Socratic Logic PDF - Peter Kreeft

Other books by Peter Kreeft from St. Augustine's Press The Philosophy of Jesus Jesus-Shock The Sea Within: Waves and the Meaning of All Things I Surf Therefore I Am If Einstein Had Been a Surfer Socrates' Children: Ancient Socrates' Children: Medieval Socrates' Children: Modern Philosophy 101 by Socrates Socrates Meets Descartes Socrates Meets Freud Socrates Meets Hume Socrates Meets Kant Socrates Meets Kierkegaard Socrates Meets Machiavelli Socrates Meets Marx Socrates Meets Sartre Sumrna Philosophica Socrates 'Students The Platonic Tradition Socratic Logic Edition 3.1 by Peter Kreeft Edited by Trent Dougherty A LOGIC TEXT USING SOCRATIC METHOD, PLATONIC QUESTIONS, & ARISTOTELIAN PRINCIPLES Modeling Socratcs 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 © S T AUGUSTINE'S PRESS South Bend, Indiana Copyright © 2004, 2005, 2008, 2010, 2014 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 3 4 5 6 20 19 18 17 16 15 14 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. I. Dougherty, Trent. II. Title. BC108.K67 2010 160 - dc22 2010032937 ooThe 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. staugust ine. net Contents PREFACE ix INTRODUCTION 1 1. W h a t g o o d is logic? 1 2. S e v e n t e e n w a y s this b o o k is different 9 3. T h e t w o logics (P) # 15 4. All of logic in two pages: an overview (B)* 26 5. T h e three acts o f the m i n d (B) 28 I. T H E F I R S T A C T O F T H E M I N D : U N D E R S T A N D I N G 35 1. Understanding: the thing that distinguishes man from both beast and c o m p u t e r (P) 35 2. Concepts, t e r m s and w o r d s (P) 40 3. T h e " p r o b l e m of universals" (P) 41 4. T h e extension and comprehension of terms 43 II. T E R M S 47 1. Classifying terms 47 2. Categories (B) 54 3. Predicables (B) 56 4. Division and Outlining (B) 62 III. M A T E R I A L FALLACIES 68 1. Fallacies of language 71 2. Fallacies of diversion 80 3. Fallacies of oversimplification 86 4. Fallacies of argumentation 92 "P" = "philosophical"; "B" = "basic." See p. 13, last paragraph. VI SOCRATIC LOGIC 5. Inductivc fallacies 100 6. Procedural fallacies 104 7. Metaphysical fallacies 109 8. Short Story: "Love Is a Fallacy" 114 IV. DEFINITION 123 1. The nature of definition (B) 123 2. The rules of definition (B) 124 3. The kinds of definition 124 4. The limits of definition 129 V. THE SECOND ACT O F T H E MIND: J U D G M E N T 138 1. Judgments, propositions, and sentences 138 2. What is truth? (P) 143 3. The four kinds of categorical propositions (B) 145 4. Logical form (B) 147 5. Euler's circles (B) 152 6. Tricky propositions 153 7. The distribution of terms 163 VI. C H A N G I N G PROPOSITIONS 166 1. Immediate inference 166 2. Conversion (B) 167 3. Obversion (B) 170 4. Contraposition 171 VII. C O N T R A D I C T I O N 173 1. What is contradiction? (B) 173 2. The Square of Opposition (B) 174 3. Existential import (P) 179 4. Tricky propositions on the Square 181 5. Some practical uses of the Square of Opposition 183 VIII. THE THIRD ACT O F T H E MIND: REASONING 186 1. What does "reason" mean? (P) 186 2. The ultimate foundations of the syllogism (P) 187 3. How to detect arguments 190 4. Arguments vs. explanations 193 5. Truth and validity 194 Contents vii IX. D I F F E R E N T K I N D S O F A R G U M E N T S 200 1. T h r e e m e a n i n g s o f " b e c a u s e " 200 2. T h e four c a u s e s (P) 202 3. A classification o f arguments 205 4. S i m p l e argument m a p s (B) 206 5. Deductive and inductive reasoning (B) 210 6. C o m b i n i n g induction and deduction: Socratic method (P) 211 X. S Y L L O G I S M S 215 1. T h e structure and strategy of the syllogism (B) 215 2. T h e skeptic's objection to the syllogism (P) 219 3. T h e empiricist's objection to the syllogism (P) 222 4. Demonstrative syllogisms 230 5. H o w to construct convincing syllogisms (B) 232 XI. C H E C K I N G S Y L L O G I S M S FOR VALIDITY 237 1. By Euler's Circles ( B ) 237 2. By Aristotle's six rules (B) 242 3. "Barbara Celarent": m o o d and figure 257 4. Venn Diagrams 258 XII. M O R E D I F F I C U L T S Y L L O G I S M S 264 1. Enthymemes: abbreviated syllogisms (B) 264 2. Sorites: chain syllogisms 275 3. Epicheiremas: multiple syllogisms (B) 279 4. Complex argument maps 282 XIII. C O M P O U N D S Y L L O G I S M S 289 1. Hypothetical syllogisms (B) 289 2. "Reductio ad absurdum " arguments 294 3. T h e practical syllogism: arguing about means and ends 296 4. Disjunctive syllogisms (B) 301 5. Conjunctive syllogisms (B) 303 6. Dilemmas (B) 306 XIV. I N D U C T I O N 313 1. What is induction? 313 2. Generalization 315 3. Causal arguments: Mill's methods 319 viii SOCRATIC LOG1C 4. Scientific hypotheses 325 5. Statistical probability 328 6. A r g u m e n t s by analogy 329 7. A fortiori and a minore arguments 335 XV. S O M E P R A C T I C A L A P P L I C A T I O N S O F L O G I C 342 1. How to write a logical essay 342 2. How to write a Socratic dialogue 344 3. How to have a Socratic debate 348 4. H o w to use Socratic m e t h o d on difficult people 350 5. How to read a book Somatically 355 XVI. S O M E P H I L O S O P H I C A L A P P L I C A T I O N S O F L O G I C 358 1. Logic and theology (P) 358 2. Logic and metaphysics (P) 359 3. Logic and cosmology (P) 360 4. Logic and philosophical anthropology (P) 361 5. Logic and epistemology (P) 362 6. Logic and ethics (P) 362 APPENDIX: P R O B L E M S W I T H M A T H E M A T I C A L L O G I C 364 1. Basic modern logic 364 2. The paradoxes of material implication 366 3. Responses to the paradoxes of material implication 367 ANSWERS T O E V E N - N U M B E R E D E X E R C I S E S 370 INDEX OF PRINCIPAL N A M E S 400 Preface This book is a dinosaur. Once upon a time in Middle-Earth, two things were different: (1) most stu- dents learned "the old logic," and (2) they could think, read, write, organize, and argue much better than they can today. If you believe these two things are not connected, you probably believe storks bring babies. It is time to turn back the clock. Contrary to the cliche, you can turn back the clock, and you should, whenever it is keeping bad time. (I learned that, and thousands of other very logical paradoxes, from G.K. Chesterton, the 20th-cen- tury Socrates.) As I write this, it is the last Sunday of October, and we have just turned back our clocks from daylight