Chapter 2.txt

Boston College Document Delivery rw: 1086481 MMIII UIE AN Journal Titie: Socratic logic : a logic text using Socratic method, Platonic questions & Aristotelian principles / Volume: Issue: Month/Year: 2010 Pages: 47-67, title+copyright pp Article Author: Kreeft, Peter. 7\] Article Title: Ch....

Boston College Document Delivery rw: 1086481 MMIII UIE AN Journal Titie: Socratic logic : a logic text using Socratic method, Platonic questions & Aristotelian principles / Volume: Issue: Month/Year: 2010 Pages: 47-67, title+copyright pp Article Author: Kreeft, Peter. 7\] Article Title: Ch. 2 Imprint: primo.exlibrisgroup.com-ALMA-BC This material may be protected by Copyright Law (Title: 17 U.S. Code) EEEEEEEELESSSSSSSSS'SS zc ccc rrr 4/29/2020 12:07:29 PM BC108.K67 2010 Theology and Ministry Library Stacks primo.exlibrisgroup.com-ALMA-BC RESERVES RESERVES (RESERVES) O'Neilllibrary Boston College Chestnut Hill, MA 02467 Socratic Logic Edition 3.1 by Peter Kreeft Edited by Trent Dougherty A LOGIC TEXT USING SOCRATIC METHOD, PLATONIC QUESTIONS, & ARISTOTELIAN PRINCIPLES Modeling Socrates as the ideal teacher for the beginner and Socratic method as the ideal method Introducing philosophical issues along with logic by being philosophical about logic and logical about philosophy Presenting a complete system of classical Aristotelian logic, the logic of ordinary language and of the four language arts, reading, writing, listening, and speaking ® ST AUGUSTINE'S PRESS South Bend, Indiana Copyright © 2004, 2005, 2008, 2010 by Peter Kreeft All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of St. Augustine's Press. Manufactured in the United States of America 23456 16 15 14 13 12 Library of Congress Cataloging in Publication Data Kreeft, Peter. Socratic logic: a logic text using Socratic method, Platonic questions & Aristotelian principles / by Peter Kreeft; edited by Trent Dougherty. --- Ed. 3.1. p. cm. Previously published: 3rd ed. c2008. Includes bibliographical references and index. ISBN 978-1-58731-808-5 (hardcover: alk. paper) 1. Logic. J. Dougherty, Trent. II. Title. BC108.K67 2010 160 --- de22 2010032937 co The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences --- Permanence of Paper for Printed Materials, ANSI Z39.48-1984. ST. AUGUSTINE'S PRESS www.staugustine.net II: Terms Section 1. Classifying terms From the viewpoint of practical logic, the most important distinction between two kinds of terms is the distinction between ambiguous terms and unambigu- ous terms. However, there are also other distinctions between different kinds of terms. Terms are either (1) unambiguous or ambiguous (2) clear or unclear (3) exact or vague (4) univocal, analogical, or equivocal (5) literal or metaphorical (6) positive or negative (7) simple or complex (8) categoregmatic or syncategoregmatic (9) universal, particular, or singular (10) collective or divisive (11) concrete or abstract (12) absolute or relative 1. Terms are either unambiguous or ambiguous. "Ambiguous" means "having more than one meaning." Strictly speaking, no term as such is ambigu- ous until it is used ambiguously. "Good" is not ambiguous when I use it in only one way --- e.g. "A saint is a very good person" and "St. Francis was a very good person." But it becomes ambiguous when I use it with two different meanings --- e.g. "That is a good axe" and "A murderer is not a good person" --- for the bad murderer needs a good axe to do the bad deed of chopping off his victim's head. If a term is used ambiguously, we are misled; we do not know what we are talking about. Worse, we think we do. Most ambiguity is hidden. We do not real- ize we are using terms ambiguously, unless we are deliberately trying to deceive or making a pun. We will say more about ambiguity in the chapter on definitions. Defining a term is the way to heal the disease of ambiguity. 48 I. TERMS 2. Terms are either clear or unclear. Clarity is not quite the same as unam- biguousness. A term is clear in the way light is clear: it "comes through" to the mind. Unambiguousness means a lack of confusion between two meanings. Unless a term is first of all clear, it cannot be either ambiguous or unambiguous. Until there is light, it cannot be either one color or two colors. Whether a term is clear or not depends not only on the term but also on the mind that tries to think it. The term "quasar" is clear to those who know modern astronomy but not to those who do not. René Descartes, often called "the father of modern philosophy," said that we could not be sure any proposition was true or false unless its terms were "clear and distinct (unambiguous)." "Clear and distinct ideas" was his criterion for cer- titude that any proposition is true. It is not a criterion of truth, for a proposition with ambiguous terms can still be true (e.g. "Life is good"). It is not even a suf- ficient criterion for certitude, for many uncertain and even false propositions can have clear and distinct terms. But it seems to be a necessary criterion for certi- tude, a minimum, a beginning. 3. Terms are either vague or exact. Vague terms are not necessarily ambiguous or unclear. "Tall" is a vague term ("six feet tall" is an exact term) but "tall" is neither ambiguous nor unclear. There is nothing necessarily wrong with a vague term. We often need vague terms rather than exact terms; they are very useful. For much of our knowledge is not exact, so the terms that express that knowledge rightly cannot be exact either. We often need a "fuzzy logic" in our terms. But although there is room for "fuzzy logic" in terms, there is no room for "fuzzy logic" in propositions or arguments. Propositions are either true or false and arguments are either valid or invalid; and there is no third possibility and no fuzziness or sliding scale or matter of degree between true and false, or between valid and invalid. However, we often cannot be certain whether a given proposition is true or false; and that dimension (namely, probability) can sometimes be "fuzzy." At other times, that dimension can be exact, as in statistics. In statistics, even inex- actness can be exact: e.g. a "5% margin of error." 