Name and Speech, and Aristotle on Learning from Pre-existing Knowledge: Syllogism, Induction, Enthymeme, Example

Orientation #

He ties the Aristotle text to “what we saw about the word discourse” in the definition of reason, and to the definition of sign “I mentioned already” (prev. lecture). He says “We’ll be coming back to these forms of argument” and that he will take up sophistical argument “later on.” The previous class treated logic as an art whose subject is definition, statement and syllogism; the next opens Thomas’s division of logic and the art of definition, beginning with names.

The class, in order #

1. Name and speech: the four common parts (“first of all a sound”) #

Point: the two fundamental definitions of logic, name and speech, agree in all parts but the last.

• Part 1: a sound (not fingers rapping the desk).
• Part 2: vocal, produced by the vocal cords. Boundary case: clearing his throat is vocal but not intended to signify (“so I can speak more clearly”).
• Part 3: signifying. Sign, from Augustine, in his two-part translation: “that which strikes the senses and brings to mind something other than itself.”
• Part 4: by custom / by agreement, as opposed to by nature.

2. By custom vs. by nature (“moaning or sighing”) #

Point: the fourth part separates names from vocal sounds that signify naturally.

• Groan when kicked in the stomach, scream when attacked in the dark, the baby’s cry: vocal, signifying, but by nature.
• Aside on the baby: crying signifies need (food, diaper); once the baby learns the changing table is followed by food it stops crying there, “looking before and after” — an illustration of the definition of reason’s phrase applied to the infant.
• Joke: new father asks the nurse, “When should we wake the little fellow?”

3. The fifth part: name vs. speech (“No part of which signifies by itself”) #

Point: a name has no part that signifies by itself; a speech has at least two parts that signify by themselves.

• Man: vocal, by custom, no part signifies. Animal: three syllables, none signifies (Greek zoon); only the whole signifies.
• Consequence: the logician’s analysis of language stops at the name — he cares about vocal sounds only insofar as they signify. The grammarian goes down to letters and syllables; the poet to letters (rhyme, alliteration) and syllables (meter).
• White man: speech; white and man each mean something and the whole depends on them. Animal has more syllables than white man but its meaning does not depend on a-n-i-m-a-l.
• Boundary case: a name compounded from two names, functioning as one name, has parts that mean nothing. Bergkvist (Swedish berg mountain, kvist branch; his father dropped the G, never fully explained); Johnson — the woman was not a son and her father not John. “It’s only the whole sound.”

4. Definition, statement, argument are all speeches (“three speeches that perfect those three acts”) #

Point: since each tool of logic is a speech, names are studied before definition and statement.

1. Definition is always a speech: square as “equilateral and right-angled quadrilateral”; reason as “ability for large discourse, looking before and after” — each part means something. So a definition is never one name but a combination of two or more.
2. Statement is a speech: man runs, man is an animal, man is not a stone.
3. Argument is composed of two or more statements (usually two), so it is speech.

• Conclusion: in terms of its end logic is about three acts of reason; as subject it is mainly about the three speeches that perfect them (definition — understanding what a thing is; statement — true or false; syllogism or other argument — reasoning). Examining these speeches we see the names they are made from, hence names first.
• Student: “So the subjects of logic are the tools?” — Yes, chiefly definition, statement, syllogism. Student presses “two fundamental definitions”: he corrects to “two fundamental things we talk about.”
• Porphyry’s work sometimes called the Book of the Five Names, the Categories the Book of the Ten Names; in Greek, “the five vocal sounds,” “the ten vocal sounds.”

5. Aristotle: all teaching and learning from pre-existent knowledge (“mathematical forms of reasoned-out knowledge”) #

Point: the text on page six of the handout applies “discourse” (coming to know the unknown through the known) to reasoning in particular.

• Mathematics (geometry, arithmetic) is the clearest case of demonstration — why Euclid always writes Q.E.D.
• Euclid’s opening shows the three acts: definitions; statements obvious from them (postulates, axioms); then demonstration, each theorem from the previous.
• Worked example (he alters the demonstration a bit): a straight line falling on parallels makes alternate angles equal; then, drawing through a triangle’s apex a line parallel to the base, the alternate angles give the interior angles equal to two right angles. Sub-proof of the alternate angles: a straight line meeting a straight line makes two right angles or angles equal to them, so a + x = 2R and b + x = 2R; equals to the same are equal (axiom); equals subtracted from equals leave equals (axiom); so a = b. “Coming to know, in a very rigorous way, something you didn’t know.”
• Knowledge produced by demonstration is episteme; Plato treats it in the Theaetetus, Socrates talking with a mathematician — as he talks courage with Laches the general and piety with Euthyphro who prosecutes his father for impiety. Aristotle touches the first kind of reasoning, treated in the Prior and Posterior Analytics.

