Logic of the Second Act Wrap-Up, Mr. Anti-Statement, and What Reasoning Is

Orientation #

He opens by recapping that the logic of the first and second acts has been treated and that the three acts are ordered (prev. lecture on statements, square of opposition). He says the syllogism “in detail” will be next time; today is a broad view of reasoning and the four kinds of argument. Verified handouts: “Foreword to Logic” p. 9 and “Reasoning and the Four Kinds of Argument” p. 2 (he refers to “the second page” for the four kinds). The previous class treated hypothetical and disjunctive statements and the square of opposition; the next works through example, induction, enthymeme and syllogism.

The class, in order #

1. The three acts are ordered (“no one ever puts the two together”) #

Point: each act presupposes the one before, and each higher act unifies what the lower act knows separately.

• Understanding what a man is and what a stone is: two different acts, not at the same time. But in the statement “no man is a stone” I understand man and stone together — a kind of unity of things known by separate acts in the first act.
• Third act: two statements thought together as premises form a unity ordered to a conclusion. “If one person thinks of the major premise and someone else thinks of the minor premise, but no one ever puts the two together,” no conclusion is drawn.
• As Thomas says, the acts are ordered: I could understand what a man is without understanding he is not a stone, but not the reverse; I could understand a statement without combining it, but not combine statements without understanding them.

2. Which half of a contradiction is true? (“what is worth saying can be said twice”) #

Point: the logic of the second act tells you which statements are contradictory and that one is true and one false, but not which; three ways settle that.

1. By the senses: “you are sitting” true, “you are not sitting” false, through my sensing you sitting. Not enough for universals.
2. By understanding what the terms are (which may require defining — logic of the first act): “no odd number is even”; “every whole is more than one of its parts”.
3. By reasoning, when neither of the first two works: from statements already known or accepted. Aside: Péguy quoted for repeating a point.

3. The exception: Mister Anti-Statement (“an irrational, right, an unreasonable hatred of statements”) #

Point: because reason can think about itself (a definition of definition, statements about statements), the logic of the second act does by itself settle a few statements’ truth. He stages an interlocutor and the class answers.

• “Statements don’t exist.” Student: that’s a statement. “Statements exist” confirms itself; “statements don’t exist” shows itself false — known true just from knowing what a statement is.
• “All statements are false; no statement is true.” Student: if that’s true you’ve contradicted yourself. If “no statement is true” is true, then one statement is true, so “no statement is true” is false; and by the square of opposition, “some statement is true”. He adds: from the definitions, a false statement says what is is not or what is not is, and its opposite says what is is / what is not is not — which is what true means.
• “No statement is known to be true or false.” Student: that statement is either true or false. If none is known, is that one known? And we already know “statements exist” is true and “statements do not exist” is false, so some statements are known.
• “I hate statements” / “people shouldn’t make statements.” He has just made a statement. Mister Anti-Statement is left speechless — like Aristotle in the fourth book of the Wisdom [ed.: Metaphysics IV]: the man who denies the statement about contradiction “goes back to the state of vegetable”, unable even to say this is sweet or not sweet.
• The logic of the second act is thus very close to what Aristotle calls the first axiom, the natural beginning of all the axioms: impossible to be and not be at the same time in the same way; must either be or not be — seen already in the square of opposition (“what is is” and “what is is not” can’t both be true).

4. The third act: reasoning as movement (“reasoning is to understanding as motion is to rest”) #

Point: reasoning is the characteristic act of reason and is a movement of the mind.

• Aquinas: reasoning is to understanding as motion to rest. English “understanding” comes from “to stand”; the Latin word [unclear in recording; he gives a Latin verb] also signifies rest.
• Reasoning is named from reason itself, as tasting from taste, smelling from smell — so it most of all fits reason. Medieval logicians used discursus for it (though the word can be broader); Shakespeare speaks of reason as discourse.
• Shakespeare, Troilus and Cressida: things in motion sooner catch the eye than what not stirs — so reasoning stands out to us more than understanding, which is rather the beginning and end of reasoning.
• Aside: bumper sticker “If you don’t change your mind, how do you know you have one?” — he dislikes the thinking behind it (Socrates, accused of always saying the same things about the same things: better than saying opposite things about the same thing), but it does show that change of opinion reveals that a mind is at work.

5. Defining reasoning: going and coming (“I’m going home for Thanksgiving”) #

Point: a motion may be defined from its start (going) or its end (coming); reasoning goes from statements, because of them, to another statement.

