The Art of Definition I: Definition of a Thing vs. a Name, Full Definition and Encircling, Cause and Effect

Orientation #

He says “today we’re going to talk about the second part of the art of definition,” recalling that the natural road (confused before distinct; outward before inward) was treated earlier and that the definition of reason as “ability for large discourse” took a long time to understand. The recording begins mid-sentence (a stray remark on dividing sins into thought, word and deed, “desire, word, deed”) and cuts off mid-sentence at the end; it also has a gap in the middle of the section on the three distinctions. He announces “three fundamental distinctions among definitions of things” but only two are reached in the recording. The previous class treated equivocal naming; the next takes up the third distinction, things defined by themselves vs. as of another.

The class, in order #

1. Definition and division as the two ways from confused to distinct (“definition and division are two ways”) #

Point: the art is called “the art of definition,” but it covers division too, since division is a secondary tool for knowing what a thing is and partly a way of arriving at definitions — as the third act of logic is chiefly about the syllogism though not only about it.

• Every reasoned-out knowledge begins with definitions and divisions: Euclid begins with definitions and divisions; Aristotle in Nicomachean Ethics II defines moral virtue and then divides it.
• Reason for the two tools: along the natural road we know things confusedly before distinctly (classical text: beginning of the “eight books of natural hearing, the so-called physics”; to be gone into more deeply in natural philosophy; every student’s experience of studying confirms it).
• Proemium: “we must think out definitions and divisions before we reason out conclusions.” Reasoning out is one form of thinking out (thinking out a conclusion). There are at least seven senses of “thinking out,” matching seven senses of “out,” matching senses of “in” — “actually, there’s eight senses” of in, but maybe seven of thinking out; in reasoning out “you’re going to find at least these seven.”
• Definition is the beginning of a syllogism: Aristotle (he thinks in the Metaphysics) gives as a sign that Socrates was trying to syllogize that he was always trying to define. “Most people don’t see that connection.”

2. Definition of a thing vs. definition of a name (“the definition of a thing and the definition of a name”) #

Point: the two kinds; we are chiefly concerned with the definition of a thing.

• Definition of a name: using some words to make known what the word means — necessary at times, but not the main kind.
• Against Mill (“all definitions are of names and names only”): laughable; what we chiefly want is to know things, not the meaning of names. The same idea shows up even in Heisenberg (whom he admires greatly, “next to Einstein”), who speaks of Plato’s dialogues as if Socrates were mainly concerned with the meaning of names; it makes definition secondary.
• Defining a thing is often a major accomplishment: it takes long to arrive at, few arrive, and the rest of us take long to understand it. Descartes quotes the definition of motion garbled and asks “who understands that?”, not realizing it is a major work to think it out or even to understand it. Our own case: reason as “ability for large discourse, looking before and after” — it took a long time to understand “discourse” and “large.”

3. First definition of definition: speech signifying what a thing is (“speech signifying what a thing is”) #

Point: definition is the first of the three speeches logic is chiefly about.

• Speech: “vocal sound signifying by custom [or by human agreement], having parts that signify by themselves” (five-part definition). The three speeches: definition = speech signifying what a thing is; statement = speech signifying the true or the false; syllogism = speech in which, some statements laid down, another follows necessarily because of those laid down.
• Should one add “distinctly”? A name can also signify what a thing is: asked “what is this?”, “a square” signifies what it is; “equilateral right-angled quadrilateral” signifies the same thing but more distinctly. Then “nothing too much”: since a speech has parts that signify by themselves, it necessarily signifies more distinctly than a name (square: no part signifies by itself; the definition can “blow up, expand”). So “distinctly” is perhaps superfluous — but one should see that a definition signifies distinctly because it is a speech and not a name.
• If the definitions of speech and name are the first definitions of logic, the first postulates would be: no speech is a name / no name is a speech; every speech is composed of names.

4. Second definition: speech making known what a thing is (“speech making known what a thing is”) #

Point: in imitation of Aristotle’s definition of demonstration (a syllogism making us know the cause, that of which it is the cause, and that it cannot be otherwise — “making something known”), definition can be defined as speech making known what a thing is. He says “definition” simply, meaning definition of a thing: “I’m not a modern in that sense, I’m a Greek.”