6. Dialectic: syllogism and induction (“sometimes Socrates reasons by syllogisms”) #

Point: the Socratic conversations (dialogue = Greek for conversation) are mainly dialectical, teaching by syllogism from the universal or by induction from singulars.

• Syllogism (Phaedo, against Simmias): the soul resists the body; the harmony of the body does not resist the body; therefore the soul is not the harmony of the body. Definition of syllogism: a speech in which, some statements laid down, another follows necessarily because of those laid down. Socrates never states the definition fully but says “this follows necessarily.”
• Second Phaedo syllogism: the soul existed before the body; the harmony does not exist before the body; therefore the soul is not the harmony. (He also notes: there is a harmony of the soul, but not a harmony of harmony.)
• “These syllogisms are not always demonstrations”: a premise may be only probable — the soul existing before the body is argued for, but perhaps not true; so the conclusion is not necessarily true.
• Induction: to show change is between contraries — what dries? the moist; what is moistened? the dry (you can’t moisten the ocean); hardened? the soft; becomes healthy? the sick; becomes sick? the healthy. Many particulars to the general.
• Why both in dialectic: it aims at knowing something about the universal, either by induction from many particulars or by syllogism from something more general.

7. Rhetoric: example and enthymeme (“speakers persuade”) #

Point: speakers persuade by example, which resembles induction, or by enthymeme, which is like a syllogism in a qualified sense.

• Example here is not a singular used to illustrate but an argument from one singular to another of the same kind. Joseph’s restaurant: a wonderful meal with his wife to the meal he and a friend could have; a car that lasted to buying the same again; MacArthur defending the Inchon landing by Wolfe’s landing at Quebec. Not necessary (Saturday vs. Monday, different chef); “the more the two are alike, the more you can reason from one to the other.” Like induction because the one meal stands as representative, but lacking its strength, which comes from many — the scientist has cut open hundreds of frogs; he has eaten there two or three times, or once.
• Enthymeme: argument from likelihood or from signs.
  • Likelihood: “Boys will be boys” — but sometimes a boy does what you expect of a man (the Dutch boy at the dike; protecting the mother). Contrast the true universal: no odd number is even, every three is odd, so no three is even — seen from what odd and even are. In human affairs universally true propositions are hard: “return what you borrow” has exceptions. So likelihood lacks the true universality of the syllogism; Aristotle calls it a syllogism in a qualified sense.
  • Signs: the most common rhetorical sign is more universal than what it signifies. Staggering out of a bar — drunk, but perhaps a physical defect or just tired; bloodshot eyes — the trooper who stopped him driving from Quebec (“You were drinking” — “No, I drove down from Quebec today” — “Go to Dunkin’ Donuts, get some coffee”); the long-haired student who cut his hair for court after a cop took him for a druggy; a cop spotting a bulge like a gun; the detective who could pick out a prostitute blocks away by her walk. Signs are not universal; the enthymeme lacks the rigor of the syllogism, which requires a true universal in the major premise.
• “We’ll be coming back to these forms of argument.”

8. The Metaphysics text: foreknowledge in definition too; Albert vs. Thomas (“contrary to Socrates’ view”) #

Point: the Metaphysics says the same of learning but extends it to definition as well as demonstration.