savings time to standard time. This is a parable for what I am convinced we must do in logic. The prevailing symbolic/mathematical logic is a logic that a computer can do; it is artificial, like daylight savings time. It is very useful where there is already much intelligence (in the minds of geniuses, especially in science), just as daylight savings time is very useful in the summer when there is a plenitude of sunlight. But as the sunlight of clear thinking, writ- ing, reading, and debating decreases in our society, it is time to make progress by turning back the clock from "daylight savings time" to real time, real lan- guage, real people, and the real world. The old Socratic-Platonic-Aristotelian logic is simply more effective than the new symbolic logic in helping ordinary people in dealing with those four precious things. This text differs from nearly all other logic texts in print in the three ways suggested by the subtitle. It does this by apprenticing itself to the first three great philosophers in history, Socrates, Plato, and Aristotle. (Do we have better ones today?) (1) No other logic text explicitly sets out to train little Socrateses. (2) No other logic text in print is so explicitly philosophical in a classical, Platonic way. (3) And only two or three other, shorter, formal logic texts bypass mathe- matical and symbolic logic for the "Aristotelian" logic of real people. X SOCRATIC LOGIC real inquiry, and real conversations. (The only other alternative to sym- bolic logic available today is "informal logic" or "rhetoric." This is use- ful, but less exact and less philosophical.) Introduction Section 1. What good is logic? This section will give you 13 good reasons why you should study logic.1 1. Order. You may be wondering, "What can I do with logic?" The answer is that logic can do something with you. Logic builds the mental habit of thinking in an orderly way. A course in logic will do this for you even if you forget every detail in it (which you won't, by the way), just as learning Latin will make you more habitually aware of the structure of language even if you forget every particular Latin word and rule. No course is more practical than logic, for no matter what you are thinking about, you are thinking, and logic orders and clarifies your thinking. No matter what your thought's content, it will be clearer when it has a more logical form. The principles of thinking logically can be applied to all thinking and to every field. Logic studies the forms or structures of thought. Thought has form and structure too, just as the material universe does. Thought is not like a blank screen, that receives its form only from the world that appears on it, as a movie screen receives a movie. This book will show you the basic forms (structures) and the basic laws (rules) of thought, just as a course in physics or chemistry shows you the basic forms and laws of matter. 2. Power. Logic has power: the power of proof and thus persuasion. Any power can be either rightly used or abused. This power of logic is rightly used to win the truth and defeat error; it is wrongly used to win the argument and defeat 1 Making numbered lists like this is the first and simplest way we learn to order "the buzzing, blooming confusion" that is our world. Children, "primitive" peoples, and David Letterman love to make lists. Thus we find "twelve-step programs," "the Ten Commandments," "the Seven Wonders of the World" "the Five Pillars of Islam," "the Four Noble Truths," and "the Three Things More Miserable Than a Wet Chicken." To make a list is to classify many things under one general category, and at the same time to distinguish these things by assigning them different numbers. 2 INTRODUCTION your opponent. Argument is to truth as fishing is to fish, or war to peacc, or courtship to marriage. The power of logic comes from the fact that it is the science and art of argu- ment. In the words of an old logic text, "Logick hath its name from logos ratio, because it is an Art which teacheth to Reason and Discourse." Thus beginneth Thomas Good's 1677 A Brief English Tract of Logick. "Dialecticke, otherwise called Logicke, is an arte which teacheth to dispute well." This is the first sentence of a 1574 book, Logicke, by Peter Ramus Martyr. Logic is so powerful that it can be dangerous to life. Socrates, the father of philosophy and the model for this book, was literally martyred for being logical - by the city of Athens, the ancient world's most famous and "civilized" democ- racy. The Apology, Socrates' "swan song," is his defense of philosophizing, of his life of logical inquiry. It is one of the greatest speeches ever made. No one should be allowed to die without reading it.2 Whether you use logic for right or wrong ends, it is a powerful tool. No mat- ter what your thought's end or goal or purpose may be, it will attain that end more effectively if it is clearer and more logical. Even if you want to do some- thing with logic rather than let logic do something with you - even if you want to deceive others, or "snow" them, or toy with them - you need to know logic in order to be a successful sophist. You must be a real logician even to be a fake ne. 3. Reading. Logic will help you with all your other courses, for logic will help you to read any book more clearly and effectively. And you are always going to be reading books; books arc the single most effective technological invention in the history of education. On the basis of over 40 years of full time college teaching of almost 20,000 students at 20 different schools, I am con- vinced that one of the reasons for the steep decline in students' reading ability is the decline in the teaching of traditional logic. Mortimer Adler's classic How to Read a Book is based on the traditional common-sense logic of the "three acts of the mind" that you will learn in this book. If I were a college president, I would require every incoming freshman to read Adler's book and pass a test on it before taking other courses. (The most important points of that book are summarized in this book on p. 355.) 4. Writing. Logic will also help you to write more clearly and effective- ly, for clear writing and clear thinking are a "package deal": the presence or absence of either one brings the presence or absence of the other. Muddled writ- ing fosters muddled thinking, and muddled thinking fosters muddled writing. Clear writing fosters clear thinking, and clear thinking fosters clear writing. 