4. Terms are either univocal, equivocal, or analogical. A univocal term has one and only one meaning. An equivocal term has two or more quite different and unrelated meanings. An analogical term has two or more meanings that are a. partly the same and partly different, and (b) related to each other. When I say "I ate two apples" and "You ate two hamburgers," I use "ate" and "two" univocally. When I say "The river has two banks" and "The town has two banks," I use "banks" equivocally, for there is no connection between a river bank and a money bank. When I say "The good man gave his good dog a good meal," 1 use "good" analogically, for there is at the same time a similarity and a Classifying terms 49 difference between a good man, a good dog, and a good meal. All three are desir- able, but a good man is wise and moral, a good dog is tame and affectionate, and a good meal is tasty and nourishing. But a good man is not tasty and nourishing, except to a cannibal; a good dog is not wise and moral, except in cartoons, and a good meal is not tame and affectionate, unless it's alive as you eat it. Strictly speaking, a term is never univocal, equivocal, or analogical in itself; it is only used univocally, equivocally, or analogically. The phrases "bark of a dog" and "bark of a tree" use "bark" equivocally; the phrases "bark of an oak" and "bark of a maple" use "bark" univocally. (So do "bark of a hound" and "bark of a poodle.") "Healthy food" and "healthy exercise" use "health" univocally (for both mean something that causes health in a human body), but "a healthy climate," "a healthy body," and "a healthy sweat" uses "healthy" analogically, for a healthy climate is a cause of a healthy body, while a healthy sweat is an effect of a healthy body. 'Exercise' is an action, 'sweat' is a substance, 'climate' is nei- ther. One of the things computers cannot do is to understand and use analogies. One of the things philosophers and poets do especially well is to understand and use analogies. See also "arguments by analogy," p. 329. Exercises: Classify each of the underlined terms as univocal, equivocal, or ana- logical. 1. love ice cream and I love you too.. To murder is evil, and to be murdered is also evil.. A litter of pups was living in the street in the middle of a pile of litter.. Two customers paid two hundred dollars each for two chairs two days ago.. After I digest this logic course, I'm going to digest my dinner.. Macbeth murdered Banquo, but he didn't murder the English language as you do.. Water is heavier than air, and the air is very fresh today.. \| will air my opinions after I air this room.. The candidate who is running for governor was running after a bus. 10. With my hands \| changed the hands of the clock. 11. Poetry is an art, and painting is also an art. 12. "Death is a great change, and it would be no surprise if a man were unpre- pared for it." "Nonsense! Throughout his life man has experienced change of many kinds every day." 13. Christian: "We call God the Father and Jesus his Son." Muslim: "For a father to have a son, he must first have a wife. Who is God's wife?" Christian: "God has no wife." Muslim: "Then God has no son." (Which of the three underlined words is used univocally by both sides here? Which is not?) A Bw b&b © oo = 50 I. TERMS 14. "Christians believe God is three persons." "Then he must be triplets. Three persons make triplets." 15. "Buddhists seek Enlightenment. Only a few attain it." "Oh, 'the Enlightenment' --- we Westerncrs went through that once, back in the 18th century." "What are you two talking about? Enlightenment happens every morning when the sun rises." 16. "I have to change the change I gave you for your dollar; I made a mistake." 5. Terms are either /iteral or metaphorical. A metaphor is not the same as an analogy. When I call my dog an "affectionate" dog, \| am using an analogy; for the dog shows some but not all of the signs of the kind of human love we cail "affection," and we think the dog feels some but not all of the same emotions feel when we are affectionate to other human beings. But even though I am using the term "affectionate" analogically rather than univocally, I am using it literal- ly, not metaphorically. But when Jesus calls wily King Herod a "fox" or St. Peter a "rock" or God a "good shepherd," he is using metaphors. The word "good" in "good shepherd" is not metaphorical but analogical (for "good God," "good man," "good dog," "good meal," and "good shepherd" are all good in different ways). But the word "shepherd" is metaphorical, for God is not literally a man with sheep at all. A metaphor is literally false; an analogy is not. 6. Terms are positive or negative. It is usually easy to tell the difference between a positive term and a negative term simply by looking for a negative syllable at the beginning, like "un-" or "non-" or "in-." But this is not always so. Some terms that begin with these syllables are not negative, like "underwear" or "interference." And some terms have an essentially negative meaning without a negative syllable, like "absence" or "blindness" or "evil." Some words are both positive and negative at the same time, like "inconvenience," which means a (negative) absence of convenience but also a (positive) presence of trouble. 7. Terms are simple or complex. A single object of thought, like "apple," is a simple term; two or more objects of thought which could be either together or apart, like "green apple," constitute a complex term. No matter how long or complex it is, if it is not a complete sentence, it is only a term. "Everything in the kitchen sink except the kitchen sink itself, including all the garbage from last night's steak dinner for four and all the dirty forks, knives, and spoons" is still only one complex term. As a term, the whole complex phrase in quotes can be the subject of a proposition with a predicate such as "can be thrown away." 8. Terms are categoregmatic or syncategoregmatic. A categoregmatic term can stand by itself as a unit of meaning, like "apple" or "green" and thus can be a subject or predicate. A syncategoregmatic term (mainly articles, prepositions, and conjunctions, like "the" or "on" or "when') cannot. In the strict sense, a Classifying terms jl syncategoregmatic term is not a term at all, only a word, because it cannot be a subject or a predicate. In another sense, it is a term because it has a definite meaning, though one that is totally relative to another word. There is no such thing as "the," only "the something," e.g. "the apple." But there is such a thing as "apple." (The term "syncategoregmatic term" will probably be less practically use- ful to you for doing logic than for doing a vocabulary "snow job.") 9. Terms are universal, particular, or singular. A universal term designates all members of a class of things, as in "all men are mortal." A particular term designates some members of a class, as in "some men are blind." A singular term designates only one member, as in "Socrates is dead." When we get to propositions and arguments, this distinction among terms will be the one we will be using the most. There are other words besides "all" that indicate that the subject of a propo- sition is being used universally, such as "every," "each," "no," "none," "never," "always." And other words besides "some" indicate that it is particular, such as "a few," "few," "not all," "sometimes," "occasionally," "seldom." In ordinary language (as distinct from logical form, which we will learn soon) we often imply rather than state whether we are using a term universally or particularly. "Triangles have three sides" means "Al/ triangles have three sides", but "Vacations are disappointing" means "Some vacations are disap- pointing." When there is no word like "all" or "some" before the subject of a proposition to indicate whether the subject term is universal or particular, a good rule is to interpret it as universal if the predicate belongs to the subject by nature, i.c. by the nature of the subject, and to interpret it as particular if not. E.g. "men" is universal in "men are mortal" because mortality belongs to the essence or nature of man, but "men" is particular in "men are unreliable" because "unreli- able" does not belong to the essence of man. (See "indesignate propositions" on p. 154.) Exercise: Tell whether the subject of each of the following propositions is uni- versal, particular, or singular. 