Defining by Names Common to Many Things: Univocal and Equivocal Names, Genus, Species and Difference

Orientation #

He is continuing “part one” of his handout, which is about names (part two will be definition itself), picking up “at the bottom of page two” and going through page five. He refers back to “a little text of Aristotle” on the word “before” treated earlier (prev. lecture). He promises to treat property later and to return to names equivocal by reason, and to the definition of species and the “lowest species”. The previous class began the art of definition with the study of names, and the next continues Porphyry’s five names into property and accident.

The class, in order #

1. Calling a thing by its own name or by the name of another (“calling a thing by some name”) #

Point: one may name a thing by its own name or by another’s name, and the latter is either a mistake or a figure of speech.

• Romeo calls Juliet “Juliet” (own name); if he slips and calls her “Rosalind” he is mistaken and “in trouble”; a child calling a cat a dog: name of another thing, mistaken.
• Romeo calls Juliet “honey” or “sweet”: name of another thing, yet not mistaken — a figure of speech; the greatest is metaphor.
• Thomas, commenting on St Paul’s use of irony (Galatians, he thinks), explains that in figurative speech the meaning of the word is not the meaning of the speaker, though there is a connection: in metaphor a likeness (honey is sweet and pleasant, so is Juliet); in irony the opposite (a drunk student under the table: “what a fine example of a college student”).
• Synecdoche: part for whole or whole for part — “he’s a brain”; Aristotle in NE X that reason more than anything else is man; “the Word was made flesh”.
• Antonomasia: “he’s a Romeo” (= a lover), a Don Juan, a Casanova; “my student is another Einstein”.
• Why we speak figuratively: to express or arouse emotion and to appeal to imagination through the likeness. Thomas in the Sentences commentary: one reason (of many) for metaphor in Scripture is that imagination, like every part of us, should be subject to God — as genuflecting brings in knees and legs, metaphor brings imagination into God’s service; imagination being higher than the legs is more dangerous in leading us astray.
• “You pig” to the one who ate the whole pie: expresses and arouses emotion better than “you glutton”.
• For definition, though, use the thing’s own name: you seek the reason, not to move emotion. “What is a pig?” is unclear where “What is a glutton?” is clear; asking “what is a cat?” when you mean dog is entirely misleading. The logician uses the thing’s own name, not even a figurative one.
• Aside: a James Bond film where someone in the theatre remarked on the electrocution scene — offered as an instance of irony [unclear in recording].

2. The dilemma of page four and its untying (“raise a little question”) #

Point: it seems a thing can be defined neither by its own name nor by the name of another.

1. Every name is either the thing’s own name or the name of another thing.
2. Define by its own name and you break the school rule against using the name of the thing defined: “dog is a dog” is true but makes dog no better known; “a rose is a rose”.
3. Define by another’s name: either an incorrect name (define dog by cat, or by triangle — “more than useless”) or a metaphor — but “a glutton is a pig” does not say what a glutton is, since pig means a four-footed animal with a tail and snout. You cannot even use metaphor to say what a metaphor is, only to exemplify it. Solution: “one’s own” has two meanings. (A) what belongs to me alone — my own nose, my own teeth; (B) what is mine yet shared — my own country, my own mother (not mine alone; brothers and sisters), my own daughter (my wife’s too), “go home to your own house” (the whole family’s house). We define a thing by names that are its own in sense B.

3. The same distinction in practical philosophy (“it’s very important”) #

Point: the two senses of “one’s own” matter for the common good, not just for logic.

• The philosopher’s good is truth — his own in sense B, a common good. Common good in the strictest sense: shared by many at once with no diminution. My understanding the Pythagorean theorem does not prevent, and may help, yours.
• Boundary cases that are not common in the fullest sense: an apple pie bought together (no one gets it all), a shared computer or chair (not usable by both at once).
• God, the first truth: my knowing and loving him does not prevent yours. My greatest goods (truth, God) are not goods belonging to me alone; so too parents’ children, the citizen’s country, the team’s victory.
• Otherwise defending one’s country would not be acting for one’s own good, “simply a slave”; defending truth, I defend my good but not my private good. People stuck on the first sense cannot see out of the objection — which is why he cast it as an objection.