2 See Philosophy 101 by Socrates: An Introduction to Philosophy via Plato's 'Apology" by Peter Kreeft (St. Augustine's Press, 2002, 2014). What good is logic? 3 Common sense expects this, and scientific studies confirm it. Writing skills have declined dramatically in the 40 years or so since symbolic logic has replaced Aristotelian logic, and I am convinced this is no coincidence. There is nothing more effective than traditional logic in training you to be a clear, effective, and careful writer. It is simply impossible to communicate clear- ly and effectively without thinking clearly and effectively. And that means logic. 5. Happiness. In a small but significant way, logic can even help you attain happiness. We all seek happiness all the time because no matter what else we seek, we seek it because we think it will be a means to happiness, or a part of happiness, cither for ourselves or for those we love. And no one seeks happiness for any other end; no one says he wants to be happy in order to be rich, or wise, or healthy. But we seek riches, or wisdom, or health, in order to be happier. How can logic help us to attain happiness? Here is a very logical answer to that question: (1) When we attain what we desire, we are happy. (2) And whatever we desire, whether Heaven or a hamburger, it is more like- ly that we will attain it if we think more clearly. (3) And logic helps us to think more clearly. (4) Therefore logic helps us to be happy. No other things that make us happy are contradicted or threatened by logic, though many people think they are: Beauty, for instance. There is nothing illogical about the beauty of a sunset, or a storm, or a baby. Take heroism, or even holiness. What's illogical about being very, very good? Even fantasy is not illogical. In fact, according to the greatest master of this art, J.R.R. Tolkien, "Fantasy is a rational, not an irrational, activity... creative fantasy is founded upon the hard recognition that things are so in the world as it appears under the sun; on a recognition of fact, but not a slavery to it. So upon logic was founded the nonsense that displays itself in the tales and rhymes of Lewis Carroll. If men really could not distinguish between frogs and men, fairy- stories about frog-kings would not have arisen." ("On Fairy-Stories") The refer- ence to Lewis Carroll (the author of Alice in Wonderland) is particularly telling. Lewis Carroll was a pseudonym or pen name for Rev. Charles Lutwidge Dodgson, an Oxford mathematician who wrote a textbook on logic. In fact, he was working on volume two when he died. 6. Religious faith. All religions require faith. Is logic the ally or enemy of faith? Even religion, though it goes beyond logic, cannot go against it; if it did, it 4 INTRODUCTION would literally be unbelievable. Some wit defined "faith" as "believing what you know isn't true." But we simply cannot believe an idea to be true that we know has been proved to be false by a valid logical proof. It is true that faith goes beyond what can be proved by logical reasoning alone. That is why believing in any religion is a free personal choice, and some make that choice while others do not, while logical reasoning is equally com- pelling for all. However, logic can aid faith in at least three ways. (And thus, if faith significantly increases human happiness, as most psychologists believe, it logically follows that logic can significantly increase happiness.) First, logic can often clarify what is believed, and define it. Second, logic can deduce the necessary consequences of the belief, and apply it to difficult situations. For instance, it can show that if it is true, as the Bible says, that "God works all things together for good for those who love Him" (Romans 8:28), then it must also be true that even seemingly terrible things like pain, death, and martyrdom will work together for good; and this can put these terrible things in a new light and give us a motive for enduring them with hope. Third, even if logical arguments cannot prove all that faith believes, they can give firmer reasons for faith than feeling, desire, mood, fashion, family or social pressure, conformity, or inertia. For instance, if you believe the idea mentioned above, that "all things work together for good for those who love God," simply because you feel good today, you will probably stop believing it tomorrow when you feel miserable; or if you believe it only because your friends or family do, you will probably stop believing it when you are away from your friends or fam- ily. But if you have logical grounds for believing this, even though those grounds are not a compelling proof, they can keep your faith more firmly anchored dur- ing storms of changing feelings, fashions, friends, etc. How could there be logical grounds for such a belief as this (that "all things work together for good") that seems to contradict common sense and experi- ence? Some logical grounds might be the following: this conclusion can be log- ically deduced from four premises which are much easier to believe: (1) that God exists, (2) that God is the Creator of the universe and thus all-powerful, (3) that God is the source of all goodness and thus all-good, and (4) that God is the source of all design and order in the universe and thus all-wise. A God who is all-powerful is in control of everything He created; a God who is all-good wills only good to everything He created; and a God who is all-wise knows what is ultimately for the best for everyone and everything He created. So to deny that all things are foreseen and allowed by God for the ultimate good of those He loves, i.e. wills goodness to, is to deny either God's existence, power, goodness, or wisdom. In a logical argument, you cannot deny the conclusion without deny- ing a premise, and you cannot admit the premises without admitting the conclu- sion. The logical chains of argument can thus bind our minds, and through them also even our feelings (to a certain degree), to God and to hope and to happiness. What good is logic? 