• Perfect number (students know odd and even but not this): a number equal to the sum of everything that measures it (measures evenly). Four: measured by 1 and 2, 1+2 ≠ 4. Five, three, two: measured only by 1. Six is the first perfect number (1+2+3), twenty-eight the second. Examples alone don’t tell what it is; the definition makes it known. Aside: Augustine and Thomas see meaning in creation in six days (first perfect number, its measures perfect in order 1, 2, 3); Plato’s Symposium has six speakers — three rhetoricians, two poets, one philosopher, going round the table from lesser to greater.
• Blank verse (Shakespeare’s exhortation): unrhymed iambic pentameter; iamb: two syllables with the accent on the second — made known by definition.
• This fits Shakespeare’s definition of reason as ability for discourse: discourse = coming to know what you don’t know through what you do know. The two kinds of discourse studied in logic are defining and reasoning; defining makes known “the simple unknown,” what something is (Albert the Great); reasoning makes known the complex unknown, the statement.

5. Third definition: speech bringing out what a thing is (“Nature loves to hide”) #

Point: since what a thing is lies within and is hidden, a definition brings it out.

• Heraclitus, “the central thinker in human thought”: “Nature loves to hide” — one of those sayings you don’t try to improve, recalling Aristotle (he believes in the Politics): say some things better than predecessors, others as well as they said them.
• “Nature” in Metaphysics V: all its meanings have the idea of something within, hence hidden at first. First meaning, birth: from within, the baby hidden (boy or girl unknown until it comes forth); later, a beginning and cause of motion within a thing; eventually, what a thing is — still within, so hidden.
• “Bring out” is a form of thinking out: what you have thought out you have brought out. Aristotle must have thought a lot about motion before bringing out what it is. Boethius thought out the definition of eternity (Consolation of Philosophy); in the Summa’s question on God’s eternity Thomas objects to every part of Boethius’ definition, explains it in the body, replies to each objection — concentrating the mind on every word; he does the same with Boethius’ definition of person.

6. Aside: the definition of definition, reflection of reason on itself (“the definition of definition”) #

Point: definition here reflects what Thomas says in the major proemium — reason can think about its own act.

• Definitions of definition, statements about statements, reasoning about reasoning.
• Tongue twister: is the definition of the definition of a thing a definition of that definition? No — “the thing is not a speech”; but it is said of the definition of square, i.e. of any definition of a thing, since “speech signifying what a thing is” is common to all definitions.
• Can a thought be about itself? A student: yes, insofar as it is common to all thoughts; a particular thought at that instant, no. A thought about the thought of a triangle is about a thought, not about a triangle — not the same, not even the same in kind. “God gets closer to this, but he doesn’t have any thoughts.” Left as “a little aside.”

7. Definition of a name and the order between the two kinds (“does it exist? … what is it?”) #

Point: definition of a name = speech making clear the meaning of a name (much less rigorous); and it is before the definition of a thing in the first sense of before.

• Posterior Analytics II (“perhaps the greatest book in logic”), the four questions: does it exist? what is it? is this that? why is this that? Order: existence before what-it-is; is-this-that before why (atom exists → what is the atom; man laughs → why; the sun’s light cut off → why; Saudi Arabia’s government overthrown → why).
• Argument: (1) to ask “does it exist?” you must use the name, so you must have a meaning for it; (2) there may or may not be something corresponding (vitamins, atoms, unicorns, Santa Claus, mermaids — Columbus’ crew sighted “mermaids,” “one of the mysteries of history”; in theology “does God exist?” needs a meaning for “God”); so (3) the definition of the name comes even before the question of existence, whereas you have no definition of the thing in the strict sense until you know it in some way exists. A name can be defined though no thing corresponds (unicorn, mermaid, centaur: figments).
• Second reason: a definition, like every speech, is composed of names, so a name in it may have to be explained.
• Euclid: some of Book I’s definitions are at first definitions of names, becoming definitions of things later — the equilateral triangle’s existence is not presupposed to Proposition 1, which constructs it in imagination; likewise the right angle, constructed by a later theorem. But something must be given as existing at the start (point, line). So to understand even Euclid fully one needs logic, though it is so easy “even the boy can learn it” (Thomas).