4. Names said of many; definition as a limit; convertibility (“names that are common to it”) #

Point: to define by a thing’s own names in sense B is to define by names said of many, whose combination fits the thing alone.

• Student flags a probable typo on p. 5 (“induction shows”; a “we” missing; lobsters was his example of induction).
• Calling a dog “animal” is calling it by its own name in sense B, though not the name that distinguishes it from cat and horse.
• “Many” has two senses: opposed to few, or to one; here, opposed to one (more than one).
• Etymology of definition: Latin finis (end, limit); Greek horos, horismos (cf. horizon), from the word for limit. A definition draws a line around the thing, like the city limits of Worcester containing every part of Worcester and no part of another town, or a farmer’s fence around his own field: neither more nor less.
• Problem: how can names common to the thing and others fit just this one thing? Answer (student): the combination.
• Convertible (not the automobile): A and B are convertible if every A is B and every B is A; definition and defined must be convertible. Square = equilateral right-angled quadrilateral, both ways. Socrates turns definitions around to test this. “A chair is something to sit on”: every chair is, but a bench or saddle is not a chair — something must be added.
• Longitude and latitude: each line gives what a point has in common with an infinity of points, yet only one point has both — so a combination of common names can fit one thing.
• Square: quadrilateral is common to oblong, rhombus, rhomboid, trapezium; equilateral to square and rhombus (“a jerked square”); right-angled to square and oblong; the combination fits only the square.
• Aristotle at the beginning of the Poetics: Homer (epic), Sophocles (tragedy), Aristophanes (comedy). Tragedy shares with epic the representation of serious things, men greater than us; with comedy, acting out rather than narrating; the combination fits only tragedy. His rendering of the definition: a likeness of an action that is serious, complete and of some magnitude, in sweetened language, acted out rather than narrated.
• Each name in a definition gives a confused knowledge of the thing (none separates it from all else); put together they yield distinct knowledge — the natural road from confused to distinct.

5. “Rational animal” a bad example; why start with names said of many (“names common to many things”) #

Point: the standard textbook example misleads, and the first topic of logic is names said of many.

• Student asks whether every name in a definition is common: “rational” seems to fit man alone. Reply: rational animal is a poor example since it does not show what almost all definitions have; “rational” is taken from a property of man (to be treated later), which is how it becomes convertible. Porphyry gives “rational mortal animal” (the Platonists held there were immortal rational animals), where no part belongs to man alone. Logic books’ use of “rational animal” is a sign of their ignorance of logic.
• Albert the Great says the first thing in logic is the universal; “more sensible” to say: names said of many. Even the name of the thing defined is common — you define man, not Socrates; dog, not Lassie; horse, not Bucephalus.

6. Univocal and equivocal; equivocal by chance and by reason (“one meaning in mind”) #

Point: the fundamental distinction of names said of many is whether one meaning or many is in mind.