5 And if these four more basic premises of God's existence, power, goodness, and wisdom are questioned, logic may also help to establish them by further rea- sonable arguments (e.g. the traditional arguments for the existence of God); and perhaps logic can give good grounds for the premises of those arguments too. The point is not that logic can prove religious beliefs - that would dispense with the need for faith - but that it can strengthen them (and thus also the hap- piness that goes with them). And if it does not - if clear, honest, logical think- ing leads you to tftsbelieve something you used to believe, like Santa Claus — then that is progress too, for truth should trump even happiness. If we are hon- est and sane, we want not just any happiness, but true happiness. 7. Wisdom. "Philosophy" means "the love of wisdom." Although logic alone cannot make you wise, it can help. For logic is one of philosophy's main instru- ments. Logic is to philosophy what telescopes are to astronomy or microscopes to biology or math to physics. You can't be very good at physics if you're very bad at math, and you can't be very good at philosophy if you're very bad at logic. 8. Democracy. There are even crucial social and political reasons for studying logic. As a best-selling modern logic text says, "the success of democ- racy depends, in the end, on the reliability of the judgments we citizens make, and hence upon our capacity and determination to weigh arguments and evi- dence rationally." As Thomas Jefferson said, "In a republican nation, whose cit- izens are to be led by reason and persuasion and not by force, the art of reason- ing becomes of the first importance." (Copi & Cohen, Logic, 10th edition, Prentice-Hall, 1998). 9. Defining logic's limits. Does logic have limits? Yes, but we need logic to recognize and define logic's limits. Logic has severe limits. We need much more than logic even in our think- ing. For instance, we need intuition too. But logic helps us to recognize this dis- tinction. In our lives, logical arguments are always embedded in a human context that is interpersonal, emotional, intuitive, and assumed rather than proved; and this colors the proper interpretation of a logical argument. For instance, in 1637 Dcscartes said "I think, therefore I am"; 370 years later, a bumper sticker says "I bitch, therefore I am." The logical form of both arguments is the same, but the contexts are radically different. Descartes was seriously trying to refute skepti- cism (the belief that we cannot be certain of anything) by a purely theoretical argument, while the bumper sticker was making a joke. We laugh at it because we intuitively understand that it means "Don't complain at my bitching; bitch- ing makes me feel more 'real,' more alive." Logical thinking alone cannot know this, but it can know what its limits are: it can distinguish what it can understand from what it can't (non-logical factors such as humor and feeling and intuition). 6 INTRODUCTION 10.Testing authority. We need authority as well as logic. But we need logic to test our authorities. We need authorities because no individual can discover everything autonomously. We all do in fact rely on the human community, and therefore on the authority of others - parents, teachers, textbooks, "experts," friends, history, and tradition - for a surprisingly large portion of what we know - perhaps up to 99%, if it can be quantified. And that is another reason we need logic: we need to have good reasons for believing our authorities, for in the end it is you the individual who must decide which authorities to trust. It is obviously foolish to buy from every peddler of ideas that knocks on your mind's door. In fact, it is impossible, because they often contradict each other. 11. Recognizing contradictions. One of the things you will learn in this course is exactly what contradiction means, how to recognize it, and what to do with it. Logic teaches us which ideas contradict each other. If we are confused about that, we will be either too exclusive (that is, we will think beliefs logical- ly exclude each other when they do not) or too inclusive (that is, we will believe two things that cannot both be true). When we consider two different ideas which seem to contradict each other, we need to know three things: (1) First of all, we need to know exactly what each one means. Only then can we know whether they really contradict each other or not. (2) And if they do, we need to know which one is true and which is false. (3) And we do this by finding reasons why one idea is true and another is false. These are the "three acts of the mind": understanding a meaning, judging what is true, and reasoning. These are the three parts of logic which you will learn in this course. 12. Certainty. Logic has "outer limits"; there are many things it can't give you. But logic has no "inner limits": like math, it never breaks down. Just as 2 plus 2 are unfailingly 4, so if A is B and B is C, then A is unfailingly C. Logic is timeless and unchangeable. It is certain. It is not certain that the sun will rise tomorrow (it is only very, very probable). But it is certain that it either will or won't. And it is certain that if it's true that it will, then it's false that it won't. In our fast-moving world, much of what we learn goes quickly out of date. "He who weds the spirit of the times quickly becomes a widower," says G.K. Chesterton. But logic never becomes obsolete. The principles of logic are timelessly true. Our discovery of these principles, of course, changes and progresses through history. Aristotle knew more logic than Homer and we know more than Aristotle, as Einstein knew more physics than Newton and Newton knew more than Aristotle. What good is logic? Our formulations of these changeless logical principles also changc. This book is clearer and easier to read than Aristotle's Organon 2350 years ago, but it tcaches the same essential principles. Our applications of the timeless principles of logic to changing things are also changing. The principles of logic apply to many different and changing things, but the principles themselves are unchanging and rigid. They wouldn't work unless they were rigid. When we hear a word like "rigid" or "inflexible," we usually experience an automatic ("knee-jerk") negative reaction. But a moment's reflection should show us that, though people should not usually be rigid and inflexible, principles have to be. They wouldn't work unless they were rigid. Unless the yardstick is rigid, you cannot use it to measure the non-rigid, changing things in the world, like the height of a growing child. Trying to meas- ure our rapidly and confusingly changing world by a "flexible" and changing logic instead of an inflexible one is like trying to measure a squirming alligator with a squirming snake. 