• Text: the one learning geometry foreknows — not the thing about which he will have reasoned-out knowledge, but that through which he learns; “all learning is through the foreknown” — either all (universal) or some (particular), as Thomas explains; both by demonstration and by definition.
• Albert the Great divides logic into two: the art of defining (about the simple unknown) and the art of reasoning (about the complex unknown), putting statement under argument. Thomas divides into three, looking at Aristotle’s works, “the father of logic.”
• Student asks how the Meno fits Albert’s division. Reply — the Meno has three parts: (1) Meno asks whether virtue can be taught; Socrates doesn’t know what virtue is; Meno fails to define it — an introduction to the difficulty of defining; (3) Socrates argues for and against whether virtue can be taught, dialectically, distinguishing knowing/certainty from opinion, even true opinion — in a way demonstration vs. dialectic; an introduction to reasoning; (2) the middle: Meno’s objection, how can you look for what you don’t know? — common to defining and reasoning (and even to counsel): logic uses what you know to reach what you don’t, but “how do you know what to use?” — the gas-station joke: “where are you trying to get to, buddy?” Socrates has trouble replying; Meno’s objection is sophistical and Socrates commits the same kind of mistake answering it (to be taken up later). Aristotle alludes to the Meno at the beginning of the Posterior Analytics. So Albert is closer to Plato’s division.
• Oesterle’s logic book, subtitle “The art of defining and reasoning,” follows Albert.

9. The same thing divided into two and into three (“Both divisions make sense”) #

Point: two-fold and three-fold divisions of one thing need not conflict.

• Nicene and Apostles’ Creeds divide the articles by Father, Son, Holy Spirit (emphasizing the Trinity); the Athanasian Creed and the Fourth Lateran creed by Christ’s humanity and divinity (six and six). Peter’s profession, “the Christ, the Son of the living God,” follows the latter and is a complete profession — why the Church is built on it.
• Aristotle divides the plot into beginning, middle, end, and also into tying and untying the knot.
• Family: parents and children. (Class ends mid-thought.)

His words #

• name — vocal sound signifying by custom, no part of which signifies by itself
• speech — same, but having parts (at least two) that signify by themselves
• sign — “that which strikes the senses and brings to mind something other than itself” (Augustine)
• by custom / by agreement — vs. by nature [ed.: conventional]
• discourse — coming to know the unknown through the known
• reasoned-out knowledge — [ed.: science, episteme]; produced by demonstration
• syllogism — a speech in which, some statements laid down, another follows necessarily because of those laid down
• induction — argument from many particulars to the general
• example — argument from one singular to another singular of the same kind
• enthymeme — argument from likelihood or from signs; a syllogism in a qualified sense
• Book of the Five Names / Ten Names — Porphyry’s Isagoge / Aristotle’s Categories [ed.: Isagoge not named]
• simple unknown / complex unknown — Albert’s objects of defining and reasoning

Texts #

Read in class

• Aristotle, Posterior Analytics, opening (“all teaching and all learning by reason come to be from pre-existent knowledge”), handout “Reasoning and the Four Kinds of Argument,” pp. 5-6 (verified)
• Aristotle, Metaphysics, on the one learning geometry (inferred: I.9)
• Plato, Phaedo, soul as harmony; change between contraries (recounted)
• Plato, Meno, three parts (recounted)
• DHB Vol II - The School of Plato, p. 35 (verified source; probably the Plato material)

Mentioned

• Augustine’s definition of sign; Porphyry (Five Names); Aristotle, Categories (Ten Names); Prior Analytics; Euclid, Elements (definitions, postulates, axioms; alternate angles; triangle’s angles — inferred I.29, I.32); Plato, Theaetetus, Laches, Euthyphro; Albert the Great’s division of logic; Thomas’s division and explanation of the Metaphysics text; Oesterle, Logic: The Art of Defining and Reasoning; Nicene, Apostles’, Athanasian, Fourth Lateran creeds; Aristotle on plot (inferred: Poetics).

His questions #

• When I clear my throat, do I intend to signify something by that sound? No — it’s so I can speak more clearly.
• What are you separating name and speech from by adding “by custom”? Moaning, sighing, groans, screams, the baby’s cry, which signify by nature.
• In animal, does each syllable signify something? No, only the whole name.
• In Bergkvist, do the two parts mean something? No, it functions as one name.
• How do you know these two [alternate] angles are equal? From straight line meeting straight line making two right angles, plus the axioms on equals.
• In what way is example like an induction? The one singular stands as representative, but it lacks induction’s strength from many.
• “Boys will be boys” — any exceptions? Yes, sometimes a boy does what you expect of a man; so likelihood falls short of universality.
• If a man comes staggering out of a bar, what would you conclude? Does everybody who staggers be drunk? Drunk — but no; physical defect or tiredness. Signs are not universal.
• How can you direct yourself to what you don’t know? (Meno) Left open — Socrates has trouble replying; he will return to it.