Logic of the Second Act: Distinctions, Division, and the Statement

Orientation #

He says they “just finished the consideration of definition,” to which the consideration of division is attached, and that this class starts the logic of the second act, “the easiest part of logic,” about statements; he hands out the text (“Foreword to Logic,” p. 8, verified) and says the “subtle things” begin only “at the bottom of page two,” i.e. later. The previous class treated division of the integral and universal whole and the rule of two or three; the next treats truth and falsity of the simple statement and contradictories.

The class, in order #

1. Logic and its three tools; definition contains a division (“logic is the art that perfects three acts”) #

Point: logic perfects three acts of reason, more precisely by three tools, and division is more universal than definition.

• Three acts and their tools: understanding what a thing is → definition; understanding the true or the false → statement; reasoning → syllogism and the lesser arguments.
• Definition contains a division (defining square “breaks it apart” into equilateral, right-angled, quadrilateral), but there can be division without definition; so division is more universal.
• Two divisions that are not definitions at all and are “very important for thinking and every reasoned-out knowledge”: (a) integral/composed whole into its parts — statement into noun and verb; (b) universal whole into its parts, chiefly genus into species — statement into affirmation and negation. Both will be done in this class, along with defining statement.

2. Distinction is wider than division; three distinctions that are not divisions (“every division is a distinction, but not every distinction”) #

Point: division in the strict sense is a distinction of the parts of some whole; three very common distinctions lack a whole and parts.

• Senses of a word. The word is not a whole put together from parts; it somewhat resembles the universal whole (said of its parts) but, having many meanings, is not said with one meaning as a genus is. Examples: “true” will be distinguished into three meanings answering to three kinds of statement; “being”/“thing” was distinguished when the categories were treated.
• Per se vs. per accidens (through itself vs. by happening; Greek kath’ hauto, kata symbebekos; also rendered “as such”). “Comes up all the time.”
  • The good defined as “what all desire”; objection: people desire bad things. Reply by the distinction: the bank robber desires the money, not the injustice as such; the boy driving too fast wants a good time, not a wreck; the last drink at the party is desired as continuing the good time, not as making you sick. One desires the good as such, never the bad as such.
  • “A pianist built my house”: true, but not as pianist — accidental.
  • Can the sick become healthy? As sick, no (contradiction); it is the body, to which sickness happens, that becomes healthy and remains when healthy.
  • Predicate accidents: it belongs to two as such to be half of four; it does not belong to triangle as such to be green.
  • A similar but not identical distinction: per se vs. per aliud. Some statements are known per se, others through other things; the end is good per se, medicine good through health (though medicine “itself is good, as it tastes good”).
• Simply vs. in some qualified/diminished way.
  • Meno’s problem: can you know what you don’t know? The man paid to find the cause of cancer knows what he is looking for in some very imperfect way. Kant–Hegel exchange: Kant says we can’t know things in themselves; Hegel asks why then he talks about them.
  • “Delicious poison” is bad to drink simply, good in a diminished sense (good-tasting); robbing the bank is good in some way, bad simply. Whenever we do something bad it is because it is good in some diminished sense; whenever we omit a good it is because it is bad in some way (some other good was left undone).

3. Where these distinctions belong: first act or third act (“three most common kinds of mistakes”) #

Point: he sometimes treats the three distinctions here, sometimes with the logic of the third act, because the three commonest errors in reasoning come from overlooking them: mixing senses of a word; mixing per se and per accidens; mixing simply and in some respect.

• In the Meno both Meno and Socrates make the third mistake — Socrates in trying to answer Meno’s. Meno: you can’t know what you don’t know, so can’t look for it — not seeing that you can know it in some respect.
• Classroom example: “How many students are in class today?” — I don’t know, yet I can reach the number with the greatest ease by counting; if I get 27, in some way I knew 27, since I knew I was looking for the number of students.
• “Do you know my brother Mark?” — “No.” “Do you know what a man is?” — “Yes.” Then in some way you know every man, every brother; yet asked simply, the right answer is “no.” Knowing in “some extremely qualified and imperfect way.” He grants the distinction is hard to grasp.
• Summary of the logic of the first act: definition most of all, but also divisions that are not definitions and distinctions that are not divisions.

4. Thomas’s strict use of “division”: the Trinity (“a real distinction between the Father and the Son”) #

Point: Thomas often uses “division” loosely, but in the strict sense it means distinction of a whole into parts, and so he always denies division of Father, Son and Holy Spirit while affirming a real distinction — “part” connotes something incomplete, imperfect, an “entirely false understanding” of the Trinity (setting aside other connotations such as conflict).

5. Definition of statement; simple and compound; three senses of “true” (“speech signifying the true or the false”) #

Point: statement shares its genus, speech, with definition (speech signifying what a thing is), differing as signifying the true or the false.