13. Truth. Our last reason for studying logic is the simplest and most impor- tant of all. It is that logic helps us to find truth, and truth is its own end: it is worth knowing for its own sake. Logic helps us to find truth, though it is not sufficient of itself to find truth. It helps us especially (1) by demanding that we define our terms so that we understand what we mean, and (2) by demanding that we give good reasons, arguments, proofs. These are the two main roads to truth, as you will see more clearly when you read Chapter II, on the three "acts of the mind": understanding, judging, and reasoning. Truth is found only in "the second act of the mind," judging - e.g. the judgment that "all men are mortal." But two paths to truth are "the first act of the mind" (e.g. understanding the meaning of the terms "men" and "mortal") and "the third act of the mind" (e.g. reasoning that "since all men have animal bodies, and whatever has an animal body is mortal, therefore all men are mor- tal"). These are the two main ways logic helps us to find truth. Truth is worth knowing just for the sake of knowing it because truth fulfills and perfects our minds, which are part of our very essence, our deep, distinctive- ly human core, our very selves. Truth is to our minds what food is to our bodies. Aristotle pointed out, twenty-four centuries ago, that there are three reasons for pursuing truth and three corresponding kinds of "sciences" (in the older, broader sense of the word "sciences," namely "rational explanations through causes"). He called the three kinds of sciences (1) "productive sciences," (2) "practical sciences," and (3) "theoretical sciences." Each pursues truth for a dif- ferent end: (I) We want to know about the world so that we can change it, improve it, and make things out of it (like rubber, or roads, or rockcts, or robots). 8 INTRODUCTION This is what Aristotle called "productive science? since its end is to pro- duce things. We call it "technology" after the Greek word techne, which means approximately "know-how" knowing how to make or fix or improve some material thing in the world. "Productive scicnces" include things as diverse as engineering, surgery, auto repair, cooking, and cosmetics. (2) We also want to know about ourselves so that we can change and improve our own lives, our behavior, our activities. Aristotle called this "practical science," knowledge in practice, in action. "Practical sci- ences" include ethics and politics as well as knowing how to do things as diverse as economics, singing, and surfing. (3) But most of all, we want to know simply in order to know, i.e. to become larger on the inside, as it were, to "expand our consciousness." Sciences that pursue this end Aristotle called "theoretical sciences," from the Greek word theoria, which means "looking" or "contemplating." ("Theoretical" does not necessarily mean "uncertain" or "merely hypo- thetical") Theoretical sciences include such diverse things as physics, biology, theology, mathematics, astronomy, and philosophy. These all have practical applications and uses, but they are first of all aimed at simply knowing and understanding the truth, even if there is no practi- cal application of it. Many people today think that theoretical sciences are the least important because they are not practical. But Aristotle argued that the theoretical sciences were the most important for the same reason that practical sciences were more important than productive scienccs: because their " p a y o f f " is more intimate, their reward closer to home. For they improve our very selves, while practical sciences improve our actions and lives, and productive sciences improve our world. All three are important, but just as our lives are more intimate to us than our external world, so our very selves are even more intimate to us than our lives, our deeds, and certainly more intimate and more important to us than the mate- rial things in our world. As a very famous and very practical philosopher argued twenty centuries ago, "What does it profit a man to gain the whole world but lose his own self?" (Mark 8:36) The original meaning of a "liberal arts" education was this: the study of the truth for its own sake, not only for the sake of what you can do with it or what you can make with it. The term "liberal arts" comes from Aristotle: he said that just as a man is called "free" when he exists for his own sake and a "slave" when he exists for the sake of another man, so these studies are called "free" ("liber- al" or liberating) because they exist for their own sake and not for the sake of anything else. Logic will prove very useful to you in many ways, but its most important use is simply to help you to sec more clearly what is true and what is false. Logic alone will not tell you what is true. It will only aid you in discovering Seventeen ways this book is different 9 truth. You also need experience, to get your premises; logic can then draw your conclusions. Logic will tell you that if all leprechauns are elves and all hobbits arc leprechauns, then it necessarily follows that all hobbits are elves; but logic will not tell you whether all leprechauns are elves, or even whether there are any leprechauns. (I once asked my very Irish neighbor whether she believes in lep- rechauns and she answered, "Of course not But they exist all the same, mind you." Perhaps the Irish should write their own logic textbook.) To have logical clarity and consistency is admirable. But to have only logi- cal clarity and consistency is pitiful. In fact, it is a mark of insanity, as G.K. Chesterton pointed out: "If you argue with a madman, it is extremely probable that you will get the worst of it; for in many ways his mind moves all the quicker for not being delayed by the things that go with good judgment. He is not ham- pered by a sense of humour or charity, or by the dumb certainties of experience.... Indeed, the common phrase for insanity is in this respect a misleading one. The madman is not the man who has lost his reason. The madman is the man who has lost everything except his rea- son... if a man says that he is the rightful King of England, it is no complete answer to say that the existing authorities call him mad; for if he were King of England that might be the wisest thing for the existing authorities to do. Or if a man says that he is Jesus Christ, it is no answer to tell him that the world denies his divinity; for the world denied Christ's... his mind moves in a perfect but narrow circle. A small cir- cle is quite as infinite as a large circle; but, though it is quite as infi- nite, it is not so large. In the same way the insane explanation is quite as complete as the sane one, but it is not so large.... 