1. Only a few planes came back. 2. The whole air force fatled. 3. Several planes crashed. 4. The pilot brought no parachute. 5. Nobody could have survived. 6. Every plane with two engines had trouble. 7. Without exception everyone experienced multiple troubles. 8. Some pilots did not pass any of their tests at all. 9. None of those planes was in the air for the last two weeks. 52 Il. TERMS 10. Terms designating groups of things are used either collectively or divi- sively. When I use a term collectively, I mean the group as a whole; when J use a term divisively, \| mean each individual member of the group. A collective term refers to a number of individuals looked at as a single group, like the soldiers in an army or the crew of a ship. Only terms designating groups can be either collective or divisive. Which of the two it is, is determined by use, by how the term is used in a sentence. For instance, "library" is used collectively in the sentence "This library is composed of ten thousand books," but the same term is used divisively in the sentence "This town has three libraries." When I say "this class is the smartest logic class I've ever taught," I use "class" collectively, because I don't mean that every sin- gle member of the class is smart, only that the class as a whole is. But when I say "all men are mortal," I use "men" divisively because I mean that every sin- gle man is mortal, not just that the species homo sapiens, or humanity, is mortal as a species. Exercise: Tell whether each underlined term is used collectively or divisively. 1. That is a tall pile of bricks.. The trees on Holly Hill make a fine sight.. None of my philosophy courses is easy.. The marbles in this bag weigh five pounds.. Men have a soul.. The United Nations decided to censure Israel yesterday. Mankind survives by the skin of its teeth. Native Americans are disappearing, and you are a Native American, there- fore you are disappearing. 9. The Cubs have lost for over 80 years in a row, and Sosa is a Cub, there- fore Sosa has lost for over 80 years in a row. OrADABRwWY 11. Terms are concrete or abstract. "Concrete" does not necessarily mean something you can touch or see, and "abstract" does not necessarily mean some- thing you cannot touch or see, Terms that mean physical things can be either concrete or abstract: "red" and "hard" are concrete, while "redness" and "thard- ness" are abstract. Terms that mean nonphysical things can also be either con- crete or abstract: "equal" and "spirit" are concrete, while "equality" and "spiri- tuality" are abstract. An abstract term is the expression of a mental act of "abstracting," in which we have "abstracted" or mentally "taken-out" some aspect or quality from a real thing and placed that quality itself before the mind. Whenever we make an adjective into a noun, it becomes abstract: "hot" becomes "heat" and "true" becomes "truth." Whenever we add "ness" to an adjective, it becomes abstract: "dry" becomes "dryness" and "kind" becomes "kindness." 12. Terms are absolute or relative. "Absolute" comes from "ab-solutus," which is Latin for "loosed-from." What is absolute is thought of as loosed from Classifying terms 53 comnection or relationship with something else. By contrast, what is relative can- not be thought without relation or reference to something else. "Father," "higher," "king," "shepherd," and "winner" are relative terms. "Father" means "father-of-a-child." "Higher" means "higher-than-something- lower." "King" means "king-over-some-kingdom." "Shepherd" means "herder- of-sheep." "Winner" means "winner-of-a-contest" or "winner-over-someone- else" (the "loser"). "Man," "mortal," "bail," "triangle," and "grass" are absolute terms because they do not require the kind of additions and qualifications given in the previ- ous paragraph. The concept "winner" is a relative term because it is meaning- less without the concept of a game or a loser. "Winner" means "winner over a loser" or "winner of a game." But the concept "man" is still meaningful even if you do not think the concept "mother" or "air," even though no man can physi- cally come to be without a mother or survive without air. Mankind is in reality physically dependent on mothers and air, but the concept "man" is not logically relative to the concept "mother" or "air." Exercises: Explain and resolve the ambiguities in the following (see also pp. 71-73):. The end of a thing is its purpose and perfection, and death is the end of life, therefore death is life's purpose and perfection.. Cancer is made of human cells, and whatever is made of human cells is human, and what is human should not be killed, so cancer should not be killed. 3. Innuendo is an Italian suppository.. Condemned prisoner to judge: "But I don't feel guilty.". Condemned prisoner to judge: "You're a bad man, judge; you're terribly judgmental." 6, Condemned prisoner to judge: "You're supposed to do justice, judge. But you've just done a bad thing, and a bad thing can't be just, because justice is a good thing, not a bad thing." "What bad thing have I done?" "You've lowered my self-esteem in declaring me guilty. Self-esteem is good, and you've taken away something good, so you're bad. You should be punished instead of me." 7. There shouldn't be laws against drugs, because the people who use drugs don't believe there should be laws against them, and that means the coun- try doesn't have consensus about it, and laws should reflect the people's consensus. Philosophy is a kind of love --- the love of wisdom. Therefore philosophy teachers who accept salaries are mercenary lovers. They're intellectual prostitutes; they sell their love for money. 