From Quantity to 'Towards Something': Categories, Chapter 7 on Relation

Orientation #

He opens by “getting back to the text itself” — the division of chapter six on quantity — and remarks he thought they had finished it but there are still Thomas texts on the handout (a collection of texts, “not a chapter of one of my books”). He skips the Trinity texts (pp. 16 and 18) as already seen, moves on to the chapter “towards something”, and stops at the start of a text of Albert the Great (p. 3 of the new handout) for next time. Sources: Categories ch. 6 matched to his handout; handout “The First Definition of Relation” p. 105 read at length [ed.: source title reads “Reason”, almost certainly “Relation”]; handout “Quantity – Chapter Six” p. 17.

The class, in order #

1. Review of chapter six (“the division of chapter six on quantity”) #

Point: recap of the structure of the quantity chapter.

• Quantities per se vs. per accidens.
• Two divisions of per se quantity into species: (a) discrete vs. continuous; (b) parts having position with respect to each other vs. not. Not identical divisions: time is continuous, yet its parts have no position, because they do not exist together.
• Species: discrete — number and speech; continuous — line, surface, body, place, time (“remember five”).
• Quantity per accidens: e.g. colour on a surface. Example: the white-painted wagon at his father’s factory on a bright July day — “blinding”, too much white; the white is quantified because the surface it is on is.
• Properties: has no contrary; not said more or less (the two go together — qualities like hot and cold have both contraries and more/less, e.g. lukewarm); strict property: equal or unequal.

2. Thomas: species of quantity by notions of measure; order in number and time (“according to diverse notions of what measure”) #

Point: the Philosopher in the Praedicamenta [ed.: Categories] distinguishes the species of quantity by diverse notions of measure.

• A thing is measured by something of its own kind: line by inches, surface by square inches, body by cubic inches. Examples: a house sold by square feet; concrete, sand, wood bought by volume.
• Text from Thomas’s exposition of Boethius/Dionysius: the notion of both time and number follows order — one species of number is naturally before another, and time is the number of motion according to before and after. He flags this as “very subtle”: a discrete and a continuous quantity put together because both have order.
• The order of number is like the order of being: three can be without four, but not four without three (his daughter’s children: one before two, twins aside; two before three). Contrast his own earlier example, bricks in a brick wall, and the student’s recalled example, one before two.

3. “All things partake of one”; being and one (“all things partake of one”) #

Point: the next text proves that all things partake of one through the case where it seems least — number, which is in some way opposed to one.

1. In the fourth book of wisdom [ed.: Metaphysics IV] Aristotle settles the subject of wisdom: both being and one. (A student asks about this; he confirms “both being and one.”)
2. So if number is a kind of being it must have some unity; each member of a plurality must be one, some being.
3. Thomas: things resist being divided, because losing unity is losing being. Examples: divide and conquer — dividing an army dissolves it; divorce destroys the family; heresy divides and so is destructive of the Church, which must be one to exist; Shakespeare’s poem on reason puzzled how two lovers become one.

• Aside on a philosophy-department colleague who held France or England “doesn’t exist” because it is many people: a narrow view of unity. Degrees of unity: a country has less than a family, a family less than one man. Aristotle criticises the community of wives that Socrates proposes in the Republic as seeking more unity than a country should have; a tyrannical father making the family “just me” makes it more one than it is.
• Aside: that is what Martin Luther did with Christianity — “it was him”; he favoured the death penalty for those who wouldn’t [unclear in recording].
• He skips the Trinity texts (bottom of p. 16, and the “three things” on p. 18) as already seen — “I don’t want to torture you anymore.”

4. Chapter seven: why “towards something” before quality (“Aristotle seems to what change the order”) #

Point: the first puzzle of the chapter — when enumerating the ten Aristotle gave substance, how much, quality, relation; when treating them he does substance, quantity, then towards something, then quality. “Read Aristotle carefully”: there should be a reason.

• The reason is Plato (or someone) defining towards something as whatever is said to be of another in any way: father of a son, teacher of students. Then knowledge, being always of something, would be in the category towards something. But is knowledge not rather a quality of the teacher’s mind?
• Medieval distinction: knowledge is a relativum secundum dici — said of another, but its whole nature is a quality with a relation following on it. Double or half: “how much is double?” — “I’ll have double for dinner tonight” leaves the wife asking “double what?” — entirely towards another, so a relativum secundum esse.
• Aristotle proceeds, as often, from what people already say. Plato “is somebody”: the Academy is named from his school (so St. Thomas Military Academy was Plato’s school); Thomas calls Plato and Aristotle the philosophi praecipui; Albert the Great says one who wants to be master in philosophy must know both.
• Problem with the Platonic definition: the arm of my body, the heart of my body would be relations; I would be a combination of relations with no substance left — “a serious problem”. So the definition is remade: what is in the category is that whose whole being is towards another; what is fundamentally a quality with a relation falling on it is treated under quality.
• Why quantity and quality are ordered before towards something: teacher and student are so because of the quality of their minds; double/half, taller/shorter follow on quantity; father/son follow on the power of generating, a quality. At first sight one should be “scandalized” by the order; it makes sense.