8. First distinction: definition in the full sense vs. encircling (“drawing the line around”) #

[Recording gap here; he had announced three fundamental distinctions, “the first two very similar.”] Point: encircling gives an outward, confused knowledge; full definition brings out what the thing is inwardly.

• Order: outward before inward (second before-and-after on the natural road), because knowledge starts from the senses, and “outward” is almost a synonym for sensible; confused before distinct, and encircling is confused knowledge (“wisdom is the best knowledge”).
• Dog: animal (so is man); four-footed (so is cat); “four-footed animal that barks” vs. “that meows” — as far as the mind penetrates, an outward knowledge through something sensible.
• Virtue as “praised quality”: the child learns what is blamed or praised before what is inwardly good or bad (grandchild giving one of two gifts to her sister Sarah, everyone pleased). Praise or blame is outside but more known than inward goodness.
• Someone may say “you haven’t told me what it is” — so in one sense encircling is not a definition; “let’s call it drawing the line around.” It is a mistake (except perhaps in geometry or arithmetic, where things are on the surface) to try to begin with the definition in the full sense.
• Names in each: full definition = genus + species-making differences; encircling = genus + a property or combination of common attributes. Being the best knowledge is a property or result of wisdom; barking follows on what a dog is. Triangle as “rectilineal plane figure with the least sides” doesn’t say what it is (least sides results from not containing a space with fewer than three lines) — but stupid to do in geometry where everything is on the surface.
• Aside: courage, temperance, vices are hidden deep down, especially pride; “stubborn” from the stub, the root of a tree that resists removal, the checkbook stub that stays in.

9. Second distinction: definition by cause vs. by effect (“is it pious because it pleases the gods”) #

Point (handout, second half of p. 3): almost the same distinction, differently stated; definition by cause is more perfect, since causes make the thing what it is.

• Euthyphro: “the pious is what pleases the gods”; Socrates’ question — pious because it pleases them, or pleases them because it is pious? — is asking cause or effect.
• Good is what all desire (first definition of good, beginning of ethics): good because we desire it, or desire it because it is good? Your whole understanding of good, bad, better, worse depends on it; it is a definition by effect, to be shown by discourse. If good because I want it, good is nothing in the thing; if wanted because good, the good is in things — “the whole of ethics depends upon” this; “if you don’t understand that, you don’t understand anything.”
• Heisenberg: the Greeks taught us to ask questions of principle, “the most powerful tool the Western mind has.”
• Augustine, De Vera Religione: “the beautiful is that which pleases when seen”; he asks the same question and says “I have no doubt that it pleases us because it is beautiful” — definition by effect; the whole understanding of the fine arts (Mozart) depends on it.
• Comedy as likeness of the laughable / a play that makes you laugh, tragedy makes you weep: definitions by effect. We often define by effect first and often get no further, because effects are more known to us than causes (the road goes from senses into reason; every “why?” knows the effect not the cause).
• Dog again: barking as property (first distinction) or as effect (second): “it’s not a dog because it barks… because it is a dog, it barks” (the barking dog in the car at Mass this morning). Great thinkers use now one language, now the other (Thomas: good as what all desire is definition by effect); one distinction is more natural in some contexts.
• Student: is cause/effect a third type? No — two distinctions among definitions of things, almost the same, since the property is in a way an effect of the species-making differences. Student: is the second broader? The first emphasises the names (genus completed by differences vs. by a property); the second emphasises cause and effect. Student: would a definition by cause be a definition in the full sense? Yes; examples: marriage, “a stable union of a man and woman by mutual choice for the sake of children” (all four causes); sacrament, “an outward sign instituted by Christ to give grace” — to give grace = end, instituted by Christ = mover/maker, sign = form, outward = matter.

10. Why effect before cause; why encircling before full definition (“the reasons we gave are not so much identical”) #

Point (handout p. 4): definition by effect very often comes before definition by cause; encircling always comes before full definition “if you need both” — but the reasons stated differ. For cause/effect: effects are more known to us, more sensible. For encircling: we know things outwardly before inwardly, indistinctly before distinctly.

11. Origin of the word “definition”: limit, hence convertible speech (“a definition must be convertible speech”) #

Point: prompted by a student on Greek horizō and boundary markers; all the kinds are definitions in the broad sense, and that sense is limit.