'So you are the Creator and Redeemer of the world: but what a small world it must be! What a little heaven you must inhabit, with angels no bigger than but- terflies! How sad it must be to be God; and an inadequate God! Is there really no life fuller and no love more marvelous than yours?... How much happier you would be, how much more of you there would be, if the hammer of a higher God could smash your small cosmos, scatter- ing the stars like spangles, and leave you in the open, free like other men to look up as well as down!'... Curing a madman is not arguing with a philosopher; it is casting out a devil." (Orthodoxy) (Especially for Teachers) Section 2. Seventeen ways this book is different There are literally hundreds of logic texts in print, and thousands more out of print. Why one more? How is this one different? How is it better? 1. It's simple. It's better for most students because it's not the best, i.e. the 10 INTRODUCTION most advanced, sophisticated, state-of-the-art text. Most beginning students need a simpler, easier, basic logic text, just as most new computer owners would love to have a simple, "dumb," obedient computer that they can master and use quick- ly and easily instead of one with so many "bells and whistles" that by the time you master it, it's obsolete. But no one makes a "dumb" computer; the geniuses who make them arc too proud to serve us "dummies." Well, I'm not. This is a "dumb" logic book: it's for beginners. For instance, its most basic points (which are summarized in Section 4 of this Introduction, "All of logic in two pages") are repeated so often that even the slowest and most confused students should not lose their way and lose hope. 2. It's user-friendly. It is for two kinds of users: it is a classroom text for teachers and also a "do-it-yourself" text for individuals. The fact that it is simple enough for an intelligent "do-it-yourselfer" does not mean it is less useful for a teacher as a classroom text - unless obscure class- room texts are more useful than clear and simple ones. 3. It's practical. It covers topics in proportion to probable student use. E.g. it devotes more space than usual to topics like (1) Socratic method, (2) inter- preting ordinary language and translating it into logical form, (3) constructing effective syllogisms, (4) material fallacies, (5) diagramming long arguments simply, and (6) smoking out hidden premises, because these are some of the log- ical skills we need and use the most outside a logic class. Logic is like praying, fishing, or learning a language: you learn by doing. Much of the work is in the will, not the mind: in resolution and persistence and dogged honesty. Actually practicing a few basic logical principles will make you a far more effective arguer, evaluator, researcher, and writer than knowing ten times more and practicing it less. Most logic students learn too much, not too lit- tle; instead of learning what they need to use, they learn what they neither need nor use. That is why this book contains many exercises on basics, and only a very introductory treatment of non-basics. When we actually argue, obeying a few basic rules well is much more rare, more difficult, and more adequate than we usually think. Just imagine for a moment how some of the arguments you have heard or read would have been different if both sides had only obeyed this one elementary principle: Don't ignore your opponent's arguments and counter with your own; don't just sit there waiting for your "turn" to attack. You must also defend by finding a logical fallacy, a false premise, or an ambiguous term in every single one of your opponent's arguments. Practical usefulness is the main reason for preferring classical Socratic, Aristotelian logic to modern symbolic logic, even if the latter may be more the- oretically adequate. It is like the difference between Einsteinian physics and Seventeen ways this book is different 11 Newtonian physics, with its basic laws of motion and its principles of simple machines. Though Einstein is theoretically superior. Newton is still much more practical for beginners. I think I have never found anyone except a professional philosopher who actually used symbolic logic in actual conversation or debate. 4. It's linguistic. It emphasizes the use and understanding of ordinary lan- guage. E.g. it devotes considerable time to translating ordinary language into logical form (and it uses the logical form closest to ordinary language) because this is a skill teachers usually assume, but students usually lack (probably because of the decline in the teaching of grammar). I find today's students much more confused by language, and less by mathematical symbols, than previous generations. They are the digital generation, not the verbal. They need to re-learn the logic of language, for thought can no more escape words than fish can escape water. There is of course a need for new and specialized forms of mathematical logic too, but this need is being well supplied, while the more basic need for the more basic logic is not being well supplied. 5. It's readable. Its linguistic style is popular, personal, informal, light, and sometimes even humorous. 