5. Outline of the chapter (handout read) (“the chapter on towards something is divided into three parts”) #

Point: the chapter’s structure, with the properties in order.

• Three parts: first definition; properties; then an objection to the first definition, a second definition, and a further property. Up to the objection the plan looks like that of substance and quantity. From the objection and second definition one sees the distinction relativa secundum dici / secundum esse and the surprising order (towards something before quality, though quality is prior in being or causality).
• First definition: things which in what they are are said of another or towards another in some way. Aristotle’s first examples are purely towards something (greater/lesser, more distinctly double/half); his second examples are mainly qualities with a towards-something following on them.
• Looser properties, belonging to some relatives: (i) to have a contrary — fits relatives that are qualities (virtue/vice), not double/half; (ii) to admit of more or less (he corrects the handout: “of”, not “or”) — one thing is more or less like another, but nothing is more or less double.
• Stricter properties: (i) reversibility — master of the slave, slave of the master; father/son. Apparent failure only when the correlative is stated wrongly: “slave of a man” does not reverse to “man of the slave”; take the correct correlative, master.
  • Digression from “I now pronounce you man and wife”: is man the correlative of wife? The correlative is husband; Greek/Latin sometimes just say “woman”. Are man and woman correlative? — “a good question”, left there. Etymology: joke that woman is “woe to man”; the etymological dictionary rather gives “she has a veil”. So “man” becomes equivocal — a woman is a man (not a dog or cat) and man is also opposed to woman. Parallel: nomen is common to nomen and verbum and opposed to verbum; the verb gets a new name because it adds signifying with time; woman gets the new name because she adds something (the veil). His other explanation — man alone has reason fully — the women like less; the one they like is that man was made from dust, woman from man, which is nobler. (“You want to know how a woman thinks? You marry one.”)
  • (ii) relatives are together by nature — true of pure relatives (double/half), not of relatives that are qualities: what knowledge and sense are of can be before and without them (the moon exists before we know it).
• Objection: each part of a substance is said of another (hand of a man, head of a man); on the first definition substance would be a collection of relations. Hence the definition is modified: that whose whole being or nature is to be towards something, not merely said of another.
• Further property: if one correlative is known, so is the other; part of the more universal truth that there is the same knowledge of opposites. Aristotle ends by noting the difficulty of the matter.

6. The name of the genus: ad aliquid, not “relation” (“concentrate on the name of this genus”) #

Point: the genus is rightly named “towards something” — Greek pros ti, Latin ad aliquid — not “relation”, since Thomas notes the more abstract word is not said towards something; it sounds like something in itself.

• Thomas on the Metaphysics: three ways things are said ad aliquid not by themselves but according to something else; the second mode is when abstract things (equality, likeness) are said ad aliquid because the concrete things having them are — simile et aequale ad aliquid sunt. Cousin Donald: “Duane, that’s just like your father” — you couldn’t say it with “likeness”. “These tables have equality” vs. “are equal to each other.” Aequalitas and similitudo secundum nomen are not said towards something, though one sees the relatives.
• Aside he “always makes fun of”: “relationship”, used even by priests — an abstraction of an abstraction, and “having a relationship” is like having lunch; “in a relationship” treats it as something one. Better: “what are you towards me?” — as our Lord to his mother at Cana, “What to me and to thee?” To speak of a relation between two things is to speak as if one accident were between them.
• Thomas, Sentences: some, as Avicenna in his Metaphysics, say the same relation in number is in both extremes — which cannot be, since one accident cannot be in two subjects. In each extreme there is one relation: differing in species where the names differ (paternity/filiation — father of you, you my son); differing only in number where the name is one (similitude, equality — if I’m equal to you, you’re equal to me). What is in one as subject is in the other as term, e converso. “So it’s really two different things.”

7. Order of nature vs. order of teaching; Porphyry’s parallel (“in the order of nature, but in the order of teaching”) #

Point: Aristotle enumerated the first four genera in the order of nature but teaches towards something before quality; Porphyry imitated this — “a brilliant comparison”.

• Isagoge proemium: to Chrysaorius, to know what genus, difference, species, property, accident are is needed not only for the Categories but to divide, define and demonstrate; yet he takes them up as genus, species, difference, property, accident — one difference in the order.
• The enumeration is the order of nature, shown from the definition of square (equilateral, right-angled quadrilateral): quadrilateral can be without square, not square without quadrilateral; equilateral without square (the rhombus); right-angled without square (the oblong — students say “rectangle”, but square is special and gets its own name). So genus and differences are before the species, and quadrilateral before the differences.
• Porphyry’s reason for changing differs from Aristotle’s: genus and species are defined through each other (genus: said of many differing in species in answer to what it is; species: what is placed under a genus) — almost relatives, compared to father and son; genus goes back to generation, a father can have many sons, a son not many fathers in the same sense.
• Aside on the precision of these two men against “sloppy writers, sloppy thinkers” in democratic times. Example: the other faction at the College of St. Thomas divided philosophy by true, good, being (logic/ethics/metaphysics) — but these are transcendentals, convertible, so all belong to the same science; Thomas at the beginning of De Trinitate, on the true, shows them convertible (the mind knows the truth about the good; the will wills the good). “That’s sloppy thinking.”
• Back to “relationship”: very bad ways of speaking that reflect their thinking.