• Why “or,” not “and”: a statement signifies one or the other. Some are always true (“two is half of four,” “man is an animal”), some always false (“two is a colour,” “two is four”), some sometimes true, sometimes false (“Berquist is sitting”) — and the statement has exactly the same parts when true and when false; it is measured by its agreement with things.
• Simple statement (affirm or deny one thing of another) vs. compound (two or more simples combined). Aristotle uses “statement, period” for the simple one. Two compounds matter most for reasoning:
  • Hypothetical/conditional — he prefers “if-then statement,” since “hypothetical” wrongly suggests something uncertain.
  • Disjunctive — he prefers “either-or statement”; may have two members (every number odd or even), three (triangle equilateral, isosceles, scalene), or five (Thomas: every name said univocally of anything is genus, species, difference, property or accident). “Disjunction” means “apart.” Aside: Shakespeare says “or … or” and “nor … nor” rather than either/or, neither/nor.
• Second paragraph of the handout: “true” does not mean the same of the simple statement, the if-then and the either-or; the fundamental meaning is that of the simple statement; “false” correspondingly has three meanings — hence in a way three definitions. To be seen later.

6. Noun and verb: the composing parts (“the verb signifies with time”) #

Point: in the Peri Hermeneias Aristotle divides the simple statement into noun and verb; the difference is signifying with or without time.

• Greek and Latin have one word (onoma, nomen) for name and noun; Ammonius Hermiae and Thomas keep pointing out when Aristotle uses onoma broadly and when as opposed to verb (rhēma, verbum). So in Greek and Latin, not English, “name” is equivocal by reason. English “name” too leans toward noun, but in logic “name” covers verb and even adjective.
• Definition of name recalled: vocal sound signifying by custom/human agreement (not by nature, like a cry or groan), no part of which signifies by itself; “man” and “walks” both fit.
• Noun vs. verb: the verb signifies with time, the noun without. “A noun is the name of a person, place, or thing” is not correct: “action” is a noun, yet not a person, place or thing; “acts / acted / will act” signify with time, “action” and “time” itself do not.
• The verb is also a sign of something said of another; hence the further division into subject, predicate (“said of” in Latin) and copula (is / is not — “copula” fits joining better than the negation, but the Thomists use it for both). So the same statement is divided into two (noun, verb) or three (subject, predicate, copula).
• Why the verb gets the new name: it adds something (time) to the common meaning, as the thumb gets a new name among the fingers.
• Two-or-three parallels: Aristotle divides plot into beginning, middle, end, and elsewhere in the Poetics into two (tied and untied part [ed.: the transcript’s “timed unit and untimed unit” is probably “tied/untied,” i.e. complication and unravelling]); he himself divides the seven petitions of the Our Father into four for goods and three against evils, while Thomas in the Summa Theologiae divides them into two about the end, two about the means, three about impediments — end and means can be joined since both concern the good.
• Aside (student remark, partly unclear in recording): the separating verb “to be” is one of the last things to come into language; “this is that” raises the puzzle of something being other than itself, so “a man walks” is a safer way of speaking.

7. Why this is a composed whole (“put together from its parts, but not said of them”) #

Point: the composed whole is put together from its parts but not said of them: a noun is not a statement, a verb is not a statement. “Man” — true or false? “Walks”? Neither; “man walks,” “man is a stone,” “man is not a stone” — one true, one false.

8. Statement and sentence; the species of sentence (“every statement is a sentence, but not every sentence”) #

Point: students identify statement with sentence; but sentence is more universal, so statement can also be defined as a sentence signifying the true or the false.

• Grammar’s subject is the construction of the sentence (English grammar, Greek grammar; word order of noun and adjective differs by language).
• Other species: question, command, prayer, exhortation. First division: sentences aiming at knowledge (statement, question) vs. at action; the latter subdivided by whom they address: command to an inferior, prayer to a superior (not only God — the beggar’s “help me”), exhortation to an equal (“let’s go eat,” “let’s go to the movies”).
• Only statement is true or false: “What time is it?” “What’s your name?” — neither; “Thomas is your name” — either. “Give us this day our daily bread” — neither; “I need my daily bread” — either. “Shut the door” when it is already shut: not false, though it may be a sign the speaker thinks the door open; “the door is shut/open” are statements. “Go to hell,” “get lost” — neither; “you should go to hell” — either.
• A question can proceed from a false understanding without itself being false: “What are the parts of God?” — God has no parts; “What place is God?” — the cosmonaut reporting “there’s no God up here” presupposes God is in a place, which is false, but the question is neither true nor false.
• The logician mainly considers the statement; questions were treated “on the way”; command, prayer, exhortation are of little concern, aiming at action, not knowledge.

9. Affirmation and negation: genus into species (“statement is not composed or put together from these two”) #

Point: the second division of statement, into affirmation and negation, is of a universal whole, said of its parts but not put together from them.