9. Antigravity should be easy. We disobey all kinds of laws, even the law of non-contradiction, so we should be able to disobey the law of gravity. = to un oe oO 34 Il. TERMS 10. How can we claim to define ambiguity? It can't be done, because to define anything is to take its ambiguity away. But if you take the ambiguity away from ambiguity, it won't be ambiguity any more. Section 2. Categories (B) To order and classify things in our mind is to put them into categories or gener- al classes of things. One of the most important disputes in philosophy is about whether all categories are simply inventions of the human mind for the sake of convenience or whether they are based on objective reality. Are they merely "conventional" or are they "natural"? E.g. are animals really different from plants and also from human beings, or is that just the way we think? As we saw in the section on the "problem of universals," this is the dispute between meta- physical realism and nominalism. Obviously, some categories are merely conventional; e.g. "those things that smell worse than a dead yak," or "all the students in the class with grades lower than 70." But the fact that we can identify these categories as conventional cate- gories means that we are judging them as not being natural categories, and thus that we have in our mind the concept of the natural category. We may not be certain whether a given category is natural or conventional, but the very distinction pre- supposes that some categories are natural, i.e. based on the real nature of things. If categories categorized only subjective thoughts and not objective things, then those (categorized) thoughts would not correspond to (uncategorized) things. Then we could never be sure of the objective truth of our judgments that used these categories. But all judgments use categories. So all our judgments would be like a dream, or a game. As G.K. Chesterton says, it is simply an "attack on thought" to say "that every separate thing is unique, and there are no categories at all... a man cannot open his mouth without contradicting it. Thus when Mr. Wells says (as he did somewhere), 'Ali chairs are quite different,' he utters not merely a misstatement, but a contradiction in terms. If all chairs were quite different, you could not call them 'all chairs." (Orthodoxy) If reality is ordered and not chaotic, categories constitute one of its most basic kinds of order. We have seen that universals, or class concepts, can be arranged in a hierarchical order of extension and comprehension, and that as either extension or comprehension increases, the other decreases. This naturally leads to the question: what are the largest, most extensive, most general of all categories? Aristotle came up with ten categories which he thought were the most fun- damental, in the sense of the most broad, the most general, the most generic. These categories are called the summa genera, the gencral classes that are the greatest in extension. Everything real, Aristotle thought, must be in one of these ten categories: Categories 55 "For there is (1) substance, in the common understanding of the term, such as man or horse; (2) how much, e.g. as being of two or three cubits; (3) of what kind, ¢.g. as being white or being grammatical; (4) being related to something, e.g. as double, half, or greater; (5) where, e.g. as being in the grove or market place; (6) when, e.g. as tomorrow or the day before yesterday; (7) having a pos- ture, e.g. as one is reclining or standing; (8) to be equipped, e.g. as one is shod or armed; (9) to act, e.g. as a thing cuts or burns; (10) to receive, e.g. as a thing is cut or burned." The traditional terms for the ten categories are: 1. substance (an individual thing or entity, not a kind of matter, like "sait") 2. quantity 3. quality 4. relation 5. place 6. time 7. posture (the internal order of a thing's parts) 8. possession 9. action 10. passion (being acted upon) "Relation" seems to be more fundamental than Aristotle thought, and "pos- ture" and "possession" less fundamental, but the rest of the list seems as fixed as the structure of language itself. For the parts of speech in language corre- spond to this list of categories: nouns and pronouns usually express substances, adjectives express qualities or quantities, prepositions and conjunctions express relations, verbs express actions or passions, and adverbs express times or places (or, more often, qualities or quantities of actions or passions). Exercises: Identify the category of each categoregmatic term (see p. 50) in the following sentences: I, In the square sat seven skinny soldiers stuck in the stocks at six o'clock. 2. Near the blasted heath at midnight, the three Weird Sisters stood, gleeful- ly stirring the round, black witches' pot filled with three tiny broken frogs. 3. Politically proper Professor Pete, painted partly pink, proffered puzzling paradoxes of pop psychology, ponderously pontificating. 4. Pooping on pieces of pork in the park is proper performance for perky pel- icans. 5. Sam was struck Saturday by scads of silver saliva spat by six scraggly singers sitting stupidly on solid seats simultaneously singing scary seven- syllable songs. 6. Categories are used to classify things. 56 IL TERMS 7. \*(H) Comment on the following passage (explain the last paragraph in different words): And what did it profit me that when I was barely twenty years old there came into my hands, and I read and understood, alone and unaided, the book of Aristotle's Ten Categories --- a book I had longed for as some great and divine work because the master who taught me Rhetoric at Carthage, and whom others held to be learned, mouthed its name with such evident pride? I compared notes with others, who admitted that they had scarcely managed to understand the book even with the most learned masters not merely lecturing upon it but making many diagrams in the dust; and they could not tell me any- thing of it that \| had not discovered in reading it for myself. For it seemed to me clear enough what the book had to say of substances, like man, and of the accidents that are in substances, like the figure of a man, what sort of man he is, and of his stature, how many feet high, and of his family relationships, whose brother he is, or where he is placed, or when he was born, or whether he is standing or sit- ting or has his shoes on or is armed, or whether he is doing some- thing or having something done to him --- and all the other countless things that are to be put either in these nine categories of which I have given examples, or in the chief category of substance. Not only did all this not profit me, it actually did me harm, in that I tried to understand You, my God, marvelous in Your simplici- ty and immutability, while imagining that whatsoever had being was to be found within these ten categories --- as if You were a substance in which inhered Your own greatness of beauty, as they might inhere in a body. But in fact Your greatness and Your beauty are Yourself; whereas a body is not large and beautiful merely by being a body, because it would still be a body even if it were less large and less beautiful. (St. Augustine, Confessions IV, 16) Section 3. Predicables (B) To "predicate" is to affirm or deny a predicate of a subject. E.g, the proposition "Blueberries are red" predicates "red" of "blueberries." The proposition "swal- lowing a whale is not easy" predicates "not easy" of "swallowing a whale." There are five possible