8. “Lover”: quality or towards something? (“What genus did you put the word lover in?”) #

Point: test case for secundum dici / secundum esse.

• A student proposes “only the second” [ed.: secundum dici]. Yes: love is fundamentally a quality of the heart with a relation following on it — that is why Plato mixed them up. Like knower, searcher.
• “What am I towards numbers?” — a knower (he will reread the seventh, eighth, ninth books, on numbers). Towards my wife and children — more a lover than a knower, though a knower too. A psychologist may be a knower of you and not a lover.

9. Different senses of order; Plato respected; Albert (“these are different senses of order”) #

Point: Porphyry is orderly both in enumerating (order of being) and in treating (order of learning); not the same order. He praises Porphyry’s “magnificent proemium”: division (genus into species), definition (genus and difference), demonstration (a property through genus and difference).

• Aristotle’s respect for Plato: proceeds as if the accepted definition is fine. Thomas notes Aristotle often gives examples in logic that were commonly accepted at the time and corrects them in other books — so beware objections drawn from the Categories (e.g. on opposites), which may follow “customary positions of Pythagoras or somebody”.
• Stops at p. 3, a text of Albert the Great. At Laval the logic course used Porphyry through Albert’s paraphrase; Albert paraphrases rather than comments, was with Thomas, “a great logician”. Teachers by the written word (Aristotle, Thomas, Albert, Boethius, Augustine) vs. by the spoken word.

His words #

• Praedicamenta: Latin name for the Categories.
• quantity per accidens: a quality quantified through the surface it is on.
• “wisdom”: the Metaphysics; “fourth book of wisdom” [ed.: Metaphysics IV].
• “towards something” / pros ti / ad aliquid: his rendering of the genus, preferred to “relation”.
• relativa secundum dici: said of another, but fundamentally a quality (knowledge, lover).
• relativa secundum esse: whose whole being is towards another (double, half).
• philosophi praecipui: Thomas’s phrase for Plato and Aristotle.
• reversibility: what is said towards something has something said reversibly towards it.
• nomen / verbum: name common to noun and verb, and opposed to verb.
• simile et aequale ad aliquid sunt; aequalitas, similitudo secundum nomen not said ad aliquid.
• paternity / filiation: relations in the two extremes differing in species.
• oblong: his name for the non-square rectangle.
• order of nature vs. order of teaching (learning).
• transcendentals: convertible, so belong to one science.

Texts #

Read in class

• Aristotle, Categories, ch. 6 (recap from handout “Quantity – Chapter Six”, p. 17).
• Thomas texts on quantity: species of quantity by notions of measure; exposition of Boethius/Dionysius on order in number and time; “all things partake of one.”
• Handout outline of Categories ch. 7 (“The First Definition of Relation”, p. 105) (inferred title).
• Thomas, Commentary on the Metaphysics: three ways things are said ad aliquid (second mode).
• Thomas, Commentary on the Sentences: against Avicenna, one relation is not in both extremes. Mentioned
• Aristotle, Metaphysics IV (subject of wisdom: being and one).
• Plato, Republic (community of wives); Shakespeare, poem on reason puzzled by lovers made one.
• Porphyry, Isagoge, proemium (to Chrysaorius).
• Thomas, De Trinitate, beginning (transcendentals convertible).
• Albert the Great, paraphrase of Porphyry (handout p. 3, next time).
• John 2 (Cana, “what to me and to thee?”) (inferred).

His questions #

• Are the two divisions of quantity identical? No: time is continuous but its parts have no position, not existing together.
• Can you measure a surface by inches? No — by square inches; a thing is measured by something of its own kind.
• What is the subject of wisdom in the fourth book? Both being and one.
• Why does Aristotle disturb the order and treat towards something before quality? Because he starts from Plato’s definition, which would put knowledge in ad aliquid; relations follow on quality and quantity.
• Is knowledge in the category towards something, or a quality of the teacher? Fundamentally a quality with a relation following — relativum secundum dici.
• Is man the correlative of wife? Are man and woman said correlatively? Husband is the correlative; man/woman left open (“a good question”).
• What genus does “lover” belong to — quality or towards something? Fundamentally a quality of the heart, relative secundum dici.
• What am I towards numbers? A knower.
• Is Porphyry speaking orderly both when he enumerates and when he treats the five? Yes, but in different senses: order of being, then order of learning.