• Going vs. coming: you say “I’m going home”, your mother says “you’re coming home” — same trip, named from the start (Assumption College) or from the end (home). He prefers “coming”.
• From what? From statements, either known or merely accepted (probable, believed, heard).
• Insufficiency of “going from statements known or accepted to another statement”: from “a whole is larger than its part” and “no odd number is even” to “man is not a stone” — all known, yet no reasoning. Student: not because of them. So: going from statements known or accepted, and because of them, to another statement.

6. Knowing vs. guessing; reasonable vs. wild guesses (“let us not guess at random”) #

Point: reasoning may end in knowledge or in a guess; a guess reached by reasoning is a reasonable guess, unlike a wild one.

• Knowing vs. guessing: not that one is true and the other false — both may be true; in one case you are certain, in the other not.
• Opinion vs. suspicion: both guesses; opinion the stronger, effect of dialectical reasoning; suspicion weaker, effect of rhetorical reasoning.
• Socrates in the Meno says “I know” there is a difference between knowing and right opinion — unusual, since in the Apology he always claims not to know. Why so sure? Student attempts (otherwise nothing could be known; he must know this to know he doesn’t know). His answer: the same thing cannot both be certain and not certain — can’t both be and not be — just as no odd number is even because nothing is both divisible and not divisible by two. This does not mean you always know whether a given thought is a guess or knowledge. And the objector who says “Socrates, you’re just guessing there’s a difference” is himself making the distinction.
• A guess from statements and because of them is not wild, not freely imagined: it has a reason, but not one sufficient to say it must be so and cannot be otherwise; the reason may be stronger or weaker.
• Fragment of “the great philosopher, the central thinker of human thought” (not named; Heraclitus, inferred), put on the board: let us not guess at random about the greatest things — if you must guess, have a reason. Wild guess: his imagining whether your parents’ home is two stories or a ranch, with no reason either way.
• In philosophy of nature he treats the pre-Socratic fragments as looking for reasonable guesses and the reasons behind them.
• A man guesses the truth before he knows it, apart from things naturally known like the axioms: one guesses the base angles of an isosceles triangle are equal, or the angles of an equilateral triangle equal, before the rigorous proof — one wouldn’t look for the reason without first guessing it true. Sometimes a reasonable guess is as far as we go.
• Two Greek arts of guessing: dialectic (general questions) and rhetoric (in part: guessing about the singular contingent — who did it, what the country should do). Modern particular arts of guessing: the weatherman (“seventy percent chance of rain”), the economist (“barring unforeseen circumstances”; Merrill Lynch on the Bush tax refund). People are paid to make reasonable, not wild, guesses. Aside: hometown newspaper contest to out-guess the weatherman.
• Einstein on the scientist’s hypothesis: not a reasonable guess but freely imagined — a wild guess — and therefore must be tested by its consequences. Weaker than a reasonable guess; a reasonable guess is less than knowledge.

7. The definition settled; calculating as parallel (“coming to know or guess a statement”) #

Point: reasoning is coming to know or guess a statement from (or through) other statements already known or accepted, and because of them.

• “Because of them” is essential: a man may pile up statements and say “and therefore”, but the conclusion doesn’t come out of his premises.
• Alternative wording: “through other statements”; “already known or accepted” is sometimes left understood.
• Calculating: coming to know or guess a number from other numbers. Why “guess” in calculating? Even correct multiplication yields only a guess if the starting numbers were guesses: number of guests times beers per guest — guests may not show, uninvited ones may come, some may be thirsty or have taken the pledge.
• Likewise in the syllogism the conclusion follows necessarily, but if you’re not sure of the premises you’re not sure of the conclusion. To be sure you need both sure premises and necessary following; either can be had without the other (true but uncertain premises; a conclusion that doesn’t necessarily follow because it isn’t really a syllogism).
• Aside: colleagues in philosophy who say they teach students to reason but have no definition of reasoning; this definition says more distinctly what reasoning is than the word does.

8. What an argument is; premise and conclusion (“speech bringing together the statements from which we reason”) #

Point: argument is not the same as reasoning; its genus is tool, and the logician’s tools are speeches.