6. It's traditional. Its master is Aristotle, "the master of common sense," the man whose philosophy has become as embedded in the Western tradition as Confucius's became embedded in the Chinese. Aristotle's master was Plato. "All of Western philosophy is a series of foot- notes to Plato," said Whitehead. In The Last Battle, C. S. Lewis has the old pro- fessor say, "It's all in Plato, all in Plato: bless me, what do they teach them at these schools?" Lewis says of his own thought: "To lose what I owe to Plato and Aristotle would be like the amputation of a limb" (Rehabilitations, "The Idea of an English School"). Plato's master was Socrates, the most interesting philosopher who ever lived, and the father of the application of logic to philosophical questions. When Aristotle wrote the world's first logic text, he was reflecting on what Socrates had already done, defining the principles of Socrates' practice. Thus our title, "Socratic Logic." This book is also traditional in the sense that it uses many classic examples from history and the Great Books. A side benefit is thus the student's exposure to these many "nuggets" of traditional wisdom, any one of which may some day enable him to win a large amount of money on a quiz show somewhere down in Plato's cave. Since tradition (i.e. all of human history up until the present) has been much more religious than the present, many of the examples are about religious ques- tions. There are at least five advantages to this. (1) Religious questions arc 12 INTRODUCTION intrinsically interesting. Only a fascinatingly dull mind is more fascinatcd with questions about life insurance rates than with questions about life after death. (2) They are not only subjectively interesting but objectively, intrinsically important, whether they are to be answered affirmatively or negatively. Religion is either humanity's most important wisdom or its most important illu- sion. (3) They are by nature not culturally and temporally relative, like most questions of politics and ideology, but universally human. (4) They are close to philosophical questions, and lead naturally into them. (5) And they are difficult, challenging, and mysterious. Believers or nonbelievers in any religion should be able to use this book with profit. It makes no religious or antireligious assumptions. 7. It's commonsensical. Logic is like psychoanalysis in that it does not impose anything upon you from outside but only clarifies what is already pres- ent in you. Good logic never contradicts common sense, if we mean by "com- mon sense" not something the polls determine (that's only "fashionable opin- ions") but something naturally and innately present in every mind. The American philosopher C.I. Lewis wrote that "everyone knows the distinction of cogent reasoning from fallacy. The study of logic appeals to no criterion not already present in the learner's mind." 3 If any principle in this book ever seems to contradict what you know by innate common sense, something is wrong with that principle. This is one of the main reasons for preferring traditional Aristotelian logic to the more fashionable modern symbolic logic. Aristotelian logic is far closer to common sense; that is why it is far easier to apply and use in ordinary conversations. We all have used logic already, unconsciously, many times every day. Even animals do that. Chrysippus, a Stoic philosopher of the 3rd century, watched a dog chasing a rabbit come to a fork in the road; the dog sniffed at two of the three paths and then ran down the third without taking the time to sniff at it. Even the dog instinctively used logic to catch a real-world rabbit! He used a dis- junctive syllogism: Either the rabbit took road A or road B or road C; not A or B; therefore C. In one of Moliere's comedies, Monsieur Jourdain suddenly discovers, to his amazement, that he has been speaking in prose all his life. You have been think- ing and speaking in "logic" all your life. This course helps you to "know thyself." 3 Interestingly, Christian apologist C.S. Lewis was once confused with C.I. Lewis, who went on to be an important developer of symbolic logic. When CS. Lewis saw a review of The Principles of Symbolic Logic which attributed the work to him, he wrote to his father "1 am writing back to tell them that they have got rather muddled. Symbolic Logic forsooth!" (Letters, 25 May 1919). Se\'enteen w ays this book is different 13 8. It's philosophical, both in its applications and in its foundations. Of all the applications of logic, philosophy is the most (subjectively) interesting and the most (objectively) important. Philosophy asks the Big Questions. This book exposes students to the ideas of the great philosophers all along the way by frequent quotations from them in its exercises, and ends with a series of chapters which use logic to introduce the fundamental questions of meta- physics, philosophical theology, cosmology, ethics, anthropology, and episte- mology. It prepares students for reading Great Books, not "Dick and Jane." Philosophy is not only an application of logic, but logic also has philo- sophical foundations. Logic is not always philosophically neutral. DifTerent kinds of logic sometimes imply or presuppose importantly different philosophi- cal positions. (See Section 3, p. 15.) This book's philosophy is Aristotelian realism. It dares to take a philosoph- ical stand on controversial issues like truth, and certainty, and universals. (It affirms all three, by the way.) This stand is neither ideological nor religious but commonsensical and traditional; but precisely because it is commonsensical and traditional, it is counter-cultural and controversial in today's philosophical mar- ketplace. 9. It's constructive. It teaches how to make good arguments as well as how to refute bad ones, and such constructive lessons as how to use the Socratic method, how to write a good essay, how to read a book, how to organize an out- line, how to debate, and how to argue logically with difficult people. For some mysterious reason these practical arts are usually neglected in logic books. 10. It's clearly divided. There are 89 sections, or mini-chapters, in the 16 chapters of the book, but most of them are very short. Each section teaches only one basic point. This enhances clarity for the beginning student. Some logic text- books try to teach too many things in a single section, and the result is confu- sion. This book does only one thing at a time. The sections arc determined by content, not by length. Since there is only one basic point per section, and since some points are easier than others, some sections are much shorter than others. (Why not? Why should quantity deter- mine quality? Why should the accidental determine the essential?) 