Aristotle's Ten Categories and Porphyry's Isagoge: Quantity, Quality, Relation, and the Predicables

Orientation #

He picks up in the middle of the division of substance (“in the beginning of our experience are the material ones”) and refers back to earlier work on genus, species, difference, property and accident and on the highest genera (prev. lecture). At the end he announces two things to be added “for the goodness of teaching about names”: names equivocal by reason and figurative naming. The previous class treated genus/species division and the Categories; the next treats the figures of speech and analogous names.

The class, in order #

1. Where you are in the scheme of substance (“in case you want to know where you are”) #

Point: substance, the first highest genus, is divided by what is said of individual substances in answer to “What is it?”

• Order of division: material vs immaterial (the division into immaterial comes later, since experience begins with material things); material into living and non-living; living into plant and animal; animal into beast and man (“following Shakespeare”).
• Socrates read upward: man, animal, living body, material substance or body, substance—all the higher ones said of the lower, signifying what they are. Substance is called “what it is” for this reason.

2. Quantity: discrete and continuous (“the measure of substance”) #

Point: Aristotle divides the second category, how much / quantity, into discrete (chiefly number) and continuous (line, surface, body in the sense of three dimensions).

• “Body” as species of continuous vs “body” as species of substance: the word is equivocal, and this equivocation “deceives Descartes and others,” who confuse length, width and depth with the substance apt to have them. Boundary case: if Descartes grew up, the substance (the man) remains, the size changed.

3. The logical definition of the continuous (“parts meet at a common boundary”) #

Point: in logic the continuous is a quantity whose parts meet at a common boundary; the discrete is one whose parts do not (discrete = “separated”).

• Straight line: left and right parts meet at a point, end of one and beginning of the next.
• Surface: take the diagonal, the parts meet at a line; circle cut by a diameter, likewise.
• Broken chalk: the two sides would meet at a plane.
• Time, “sometimes” counted continuous: past and future come up to the now, which is the end of the past and beginning of the future.
• USA/Canada: the imaginary boundary is the end of one and the beginning of the other.
• Number: seven into three and four—“Do three and four meet somewhere? No.”

4. The natural-philosophy definition and the sign about reason (“divisible forever”) #

Point: in natural philosophy the continuous is defined as what is divisible forever (shown in Physics Book VI); the discrete is not.

1. Seven → four and three → two twos → ones; the one that begins number cannot be divided (it is simpler than the point—the Greeks called the point “a one having position”; if the point can’t be divided, neither can the one).
2. De Anima Book I (proceeding dialectically): our thoughts are like numbers, not like the continuous—the species divides into genus and difference, a genus into a higher genus and difference, “but doesn’t go on forever”: there are highest genera, quantity being one.
3. Everything material is continuous; even our thoughts about continuous things are not continuous; this is not explained by what they are about, so it is explained by the nature of our reason. Hence a sign that universal reason is not a body, and “the brain, in fact, is not the organ of thought,” though related to thought in some other way (to be seen in the three books on the soul).

• Motion, especially local motion, is continuous: walking down the garden path, the path, the motion and the time are each divisible forever.

5. Arithmetic, geometry, and a contrast with logic (“how much or how many”) #

Point: the discrete/continuous division is even more basic to mathematics than to natural philosophy—arithmetic is about number, geometry about line, angle, surface, body—and both are in Euclid’s Elements.

• The most basic division of the continuous: one dimension (line), two (surface), three (body); geometry later shows only three lines can each be at right angles to the other two.
• Contrast: logic has three acts and three parts corresponding; here three species of continuous but only two parts of geometry, plane and solid. Reason: plane geometry is about both the line and figures—Euclid’s first theorem is ordered to the second and so on to cutting off a line equal to a line, but circles and figures are used, so one is already in a plane. Books I-VI are plane geometry, XI-XIII solid, interrupted by the arithmetical Books VII-IX (“there’s a reason for that but we won’t go into that”).

6. Student: why is that a sign of immateriality? (“according to the nature, the condition of receiver”) #

Student clarifies: thoughts are not quantities at all but like numbers; why a sign of immateriality? Answer:

1. Every body is continuous, so what is received in a body is received as continuous.
2. We receive the continuous into reason as thoughts that are not continuous.
3. This is not because of what is received (that is continuous), so it must be due to the receiver: “whatever is received is received according to the nature, the condition of receiver.”
4. So reason knows bodies in a non-bodily, non-continuous way.