• “Man is a stone” / “man is not a stone,” “man is an animal” / “man is not an animal”: each is a statement, but statement is composed of noun and verb (or subject, predicate, copula), not of affirmation and negation.
• Student: why “subject parts” rather than “subjective parts”? He avoids “subjective” because of the “crazy complications” of subjective/objective in modern thought; a subject is that of which something is said.
• Aside on translation: sensus literalis rendered “literal sense” in English is narrower than Thomas’s usage, since for Thomas the metaphorical sense is the sensus literalis — “the Lord is my rock” means the meaning intended by the speaker (firm, my foundation), not that God is a rock.

10. Which division comes first? (“divide a whole into its composing parts before its subject parts”) #

Point: when a thing is both a composed and a universal whole (as the object of reasoned knowledge, being universal, always is), dividing into composing parts seems to come first because it helps one understand the division into species.

• Statement: the division into subject, predicate and copula (is / is not) is the basis of the division into affirmation and negation — the affirmation joins subject and predicate.
• Atom: into nucleus and shell, or proton, neutron, electron, before hydrogen, oxygen, nitrogen … (the periodic table) — you need the first to do the table.
• Sonnet: fourteen lines (composing parts; sonnet is not said of the lines, else fourteen sonnets) before English/Shakespearean vs. Italian/Petrarchan — three alternately rhyming quatrains completed by a couplet vs. an octet answered by a sestet; one must have the fourteen lines in mind to see how each species orders them.
• Government: legislative, executive, judicial vs. monarchy, oligarchy, democracy — which first? Then one sees what the different kinds are: Henry VIII’s parliament, where the king was dominant, differs from parliament today.
• He leaves it as “something to think about,” saying it “makes some sense” at least in these examples from quite different areas.

His words #

• “tools” of logic — definition, statement, syllogism, each perfecting one act of reason.
• “composed whole” — his preferred term for the integral whole: put together from its parts, not said of them.
• “universal whole” — said of its parts, not put together from them; its parts he calls “subject parts” [ed.: subjective parts].
• “distinction” — wider than division; division strictly = distinction of the parts of a whole.
• “through itself / by happening” — per se / per accidens, kath’ hauto / kata symbebekos; also “as such.”
• “per aliud” — through another; a similar, not identical, distinction.
• “simply / in some respect (qualified, diminished way)” — his rendering of simpliciter / secundum quid [ed.].
• “speech signifying the true or the false” — definition of statement.
• “statement, period” — Aristotle’s use of statement for the simple statement.
• “if-then statement” — hypothetical/conditional.
• “either-or statement” — disjunctive; “disjunction” means “apart.”
• “name” — vocal sound signifying by custom, no part of which signifies by itself; wider than noun.
• “onoma / rhēma; nomen / verbum” — noun and verb.
• “copula” — the is / is not joining (or separating) subject and predicate.
• “predicate” — merely the Latin for “said of.”
• “sensus literalis” — for Thomas includes the metaphorical sense.

Texts #

Read in class

• Handout, “Foreword to Logic,” p. 8 (verified): definition of statement, first and second paragraphs of the section on simple and compound statements; page 2 on affirmation and negation.

Mentioned

• Plato, Meno (knowing what you don’t know; Meno’s and Socrates’ mistake).
• Aristotle, Peri Hermeneias (division of statement into noun and verb).
• Ammonius Hermiae and Thomas Aquinas, commentaries on the Peri Hermeneias (broad vs. narrow onoma).
• Aristotle, Poetics (plot divided into three, and into two).
• Thomas Aquinas, Summa Theologiae (division of the petitions of the Our Father; locus not stated).
• Thomas on the five ways a name is said of something (genus, species, difference, property, accident) and on distinction vs. division in the Trinity (loci not stated).
• Shakespeare (or/or, nor/nor); sonnets, English and Italian.
• DHB Vol. III, The School of Aristotle, pp. 479–635 (verified as printed source).

His questions #

• Every division is a distinction, but is every distinction a division? No; division strictly is a distinction of the parts of a whole.
• Does the bank robber desire the bad because it is bad? No; he desires the money — the good as such, not the bad as such.
• Can the sick become healthy? Not as sick; the body, to which sickness happens, becomes healthy.
• Can you know what you don’t know? In some way, yes — as you know the number of students before counting.
• Why “the true or the false” and not “and”? A statement signifies one or the other; some always true, some always false, some either.
• Is “action” a verb or a noun? A noun — so “person, place or thing” is not the right account of noun.
• Is “shut the door” true or false? Neither; only “the door is shut / open” is.
• Is statement put together from affirmation and negation? No; it is said of them (genus into species), put together from noun and verb.
• Should one divide a whole into its composing parts before its subject parts? Seems so in these examples (statement, atom, sonnet, government) — left as “something to think about.”