium. Conclusion: you could not give one definition of species by what is below (said of many other in kind — yes for some, no for others), so Porphyry defines it by what is above; “maybe smarter than we thought.”
• “The great stepping stone” to the Categories: the same name can be both genus and species, genus of what is below, species of what is above — as one man is father and son, not towards the same man. Aristotle’s “figures of predication” borrows “figure” from mathematics: a figure is contained by limits, suggesting a limit both upward (highest genera) and downward (lowest species).
• Does it go on forever? Parallel great questions: every cause an effect, every effect a cause (there is a first cause); every father a son (not Adam), every son a father (no); whole and part — the same thing can be whole and part, not of the same thing (New England: part of the United States, whole of six states). Heisenberg, going down through water, hydrogen, proton and electron, sought a part that is not a whole and thought it went on forever; Einstein from special to general relativity concluded the universe is finite, a whole that is not a part, “like Aristotle said.” The Categories is the discovery of highest genera and lowest species.
• Aside on whether one has reached a lowest species: comedy — perhaps two species, good-natured comedy and satire (Troilus and Cressida “a rather dark one”; Swift; Merry Wives of Windsor).

9. Close (“start to look at the categories next time”) #

Next time the Categories; he passes out a review sheet, “First distinctions and definitions in logic,” with his own numbering added.

His words #

• difference: what the species has in addition to the genus / what separates species under the same genus; from dia-phora, “carry apart”
• said with one meaning of many things other in kind: the common formula for genus and difference
• how it is what it is: what the difference signifies; quale, qualis, poion; “essential how”
• towards something: his rendering of relation [ed.: ad aliquid]
• relativa secundum dici: things said to be of another (knowledge, son) that are not relations in their whole being
• order of being vs. order of knowing: the two orders behind Porphyry’s enumeration and treatment
• property (fullest sense): belongs to only one species, to every member, always
• accident: outside the nature and not connected with it; distinct from accident as opposed to substance
• equivocal by reason: a name generalized by dropping out part of its meaning [ed.: analogy]
• undergoing: his rendering of Greek suffering / being acted upon [ed.: paschein, passion]
• hodos, road; methodos: before-and-after in knowledge; the three roads of the mind
• Book of the Five Names / Book of the Ten Names: Greek commentators’ names for the Isagoge and the Categories
• lowest species; highest genus: the limits up and down
• figures of predication: Aristotle’s name for the categories, “figure” borrowed from mathematics
• amphiboly: “knowledge of God” in two senses

Texts #

Read in class

• Porphyry, Isagoge, proemium (address to Chrysaorius; usefulness for the Categories, definition, division, demonstration) — quoted twice
• Porphyry, Isagoge, on difference (two descriptions), species (turning round the definition of genus), property (three marks)

Mentioned

• Aristotle, Categories: enumeration and treatment order of the categories; quality defined by “how”; figures of predication; highest genera and lowest species
• Aristotle, On the Soul: sensing and understanding as undergoing; immortality of the soul
• Thomas Aquinas, proemium to the commentary on On the Soul (desirous, teachable, attentive); “virtue is the road to happiness”
• Euclid, species of quadrilateral (inferred: Elements I definitions)
• Plato and Aristotle on wonder as the beginning of philosophy (loci not stated)
• Augustine on Porphyry (locus not stated); Homer’s “mortals” and “immortals”; Shakespeare (“look before and after”; Troilus and Cressida; Merry Wives of Windsor); Swift

His questions #

• Is knowledge really a relation or a quality of us? A quality; it is only said to be of another, unlike half, whose whole being is towards another.
• Why does Porphyry enumerate genus, difference, species but treat genus, species, difference? Enumeration follows the order of being; treatment the order of knowing, where species and difference are made known through genus.
• Can there be a quadrilateral without a square? an equilateral quadrilateral without a square? a square without equilateral? Yes; yes (rhombus); no — so genus and difference precede species in being.
• Is it a property of two to be less than ten? In a lesser sense: every two, always, but not two alone; connected with the nature, so “property” by reason.
• Is every square green? No — an accident, unconnected with the nature.
• Why doesn’t Porphyry define species by what it is said of? Because under a species may be individuals or further species; only the lowest species has individuals immediately under it.
• Is virtue a genus or a species? Both — genus of courage, temperance, justice; species of habit; like being father and son, not towards the same.
• Is every genus a species and every species a genus — does it go on forever? No: the Categories finds highest genera and lowest species, as there is a first cause and a whole that is not a part.
• Is comedy a lowest species? Left open; he inclines to two species, good-natured comedy and satire.