• “Bat” said of the baseball bat and the flying mouse in the belfry: equivocal, not called bat for the same reason; said of three baseball bats: univocal. A name with many meanings can still be said univocally of many.
• Univocal: said with one meaning (same reason) of many — man of each of us (animal with reason); animal of man and dog (living body with sensation); quadrilateral of square, oblong, rhombus, rhomboid (rectilinear plane figure contained by four straight lines).
• Footnote added: equivocal by chance vs by reason. Bat is by chance (no connection seen). “I see you” / “I can see my son now” (picturing him): a likeness, so by reason; in dreams imagining is like seeing and deceives us.
• Names equivocal by reason are the key words of wisdom and of the axioms; Aristotle discovered that the most common words are equivocal by reason and devoted one of the 14 books of metaphysics to distinguishing their meanings. Earlier example: “before” (in time, in the discourse of reason, in the sense of better — four meanings; “reason looks before and after”). In a name equivocal by chance there is no order among meanings; by reason there is order and connection.
• Logic called philosophy: not in the same sense as geometry, natural philosophy, wisdom, but as a tool for acquiring them (Euclid starts with definitions and statements, then syllogisms) — so not purely by chance. “Convertible” (logic vs car): almost purely equivocal.
• Some call the by-reason names “analogous” and the by-chance ones “equivocal” or “purely equivocal”; he prefers by chance / by reason, since “analogous” is taken from one kind of by-reason name and narrows the understanding.
• Aristotle in On Sophistical Refutations: the most common mistake is mixing up senses of a word, mainly the by-reason ones. “Idea” in English: image (“don’t get ideas”) vs thought (the philosopher’s ideas); Locke confuses them. Thomas notes the Arab philosophers called the first act of reason a kind of imagination through the understanding — there is a likeness. In defining, first fix on one meaning; so next: names said univocally of many.

7. Porphyry’s Isagoge and the first division (“inside their nature”) #

Point: Porphyry divides names said of many into those signifying inside and outside the nature.

• Porphyry, a Neoplatonist, wrote the Isagoge (Greek: introduction) to Aristotle’s Categories — the only book from Aristotle on the logic of the first act — for a student who found the Categories hard. In the proemium he says it is useful for the Categories, for definition, for division, and for demonstration (the most perfect syllogism).
• Division: a name said of many signifies something inside their nature (what they are) or outside it. Three triangles called “triangle”, “plane figure”, “figure”: inside; called “green”: outside. Obviously exhaustive. The first branch subdivides into three, the second into two.

8. Genus (“what is a dog”) #

Definition: a name said with one meaning of many things other in kind, signifying what they are. “What is a dog?” — “an animal”: genus, said of dog, cat, horse, dolphin, signifying what it is in a very general way. We start with the genus because we know first confusedly: the genus grasps what it is in common with others and does not distinguish kinds. Sonnet — a poem (one kind among many); tragedy or comedy — a play or drama; reason — an ability (one of many).

9. Species (“the form or shape you see”) #

Greek eidos, Latin species: a form you can see (eidos akin to eidenai, to see; species to speculor, to look); in English “species” or “form”. The name of a particular kind under a genus: cat, dog, horse, elephant under animal; monarchy, oligarchy, democracy — “forms of government”; tragedy and comedy under play (maybe another species between); square, oblong, rhombus, rhomboid, trapezium under quadrilateral; equilateral, isosceles, scalene under triangle — where no name exists, a speech stands in; virtue and vice under habit. Aside: species is spelled the same in singular and plural.

10. Difference (“species making difference”) #

Point: a third name is needed to say what the species has beyond the genus and what separates species.

• Two is often not enough — Aristotle in Natural Philosophy I; language shows it: three is the first number about which we say “all”. “What is democracy?” — “a form of government” — so is oligarchy; so a name is needed for what the species adds to the genus, i.e. what separates species other in kind: the difference, or species-making difference.
• Porphyry gives three definitions. Two are by role: (i) the name of what the species has in addition to the genus (its use in defining); (ii) the name of what separates one species from another under the same genus (its use in dividing). [He says “a species is the name of what separates…” — evidently a slip for “difference”.] It is the same name in both roles: right-angled names what square and oblong have beyond quadrilateral and separates them from rhombus, rhomboid, trapezium; equilateral names what square and rhombus share and separates them from the rest; the combination separates the square from all. Mnemonic: rhombus ends in S, S for square. Euclid uses the difference both to complete definitions and to divide quadrilateral.
• Etymology: Latin difference; Greek diaphora, from dia (apart) and phero/phora (carry): quadrilaterals seem together, the difference carries them apart.
• (iii) Definition by return to the division: a name said with one meaning of many things other in kind, signifying not what they are but how they are what they are — the added clause because it is an essential difference, not an accidental “how” (“How are you today? I’m sick”). Same definition as genus except the last part.
• Porphyry has not yet defined species as a name said of many; that comes after seeing how the same thing can be genus and species, the exception being the lowest species.
• Summary: species is the name of the thing defined; genus begins the definition; differences (usually two or more) complete it; the genus is the fundamental name, the difference determines how it is what it is.
• Closing, cut off: the names signifying outside the nature might seem superfluous for definition, but there is reason to subdivide them, both for definition and later for demonstration.