• Argument: a speech bringing together the statements from which we reason. Those statements are the premises; the statement to which we reason is the conclusion.
• Spelling aside: he spells “premiss” (P-R-E-M-I-S-S), a minority, against “premise” (as in premises of property).
• Latin praemissa: sent before. Greek protasis, from proteinō: to stretch forward — more accurate, since premises not only come before but stretch forward producing the conclusion.
• Reasoning and calculating belong to two arts the Greeks called logikē and logistikē; both are arts for coming to know what you don’t know. Art imitates nature: two dogs produce a dog, two elephants an elephant, so two statements produce a statement and two numbers a number. Eddington: put in numbers, you grind out more numbers. And as two parents suffice for a third, in the most exact reasoning (the syllogism) two premises produce a third statement; at least two numbers are needed to add or multiply.

9. The four kinds of argument along the natural road (“the road from the senses into reason”) #

Point: before dividing the four arguments (done toward the end of the handout pages), meet each along the natural road from sense to reason.

• He draws the road uphill: sensing is easy, the further into reason the harder; the more universal is placed above the less universal.
• Aquinas: a thing when sensed is singular, when understood universal — this chair seen and felt is singular; “this is a chair” grasps what is common to this and other chairs.
• So arguments beginning from the singular are more known and easier for us: example begins from one singular; induction from many singulars. Enthymeme begins from something general, usually true for the most part rather than quite universal; syllogism begins from something completely universal and so is most into reason.
• Order to be followed: example, induction, enthymeme, syllogism.

His words #

• logic of the first / second / third act: logic of understanding what a thing is; of statements; of reasoning.
• first axiom: “impossible to be and not be at the same time in the same way”; “must either be or not be” [ed.: principle of non-contradiction / excluded middle]; “natural beginning of all the axioms”.
• the Wisdom, fourth book: [ed.: Aristotle, Metaphysics IV].
• reasoning: coming to know or guess a statement from (through) other statements already known or accepted, and because of them; to understanding as motion to rest.
• discursus: medieval logicians’ word for reasoning.
• going / coming: same motion named from its beginning or its end.
• knowing vs. guessing: certain vs. not certain; both may be true.
• opinion / suspicion: stronger / weaker guess; effects of dialectical / rhetorical reasoning.
• reasonable guess / wild guess: a guess with a reason not sufficient for necessity / freely imagined, no reason.
• calculating: coming to know or guess a number from other numbers.
• argument: speech bringing together the statements from which we reason; genus: tool.
• premiss: his spelling; statement from which we reason; praemissa “sent before”; protasis / proteinō “stretch forward”.
• logikē / logistikē: Greek names for the arts of reasoning and of calculating.
• example, induction, enthymeme, syllogism: from one singular; from many singulars; from the general (for the most part); from the completely universal.

Texts #

Read in class

• Handout, “Foreword to Logic”, p. 9
• Handout, “Reasoning and the Four Kinds of Argument”, p. 2 (“the second page”, the four kinds)
• Fragment “let us not guess at random about the greatest things” (author unnamed; Heraclitus, inferred), written on the board

Mentioned

• Aquinas: the acts of reason are ordered; reasoning is to understanding as motion to rest; a thing is singular when sensed, universal when understood (no locus given)
• Aristotle, fourth book of the Wisdom [Metaphysics IV]: denier of contradiction reduced to a vegetable; the first axiom
• Plato, Meno (Socrates knows the difference between knowledge and right opinion); Apology (Socrates claims not to know)
• Shakespeare, Troilus and Cressida (“things in motion sooner catch the eye”)
• Péguy (“what is worth saying can be said twice”)
• Einstein on the scientist’s hypothesis as freely imagined; Sir Arthur Eddington (“put in numbers, grind out more numbers”)

His questions #

• What would you say to Mister Anti-Statement: “statements don’t exist”? That’s a statement; it shows itself false, and “statements exist” confirms itself.
• “No statement is true” — what do you say? If true, it is a true statement, so it is false; then by the square of opposition some statement is true.
• “No statement is known to be true or false” — is that statement known? If so he contradicts himself; and we already know “statements exist” is true.
• Are you and your mother referring to a different trip when you say “going home” and she says “coming home”? No; same motion, named from the beginning or from the end.
• From “a whole is larger than its part” and “no odd number is even” to “man is not a stone” — why haven’t I reasoned? Not because of them.
• What’s the difference between knowing and guessing? Certainty; both may be true.
• Why is Socrates so sure there is a difference between knowing and right opinion? The same thing can’t both be certain and not certain — can’t both be and not be.
• Why use “guess” of calculating, which is rigorous? The numbers you start from may be guesses (guests times beers).
• What’s the genus of argument? Tool — a speech.
• How do you get the four kinds of argument? Left for the end of the handout; today met one by one along the road from sense to reason.