relationships that any predicate may have to its sub- ject. A predicate may be a genus, specific difference, species, property or acci- dent of its subject. These are called the five "predicables," or predicate possi- bilities, the five things a predicate can predicate of its subject. The ten categories are a classification of (a) all terms, (b) absolutely, or - A. designates an unusually hard exercise; (E) an unusually easy one. Predicables 57 simply, or in themselves, (c) whether they are in a proposition or not. But the five predicables are a classification of (a) only predicate terms, (b) relatively, in relation to their subjects, (c) in a proposition. Symbolic logic has no room for the predicables because the predicables pre- suppose the forbidden idea of nature, or essence, or whatness. The five predica- bles are a classification of predicates based on the standard of how close the predicate comes to stating the essence of the subject: 1. The species (not a biological species) states the whole essence of the subject. In the proposition "Man is a rational animal," "rational animal" is the species of "man." In the proposition "A triangle is a three-sided plane figure," "three-sided plane figure" is the species of "triangle" In the proposition "Democracy is government by the people," "government by the people" is the species of "democracy." 2. The genus states the generic or general or common aspect of the essence of the subject. (This is to define "genus" in terms of comprehension; to define it in terms of extension, a genus is a more general class to which the subject essentially belongs.) "Animal" is a genus of "man." "Plane figure" is a genus of "triangle." "Government" is a genus of "democracy." Note that the genus is part of the species, i.e. part of the species' comprehension. (In modern logic we usu- ally say a species is part of a genus because modern logic thinks in terms of extension rather than comprehension.) 3. The specific difference states the specific, or differentiating, or proper aspect of the essence of the subject, the aspect of its essence that differentiates it from other members of the same genus. "Rational" is the specific difference of "man." "Three-sided" is the specific difference of "triangle." "By the people" is the specific difference of "democracy." 4. A property or "proper accident" is any characteristic that is not the essence itself but "flows from" the essence, is caused by the essence, and there- fore is always present in the subject because the essence is always present. A property is necessarily connected with the essence and therefore inseparable from it. "Able to speak," "able to laugh,' and "mortal" are properties of "a man." "Having its three interior angles equal to two right angles" is a property of "tri- angle." "Able to change laws by popular consent" is a property of "democracy." 5. An accident is any characteristic of the subject that is not essential (nei- ther the essence nor necessarily present as "flowing from" or caused by the essence), and therefore can come and go, is sometimes present and sometimes not. "Bald" and "Athenian" are accidents of "man." "Equilateral" and "tiny" are accidents of "triangle." "Modern" and "bicameral" are accidents of "democra- cy." In ordinary language any attribute , essential or accidental, is often called a "property," but in logic "accidents"\*are distinguished from "properties." A technical point about singular terms: the purists among Aristotelian logicians say that predicables are only relations between universal terms; more 58 I. TERMS pragmatic logicians allow them to be applied also to singular terms like "Socrates" --- e.g. "rational" is the specific difference of "Socrates" as well as the specific difference of "man." The theoretical dispute seems unimportant for pur- poses of practical logic. A clarification regarding the two uses of the term "accident": The same word, "accident," is used in logic both for nine of the ten categories (all of them except "substance" are "accidents") and for one of the five predicables. Do not confuse categories with predicables, remember that the categories classify terms absolutely, in themselves, while the predicables classify terms relatively, as rela- tions of a predicate to a subject in a proposition. However, individuals cannot be predicate terms in strict logical form, since the predicate is some aspect of the nature of the subject, and individuals are not (universal) natures. They Aave natures. Thus, "The murderer is Lucretia" must be translated into "Lucretia is the murderer" before we can speak of a predica- ble relationship (here, accident). "Clark Kent is Superman" is not a proposition with a predicable relationship at all but an equation between two names. Here "is" is the same as "=" in math. That is not its usual meaning: see p. 140. A clarification regarding the two uses of the terms "genus" and "species": The words "genus" and "species" are used in popular speech, and often in sci- ence, to mean any larger or smaller classes, relative to each other (a "genus" con- tains a "species" or subclass) and relative to the mind that classifies them. That is, these classes of things are thought of as mere conventional concepts that a mind arranges at will without reference to the essence or nature of anything, since "essence" and "nature" are philosophical concepts about which there is much confusion and skepticism today. But in Aristotelian logic, genus and Species presuppose the notion of essence because they are relative to the essence of the subject of a proposition. They are relative not to the subjective will or pur- poses or interests of the classifier, but to the objective nature of the subject. We can also speak of genus and species outside propositions. When we do this, we are usually treating genus and species in terms of extension (larger or smaller classes, classes and subclasses). We repeat, because the point can be con- fusing: in terms of comprehension, a genus is part of a species; in terms of exten- sion, a species is part of a genus. In terms of the inner meaning of a term (com- prehension), a genus (e.g. "animal'') is part of the meaning of a species (e.g. "man," who is "the rational animal'). But in terms of the population designated by the term (extension), a species (e.g. "man'") is part of a genus (e.g. "animal"). in terms of COMPREHENSION \| in terms of EXTENSION Genus is part of species Species is part of genus The concept "animal," which is man's \| The class "man" is only a part of the genus, is part of the concept "rational \| class "animal." animal," which is man's species. Predicables 59 A clarification about two meanings of "essence": The word "essence" also has two meanings. (1) It could mean simply what a thing is, the whole nature of a thing. It is then contrasted with existence or with activity or with appear- ance. For instance, unicorns and cows both have an essence, but