• Latin finis (limit, boundary); Greek horos (limit) and Aristotle’s horismos, close to “horizon,” the line separating sky from earth. Farming: a fence defines property — all mine, none of my neighbour’s; city limits of Worcester contain all Worcester, none of the surrounding towns; Massachusetts, none of Connecticut, Maine, New Hampshire.
• So the logician says a definition must be convertible speech (not the whole meaning, but the first condition, suggested by the name itself). Convertible: if every A is B and every B is A. Every square is an equilateral right-angled quadrilateral and vice versa. Socrates turns proposed definitions around.
• Love as “an emotion”: not every love is an emotion, and even if it were, not every emotion is love — not yet defined. Chair as “something to sit on”: bench, sofa, saddle; “for one person”: saddle, stool; add “legs and a back” and you may reach convertible speech — Posterior Analytics II: keep adding differences until the speech is convertible. Recording ends: “There we have a little bit of the origin of…”

His words #

• art of definition; covers definition (chief tool) and division (secondary, also a way to definitions)
• thinking out / reasoning out; reasoning out = thinking out a conclusion; seven senses of thinking out, eight senses of “in”
• natural hearing [ed.: Physics]
• speech: vocal sound signifying by custom, having parts that signify by themselves; name: no part signifies by itself
• definition (of a thing): speech signifying / making known / bringing out what a thing is
• definition of a name: speech making clear the meaning of a name
• discourse: coming to know what you don’t know through what you do know; simple unknown (what it is) vs. complex unknown (statement)
• the “four questions” [ed.: Posterior Analytics II]: does it exist? what is it? is this that? why is this that?
• definition in the full sense vs. encircling / drawing the line around; genus + species-making differences vs. genus + property (or common attributes)
• definition by cause vs. definition by effect
• horos, horismos; finis; convertible speech (every A is B and every B is A)

Texts #

Read in class

• Berquist, “Foreword to Logic” handout, proemium and pp. 3-4 (definitions of definition; the two distinctions; why effect and encircling come first)
• Heraclitus, “Nature loves to hide” (quoted)
• Euclid, Elements: definition of perfect number; Book I definitions and Proposition 1 (equilateral triangle)

Mentioned

• Aristotle, Posterior Analytics II (four questions; adding differences until convertible); Metaphysics V (senses of “nature”); Metaphysics (Socrates always defining, “I think”); Physics I (confused before distinct); Nicomachean Ethics II (moral virtue); Politics (say some things better than predecessors, “I believe”)
• Plato, Euthyphro (piety); Symposium (six speakers)
• Augustine, De Vera Religione (the beautiful); Augustine and Thomas on six days of creation
• Thomas Aquinas, Summa, question on the eternity of God; on Boethius’ definition of person; major proemium to the logic (reason reflecting on its act)
• Boethius, Consolation of Philosophy (eternity)
• Albert the Great (simple vs. complex unknown); Mill (definitions of names only); Heisenberg (Plato; the Greeks and questions of principle); Descartes (definition of motion); Shakespeare (reason as ability for large discourse; blank verse); Columbus’ voyage (mermaids)

His questions #

• What is a perfect number, and how do I make it known? By Euclid’s definition: a number equal to the sum of what measures it; six first, twenty-eight second.
• Is the definition of the definition of a thing a definition of that definition? No — the thing is not a speech; it is a definition of any definition of a thing.
• Can you have a thought that is about itself? Only insofar as common to all thoughts; a thought about a thought is not the same, not even in kind.
• Why does the definition of a name come before the definition of a thing? You need a meaning for the name even to ask whether it exists, and definitions are composed of names.
• Are Euclid’s first definitions definitions of things? Some are at first definitions of names, shown to be of things by construction (Prop. 1).
• Is it pious because it pleases the gods, or does it please them because it is pious? Is “good is what all desire” a definition by cause or by effect? By effect (to be shown by discourse); the whole of ethics depends on it.
• Is cause/effect a third kind of definition of a thing? Is it broader than full/encircling? No: two nearly identical distinctions, one emphasising names, the other cause and effect.
• Is “something to sit on” the definition of chair? Is “an emotion” the definition of love? No — not convertible; keep adding differences until the speech is convertible.