• Do genus and difference in a definition meet at a point, a line, a surface? If a point, the definition would be a line; if a line, a surface—it is neither. Every quantity has parts; either they have a common boundary or not.
• Anaxagoras first suspected the mind is not material; Plato and especially Aristotle brought it out more fully.

7. Quality divided into four (“division into four by the master himself”) #

Point: Aristotle divides quality (“how”) into four species—“one of the prime examples that I give why I don’t think one should always divide into two or three”; the rule is good because true for the most part.

1. Disposition or habit: a habit is a firm disposition, hence its own name; later divided into virtue and vice.
2. Natural ability or inability: ability to digest, to see, “the ability for a large discourse, looking before and after.”
3. Sense qualities. (He adds that the passions, “what we call feelings,” come under quality too.)
4. Figure or shape.

• Use: Thomas, Prima Secundae (moral theology), recalls that virtues and vices are qualities, then this four-fold division, then shows they fall under the first. Aristotle does the same in NE Book II: is virtue a natural ability, a passion, or a habit/disposition? (“He’s pretty sure they’re not” figure.) Anger, the ability to feel anger, or the disposition to feel anger when one should or shouldn’t? Conclusion: the genus of moral virtue and vice is habit. Temperance: not the ability to be hungry, not hunger, but being disposed to desire moderately (or more than one should).
• Why the first division matters: a highest genus has no genus above, so cannot be strictly defined; it is made clearer by what it is divided into, and the division is a starting point for the sciences (geometry/arithmetic from quantity; the genus of virtue from quality).

8. Relation, “towards something” (“based upon something more fundamental”) #

Point: relations are founded either on quantity or on acting upon and undergoing.

• On quantity: taller, shorter, double, half, third, greater, lesser—being towards another, but presupposing my size and yours; one can be taller than one person and shorter than another. Equal, same, like belong rather with the side of unity (“actually, equal should be over here”).
• On acting/undergoing (which presuppose qualities): father/son, mother/son, teacher/student, mover/moved. Knowing something is a quality of me, but I must act upon you before I am your teacher; I can have muscles, but must move something before there is mover and moved.
• Student: was it “based upon quantity and quality”? Answer: they usually say acting upon and undergoing, which presuppose qualities; Thomas divides relations into those based on action/undergoing and those based on measure—“the same thing,” quantity.
• Aside: his brother Richard’s friend teaching at the University of Colorado describes looking down on faces saying “Why are you doing this to me?”

9. The last six categories, and a puzzle about “where” (“more like whole and part”) #

Point: where, when, position, “outfitted” (his liberty for “to have”), acting upon, undergoing—Aristotle only enumerates and exemplifies them; whole chapters only for substance, quantity, quality, relation.

• Puzzle: is “in Massachusetts” the genus of “in this room” / “in [Pynchon—unclear in recording]”? It seems more like whole and part than genus and species, at least not as in the first four; likewise here today / this week / this month, and suit / tuxedo.
• In the Metaphysics, on the word “how,” he distinguishes four senses but reduces them to two (“I’ll leave that for clarification”).

10. The Isagoge: title and the five names (“it got kind of contracted to what?”) #

Point: the two fundamental works of the logic of names (first act) are Porphyry’s Isagoge and Aristotle’s Categories.

• Eisagoge = “leading in,” etymologically our “introduction.” Occasion: someone could not understand the Categories, where genus, species, difference are used as if known. Written as introduction to the Categories, the title contracted to “Introduction”—as Newton’s Principia Mathematica Philosophiae Naturalis became “the Principia.” Since logic is the tool of all philosophy, “the introduction” is antonomasia.
• Also “the book of the five names” (Greeks: five vocal sounds): genus, diaphora, eidos, idion, sumbebekos.
• Porphyry’s proemium: useful for the categories, but also for definition, division, demonstration.
  • Definition: genus begins it, difference completes a perfect one, species is what is defined, property is what you investigate the difference by and substitutes as an imperfect definition, accident is useless for naming or defining (green for triangle).
  • Division: a genus into species by differences—Euclid’s quadrilateral into square, oblong, rhombus, rhomboid.
  • Demonstration: proves a property of a species and why it belongs—Elements I.32 (interior angles equal to [two] right angles); man is risible: as animal he can make the sounds, as having reason he can see the laughable, absurd, preposterous. The middle term is the definition (genus and difference).
• Thomas’s summary of scientific method, “the three Ds”: definiendo, dividendo, demonstrando—as Euclid defines triangle, divides into equilateral, isosceles, scalene, then demonstrates properties (locus not given: “I detect where it is”).
• Asides: apodeixis / demonstrare, “to show”; Euclid’s QED; “I’m from Missouri. Better show it to me.”