unicorns do not exist, while cows do. Cows act in certain ways (e.g. they make calves and give milk) because of their essence, their cowness. And cows may appear to be unappetizing but are really very tasty by their nature. (2) "Essence" can also have a more restricted meaning: the fundamental and unchangeable nature of a thing, as contrasted with its changeable accidents. For instance, a cow is not essentially a brown cow or a healthy cow, but it is essentially a mammal. It could become a white cow or a sick cow, but it could never become a reptile or a fish. In this second, restricted meaning, essences are often hard to define exact- ly when it comes to things in nature like cows, as distinct from man-made objects like democracy or cathedrals or corkscrews. The reason is obvious: we designed democracy, cathedrals, and corkscrews, so we know clearly what their essence is. But we did not design cows. Presumably the Creator knows the essence of a cow as clearly as we know the essence of a corkscrew. Yet we have some knowledge of the essence of a natural thing like a cow. If we didn't, we couldn't make the distinctions above --- e.g. we are not surprised to see a change of health or color in a cow because we know that that does not change the essence of a cow; but we would be amazed to see a cow become a reptile or become a fish, because that would be a change of essence. It is much easier to distinguish the essence of a thing in nature from its acci- dents than from its properties. Is mass the essence of matter and energy a prop- erty of matter, or is it the other way round? Is taking-up-space a property of mat- ter? Is it a property of energy? Is three-sides the essence of a triangle and three- angles a property or is it the other way round? The chemical elements are dis- tinguished by their atomic weights, not by their essence, because we simply do not know what it is in the essence of any element that determines it to have the atomic weight it has. We may not know way it is that water boils at 212 degrees Fahrenheit at sea level, but there must be something in the very nature of water that makes it do that, for all water does it and nothing else does. We know our- selves better than we know water, so we know what there is in us that accounts for our properties --- it is our ability to understand that accounts for our ability to laugh, and to use language, and it is our ability to freely choose that accounts for our moral responsibility. But whether we know its essence or not, a thing acts as it is ("operatio sequitur esse"); its observable activity flows from its being, its nature, its essence. A cow does bovine things because it is a cow. What could be mote commonsensical than that? Even though it is no longer fashionable to do so in modern philosophy or modern logic, the human mind by nature (i.e. by its essence!) still meaningful- ly asks the question of the essence of anything. I remember our son at age 2 60 1. TERMS running around the house pointing to each object and demanding, "Wot dat? Wot dat?" We have an intuitive, commonsensical knowledge of essences which is use- ful enough for everyday conversation, but not clear enough for scientific pur- poses. Because science cannot usefully deal with this implicit, everyday, intu- itive, commonsense knowledge of essences, science has rightly put aside the notion and demanded more empirically verifiable and "operational" definitions of things. Things are defined by scientists in terms of what we can see them do, rather than in terms of what they are. Medieval science did not clearly take this useful step. However, the mistake typically made by medieval science, in confusing common sense (which knows essences), with science (which does not), is still with us, but in its opposite form: where the medievals reduced science to com- mon sense, we reduce common sense to science if we reject the notion of essences entirely. And since logic and philosophy (at least any logic and philos- ophy applicable to the humanities) are based on common sense rather than on the scientific method, it is a mistake to drop the commonsense notion of essences --- and to drop from logic the doctrine of the predicables, which is built on it. Because it has dropped the notion of essence and therefore has no doctrine of the predicables, modern logic has difficulty answering the question of the ancient skeptic Antisthenes, who claimed that every proposition was a self-con- tradiction because it asserts that one thing, the subject, is another thing, the predicate. He argued that on the basis of the law of non-contradiction, we should only say that S\$ is S, not that S is P. In terms of modern logic, Antisthenes' argu- ment is a dilemma: either the proposition is a mere tautology (if P is identical with S), or it will be self-contradictory (if P is not identical with S). E.g. Antisthenes argued, "How can you say a cloud is white? A cloud is one thing and whiteness another. To say that a cloud is white is saying a cloud is not a cloud. That is a contradiction." If you have understood the doctrine of the predicables above, you will be able to answer Antisthenes easily. But not by the law of non- contradiction alone, not by "computer logic" alone. The "Tree of Porphyry": The ancient Greek logician Porphyry arranged the basic genera and species in the universe into a kind of upside down tree, as seen on page 61. The Tree is useful for a number of things. For one thing, it helps us to see the inverse relationship between extension and comprehension. As you move down the tree, each successive branch has more comprehension (more proper- ties) but less extension (fewer members). It also helps us to see the categories as the "summa genera," highest genera, most general classes. It gives us a meta- physical road map, a basic map of being. With this map, we at least know what continent we are on; without it, we are lost: we do not know where or even what we are. Predicables 61 The Tree of Porphyry Being Substance Accidents (that which (that which exists in exists only itself) in a substance) Immaterial Material (pure spirits) UN Inorganic Organic Non-sentient Sentient (plants) (animals) Non-rational Rational ("brutes") (man) Exercises: Identify the predicable in each of the following propositions:. Regicide is murder of a king.. Regicide is murder,. Predicables are relations between terms.. Purple is a color.. Men are often hot-tempered.. To be human is to have a temper.. Justice is more profitable than injustice.. Justice is a virtue.. Justice gives to each his due.. Justice will improve your soul.. Justice was done to Socrates. --- OO WDAIAMN WH = ---\_--- 62 Il. TERMS 12. Biology is the science of living things. 13. Biology studies mammals. 