His words #

• figure of speech; the meaning of the word is not the meaning of the speaker (Thomas), with a connection between them
• metaphor; connection by likeness; irony; connection by opposition
• synecdoche; whole for part or part for whole
• antonomasia; a proper name for what it is famous for (“he’s a Romeo”)
• one’s own; (1) what belongs to me alone, (2) what is mine yet shared
• common good in the strictest sense; shared by many at once with no diminution
• many; opposed to few or opposed to one; here, more than one
• definition; from finis, horos, horismos: a limit drawn around the thing
• convertible; every A is B and every B is A
• natural road; from confused to distinct knowledge
• univocally; said with one meaning (the same reason) of many
• equivocal by chance vs equivocal by reason; the latter with order and connection among meanings [ed.: “analogous” for the latter, which he declines]
• wisdom; [ed.: metaphysics] “the 14 books of wisdom”
• inside their nature / outside their nature; the first division of names said of many
• genus; name said with one meaning of many things other in kind signifying what they are
• species (eidos); the form you see; a kind under a genus
• difference (diaphora); species-making difference; signifies how they are what they are
• lowest species; where genus and species do not coincide (to come)

Texts #

Read in class

• Berquist’s handout, part one on names, bottom of p. 2 through p. 5
• Porphyry, Isagoge: proemium (uses of the work) and the chapters on genus and difference (three definitions of difference)

Mentioned

• Thomas Aquinas, commentary on an epistle of St Paul on irony (“might be the Galatians”)
• Aristotle, Nicomachean Ethics X (reason more than anything is man)
• Thomas Aquinas, commentary on the Sentences (metaphor in Scripture subjects imagination to God)
• Aristotle, Poetics, beginning (Homer, Sophocles, Aristophanes; definition of tragedy)
• Aristotle, Categories
• Aristotle, Metaphysics, the book distinguishing meanings of key words (Book V inferred); “a little text of Aristotle” on “before” (prev. lecture)
• Aristotle, On Sophistical Refutations (mixing up senses of a word)
• Aristotle, Natural Philosophy [ed.: Physics] I (two is not enough)
• Albert the Great, logical works (the universal first)
• Euclid (definitions, then statements, then syllogisms; use of differences)
• John Locke on ideas; Thomas on the Arab philosophers’ “imagination through the understanding”
• Plato’s dialogues (Socrates testing convertibility); Shakespeare’s Romeo and Juliet (implied)

His questions #

• When Romeo calls Juliet “honey”, is he calling her by her own name? No, by the name of another thing, yet not mistaken — a figure of speech.
• If you want to define something, should you call it by its own name or another’s? Its own, because you want the reason, not to move emotion.
• Are we to define a thing by its own name or by the name of another thing? By its own name in the second sense of “own” — names it shares with others.
• Is truth my own good as a philosopher, and in what sense? In the second sense: a common good.
• When I call a dog an animal, am I calling it by its own name? Yes, in the second sense; it is not the name that distinguishes it.
• How can you define a thing by names common to it and other things? By the combination, which fits that one thing and is convertible with it.
• Is everything to sit upon a chair? No (bench, saddle); something must be added.
• Is it by chance that we call both seeing and picturing my son “seeing”? No, there is a likeness: equivocal by reason.
• Why do we tend to start with the genus? Because we know first confusedly, and the genus is a confused understanding of what it is.
• Given genus and species, can you see the need for a third name? Yes: the genus does not tell distinctly what the species is; the difference names what it adds and what separates it.