11. Predicables, predicaments, and the courthouse (“the ten supreme accusations”) #

Point: the Latin names of the two sets—praedicabilia (five predicables, “able to be said of”) and praedicamenta (ten predicaments)—and the origins of the words.

• “I’m in a real predicament”: you can’t get out of a category—a habit never becomes a substance, a number is always a quantity.
• Categoria in Plato’s Apologia is the legal accusation; apologia the defense (Socrates defends his whole life; Newman’s Apologia Pro Vita Sua). To accuse is to say something of someone (murderer, thief, embezzler); so the categories are the ten ways something can be said of individual substances—a friend’s phrase, “the ten supreme accusations.” Philosophy borrows from practical life, as science borrows “law” without physicists being called lawyers.
• Both names come from praedicare, “to be said of”; like the names of the figures of speech, they don’t really bring out the distinction. Albert the Great’s paraphrases: De Praedicabilibus, De Praedicamentis. The Categories is also “the book of the ten names.”
• Difference he notices: the five names are names of names; the ten are names of things—I am a substance, my health a quality, my size a quantity, being a father or taller a relation, being in this room; “these are all real.”
• First and second placing of names: in the beginning things but no names (Adam naming the animals; “the father should name the child”); we place names on things (dog, cat, tree), then place names on names—the second placing.

12. Two additions announced (“name equivocal by reason”) #

Point: two things to attach to the teaching on names.

• Name equivocal by reason (or “equivocally of things”): the five names were said univocally, with one meaning, of many; a name can also be said with different meanings—his mother’s “I see, said the blind man.” Same name by chance = purely equivocal; by reason = very important in philosophy, especially the most common names, those in the axioms and in wisdom (about what is said of all).
• Figurative naming, figures of speech: hard to reach a universal understanding; Monsignor Dionne referred him to Quintilian, whose lengthy discussion is imperfect, as Dionne agreed.

His words #

• “what it is”: his name for substance, from how it is said of individuals [ed.: quid est]
• how much / quantity; how / quality; towards something / relation: the concrete words, then “the more abstract word”
• discrete: “separated”; parts without a common boundary
• continuous (logic): parts meet at a common boundary; (natural philosophy): divisible forever
• “ability for a large discourse, looking before and after”: reason (Shakespeare)
• disposition or habit: habit is a firm disposition
• “outfitted”: his rendering of the category “to have” [ed.: habitus]
• Isagoge / Eisagoge: “leading in,” introduction
• genus, diaphora, eidos, idion, sumbebekos: the five names
• apodeixis / demonstrare: “to show”
• definiendo, dividendo, demonstrando: Thomas’s three Ds
• praedicabilia / praedicamenta: predicables, predicaments; from praedicare
• categoria / apologia: accusation / legal defense
• first placing / second placing of names: names on things / names on names
• equivocal by chance (purely equivocal) vs equivocal by reason

Texts #

Read in class (commented on):

• Aristotle, Categories: chapters on substance, quantity, quality, relation; the remaining six enumerated
• Porphyry, Isagoge, proemium (the four uses)

Mentioned:

• Aristotle, Physics Book VI (continuous divisible forever); De Anima Book I (thoughts like numbers); Nicomachean Ethics Book II (genus of virtue); Metaphysics (four senses of “how”)
• Euclid, Elements: Book I first theorems, I.32; Books I-VI, VII-IX, XI-XIII
• Thomas Aquinas, Summa Theologiae, Prima Secundae; an unlocated text with definiendo, dividendo, demonstrando
• Plato, Apologia; Newman, Apologia Pro Vita Sua; Newton, Principia; Albert the Great, De Praedicabilibus, De Praedicamentis; Quintilian
• Genesis, Adam naming the animals (inferred)

His questions #

• Do three and four meet somewhere? No—discrete quantity’s parts have no common boundary.
• Why is it that thoughts being like numbers is a sign that reason is immaterial? (student) Because what is received is received according to the receiver; the continuous is received non-continuously, so the receiver is not a body.
• Do the genus and the difference in a definition meet at a point, a line, a surface? None; the definition is not a line or a surface.
• Is anger a virtue or a vice, or the ability to feel anger, or some habit or disposition? The genus of moral virtue and vice is habit.
• Is “in Massachusetts” the genus of “in this room”? Seems more like whole and part; left open.
• What is the difference between the five names and the ten names? The five are names of names; the ten are names of things.
• What does the “first placing of names” mean? Names placed on things; the second placing is names placed on names.