14. Biology is hard for me. 15. Logic is an art. 16. Logic is a science. Section 4. Division and outlining (B) This is one of the simplest but also most practical sections. It is simplest because its rules are commonsensical. It is practical because the only alternative to out- lining is confusion, whether in life or in writing. If we do not distinguish things (in the world) or points (in our thought or writing or speech), we confuse them; and if we confuse them, we are confused. To have a clear idea, the idea must also be distinct. Modern minds often have a vague ideological aversion to distinctions; they think they are "discriminatory." In other words, they fail to distinguish three very different kinds of distinctions: (1) distinctions between thoughts, which are always helpful, (2) just and reasonable distinctions between things and people, such as distinguishing between medicines and poisons, or between students who pass and who fail, and (3) unjust and unreasonable distinctions between people, "discrimination" in the ideological sense, e.g. basing salaries on gender or race instead of performance. Outlining is the most practical application of logical division. Like most teachers in the humanities, I have read tens of thousands of student essays and papers. No matter what the content of those papers, no matter what is said, those that are not outlined, or not clearly or intelligently outlined, always receive a lower grade than those that are. We can (1) divide terms or we can (2) divide something more complex than terms: propositions, points, theses, or topics in a discourse, by outlining it. The two kinds of division have somewhat different rules. Dividing terms When we divide a term, we divide the extension of the term. When we define a terms, we define the comprehension of the term. (see page 43.) There are three rules: the division must be exclusive, exhaustive, and use only one standard. 1. The division must be exclusive; i.c., the things divided must be really distinct, and not overlap. Dividing political systems into monarchical, constitutional, and democratic violates this rule because a regime could be both monarchical and constitution- al, as well as both democratic and constitutional. Dividing regimes into totalitarian and democratic also violates this rule, for Division and outlining 63 the two could overlap. You could have a totalitarian democracy. For totalitarianism and democracy are not two mutually exclusive answers to the same question, but answers to two different questions. Democracy is an answer to the question of sovereignty: who ultimately holds the power? Its answer is: the demos, the peo- ple at large, or the majority. Totalitarianism is an answer to the question of quan- tity: how much power, or power over how much of human life, especially private life, is there? Its answer is: total, unlimited power. Brave New World is a totali- tarian democracy; so is Rousseau's idea of "the general will" as infallible (vox populi, vox dei: "The voice of the people is the voice of God"). Dividing attitudes into loving, hating, and indifferent also violates this rule because although love and hate both exclude indifference, they do not exclude each other. Though an attitude cannot be loving and indifferent at the same time, it can be loving and hating at the same time. Dividing attitudes into amoral, moral, and hateful also violates this rule because an attitude of hatred toward evil --- evil that harms persons --- is quite moral. The division should be between the amoral, the moral, and the immoral. One simple way of obeying this first rule is to divide in an "either/or" way, into only two subclasses, one of which negates the other. For instance, "loving and non-loving" are exclusive, while "loving and hating" are not. "Democratic and non-democratic" are exclusive, while "democratic and totalitarian" are not. Such a division is called dichotomous (literally, "cut in two"). 2. The division must be exhaustive; i.e., the divided parts should add up to a whole. This rule must always be obeyed in dividing terms, but not always in out- lining. Dividing the term "meat" into beef and lamb violates this rule because it omits pork. But we can divide "examples of healthy meats" in an outline into beef and lamb if we wish, omitting pork. Dividing tools into hand tools and electrical tools is a non-exhaustive divi- sion, thus violates this rule, because it omits tools that use power sources such as gas or steam. Such non-exhaustive divisions are sometimes useful, though, because they often do exhaustively divide a part of the class, the part we are con- cerned with. For instance, in the above division, "tools" may be shorthand for "the tools at hand" or "the tools in my house" or "the tools I can afford," and electrical and hand tools may be the only two kinds of those tools. Dividing the parts or aspects of a person into head and body violates this rule because it omits the soul or mind. Even dividing a person into body and soul might be said to omit the spirit, if spirit is distinguished from soul, as it some- times (but not usually) is. But "head and body" do exhaustively divide a person's body, in the narrower sense of "body" as "what's below the head." 3. The division should have only one basis or standard. We should not divide people simultaneously by their race and by their intelligence, e.g., or books by their objective truth and their subjective appeal. One of the things we 64 Il. TERMS should clearly divide and distinguish is the basis or standard by which we divide and distinguish. Exercise: Evaluate the following divisions of terms and tell which, if any, of the three rules they violate: 1.. men into bald and hirsute. parts of speech into nouns, verbs, adjectives, and adverbs. cats into tailless and those with tails. animals into reptiles, mammals, amphibians, marsupials, birds, and fish. regimes into popular and totalitarian BA AA RLY 13. 14. 15. 16. women into blondes, brunettes, and redheads human acts into those that are morally good and those that cause pain human beings into male and female. animals into rational animals ("men") and irrational animals ("brutes") 10. 11. 12. organisms into plants and animals things ("substances") into physical things and spiritual things reality into that which is real in itself and that which is real only relative to something else beings into mental beings and objectively real beings musical keys into major and minor H. "All Gaul is divided into three parts. The Belgians inhabit one part, the Aquitanians another, and those who call themselves Celts --- in our Jan- guage, Gauls --- inhabit the third." (Julius Caesar) I. "Democracy has therefore two excesses to avoid: the spirit of inequal- ity, which leads to aristocracy or monarchy, and the spirit of extreme equality, which leads to despotic power, as the latter is completed by con- quest." (Montesquieu). (A) "Let me ask you now: How would you arrange goods? Are there not some which we welcome for their own sakes, and independently of their consequences, as for example harmless pleasures and enjoyments, which delight us at the time though nothing follows from them?" "T agree in thinking that there is such a class," I replied. "Js there not also a second class of goods, such as knowledge, sight, health, which are desirable not only in themselves but also for their results?" "Certainly," I said "And would you not recognize a third class, such as gymnastic and the care of the sick, and the physician's art; also the various ways of money- making? These do us good but we regard them as disagreeable, and no one would choose them for their own sakes." (Plato, Republic, Book ID. (A) "Now order can be compared to reason in four ways. There is a cer- tain order which reason does not make but only considers, such as the 20. 2 \_ 22. Division and outlining 65 order of natural things. There is another order which reason in carrying on its considerations makes in its own proper act, as when, for example, it orders its own concepts and the signs of these concepts in so far as these are significant sounds. There is a third order which reason makes in the operations of the will. There is a fourth order which reason makes in exter- nal things of which it is the cause, as for example in a chest or in a house." (St. Thomas Aquinas). (H) "Before the end of the present century, unless something unforesee- able occurs, one of three possibilities will have been realized. These three are: I. The end of human life, perhaps of all life on our planet. II. A rever- sion to barbarism after a catastrophic diminution of the population of the globe. II\]. A unification of the world under a single government, possess- ing a monopoly of all the major weapons of war." (Bertrand Russell) H. Plato's division of states into (a) aristocratic (rule by "the best"), (b) timocratic (rule by "the brave'), (c) plutocratic (rule by the rich), (d) dem- ocratic (rule by the masses), and (e) despotic (rule by a tyrant). (H) Aristotle's division of states into (a) monarchies, (b) despotisms, (c) aristocracies, (d) oligarchies, (e) democracies, and (f) anarchies (What are the bases for his division? How many bases does he use? Is this one divi- sion or two?) H. From the Catholic point of view there are thirteen religious options. First, there is Agnosticism, or Skepticism, which is the negative answer to the question: Is there any hope of finding the truth about religion? All twelve other options answer Yes. Second, there is Atheism, which is the negative answer to the question: Is there any kind of God, any ontologi- cally superhuman mystery that justifies the fundamental religious attitude of piety? Ail eleven other options answer Yes. Third, there is Polytheism, which is the negative answer to the question: Is there an ultimate oneness to this mystery? All ten other options answer Yes. Fourth, there is Pantheism, which is the negative answer to the question: Is this mystery transcendent and distinct from the universe and human consciousness, rather than simply the sum total of all being, or another word for Everything, or that which everything really is? All nine other options answer Yes. Fifth, there is Vague Philosophical Theism, which is the neg- ative answer to the question: Is this mystery a Person, an "I" who could say "I AM," rather than a Force or a Principle? All eight other options answer Yes. Sixth, there is Non-religious Philosophical Theism, which is the negative answer to the question: Did this "J AM" reveal Himself through prophets? All seven other options answer Yes, and stem from the Hebrew Bible. Seventh, there is Judaism, which is the negative answer to the question: Did this "\] AM" send any prophet greater than Moses? All six other options answer Yes. Eighth, there is Islam, which is the negative 66 I. TERMS answet to the question: Is this greatest prophet Jesus rather than Muhammad? All five other options answer Yes. Ninth, there is Unitarianism, which is the negative answer to the question: Is Jesus a divine person as well as a human person, and is God three Persons rather than one? All four other options answer Yes. Tenth, there is Protestant Christianity, which is the negative answer to the question: Did this Jesus establish a single, visible, infallible Church with authority to teach in His name? All three other options answer Yes. Eleventh, there is Eastern Orthodox Christianity, which is the negative answer to the question: Is the Pope in Rome the present universal head of this Church? The two other options answer Yes. Twelfth, there is orthodox Catholicism, which is the negative answer to the question: May I pick and choose which teaching of the Church to believe and obey? The other option answers Yes, and this is the thirteenth option, which is "cafeteria Catholicism." @ (1) Diagram this, (2) evaluate it, and (3) if you think you can, give an alternative classification of religions. 23. H. Do the same for philosophies, political systems, or moral systems as \#22, above, did for religions. Outlining The principles of outlining are like the principles of morality in that they are usually simple and easy to understand but hard to obey. They are not hard in themselves; we are just lazy! But their practice has a big payoff. Few things clar- ify and improve writing and thinking more. By far the most important rule about outlining is: JUST DO IT! The basic rules are these: 1. Titles and subtitles are not parts of the outline but placed above it. 2. Use Roman numerals for main topics, capital letters for main subtopics, then Arabic numerals for sub-subtopics, then small letters, then Arabic numer- als in parentheses, then small letters in parentheses. 3. For each number or letter there must be a topic. Each must stand on a line by itself. E.g. never write "AI" or "TA." 4, There must always be more than one subtopic under any topic. (No A without a B, no \| without a 2.) 5. A subtopic must be placed under the main topic which it qualifies. This is the rule that gives many students the most trouble: distinguishing the relative rank of each point, deciding which are coordinate with which, and which are subordinate to which. This is an ability that is more intuitive than teachable; but it can be greatly improved by practice, and cannot be greatly improved without practice. 6. Subtopics are indented, so that all numbers or letters of the same kind come directly under each other vertically. Division and outlining 67 7. Begin each topic with a capital letter, even if they are not complete sen- tences. 8. Do not include Introduction or Conclusion as points within the outline. Outlining is not simply putting numbers and letters in order before sen- tences or before headings. They must be in logical order and logical subordina- tion. Students usually dislike outlining because they find it mechanical and inflexible. But when we construct any work of art with a complex structure, whether a garage or a symphony, there is simply no comparison between having a plan or outline and not having one.