11. It's flexible. The division into so many sections gives the teacher the option to select a "mix and match" of sections in many different ways, depend- ing on the emphasis desired. There are four kinds of sections: basic logic, advanced logic, practical appli- cations, and philosophical logic. The Table of Contents marks the basic sections "(B)", marks the philosophical sections "(P)", and puts the practical application 14 INTRODUCTION sections in Chapter 15. This allows the book to be used in at least ten different ways, ranging from the very short to the very long: (1) the bare basics only (2) the basic sections plus the philosophical sections (3) the basic sections plus the more advanced sections in logic (4) the basic sections plus the practical application sections (5) the basic sections plus any two of these three additions (6) all of the book (7) all or some of it supplemented by a text in symbolic logic (8) all or some of it supplemented by a text in inductive logic (9) all or some of it supplemented by a text in rhetoric or informal logic (10) all or some of it supplemented by readings in and applications to the great philosophers The first option should take about half a semester, (2) through (6) a whole semester, and (7) through (10) up to two semesters. In a one-semester, 14-week, one-class-a-week course, you can combine any or all of the following chapters into single-class lessons: (1) the Introduction and chapter 1; (2) chapters 6 and 7; (3) chapters 8 and 9; (4) chapters 10 and 11; (5) chapters 15 and 16. 12. It's short. The first few options above give you a short, basic, no-frills, no-fat logic text. 13. It's selective. It emphasizes a relatively small number of "big ideas" that the student will always need and use and remember, rather than the usual logic text's many "bells and whistles" that students will rarely use. 14. It's innovative where it needs to be. It includes some specific things most other logic texts do not, such as: a clear distinction between six quite different kinds of induction a unique explanation of the Square of Opposition that is much cleaner and simpler than any other a simple, streamlined solution to the problem of existential import an overview of the difference between the two logics and its philosoph- ical significance practical advice on Socratic method, Socratic debates, and writing Socratic dialogues many interfacings with philosophy -A- practical applications of logic to writing and debating an expanded list of material fallacies (49) divided into seven categories. (This is the most complete list of material fallacies 1 know of, except for two books entirely devoted to fallacies, Fallacy; The Counterfeit of Argument by Fernside & Holthcr [Englewood Cliffs, N.J.: Prentice- The too logics 15 Hall, 1959], which lists 51, and Historians' Fallacies by David H. Fischcr [New York: Harper & Row, 1979], which lists 112.) 15. It's interactive. It includes many exercises, because this is how a logic course "takes" in students' minds and lives. It is more effective to master a few important principles, by much practice, than to be exposed to so many principles and so little practice that you cannot remember and apply the principles after the course is over. We remember general principles only by particular experiences in applying them. (This "practical empiricism" is part of the Aristotelian her- itage behind the book.) A suggestion for teachers: Instead of lecturing on the text, which would probably be only rehashing it, let it teach itself, but leave plenty of time for stu- dent questions on it. A suggested class format: (1) first, discuss all student questions about the pages that were assigned, including exercises; (2) then, a short quiz (weekly or even daily); (3) then go over the correct answers to the quiz, so students can immediately learn from their mistakes; (4) then introduce the next assignment. One more suggestion: If there are not enough questions, and only a small number of students, require at least two written questions from each student at the very beginning of each class, for you to answer (or have other students answer). 16. It's holistic. It emphasizes the whole, the "big picture," the structure and outline of the whole of logic. It repeatedly situates each topic within the "three acts of the mind" overview of the course, so that the student has a sense of where everything fits, and does not feel lost. (Teachers tend to underestimate this need for a continual orientation check, and how much confidence it gives the confused student.) 17. It's classroom-tested, based on the experience of teaching many kinds of logic in many kinds of ways to many kinds of students at many levels of intel- ligence and background at many kinds of schools over many years. Section 3, The two logics (P) (This section can be omitted without losing anything you will need later on in the book. It's here both to satisfy the advanced student's curiosity and to sell the approach of this book to prospective teachers who may question its emphasis on Aristotelian rather than symbolic logic, by justifying this choice philosophically.) Almost four hundred years before Christ, Aristotle wrote the world's first logic textbook. Actually it was six short books, which collectively came to be known as the Organon, or "instrument." From then until 1913, when Bertrand Russell and Alfred North Whitehead published Principia Mathematical the first 16 INTRODUCTION classic of mathematical or symbolic logic, all students learned Aristotelian logic, the logic taught in this book. The only other "new logic" for twenty-four centuries was an improvement on the principles of inductive logic by Francis Bacon's Novum Organum ("New Or- ganon"), in the 17th century, and another by John Stuart Mill, in the 19th century. (Inductive reasoning could be very roughly and inadequately defined as reasoning from concrete particular instances, known by experience, while deduction reasons from general principles. Induction yields only probability, while deduction yields certainty. "Socrates, Plato and Aristotle are mortal, there- fore probably all men are mortal" is an example of inductive reasoning; "All men are mortal, and Socrates is a man, therefore Socrates is mortal" is an exam- ple of deductive reasoning.) Today nearly all logic textbooks use the new mathematical, or symbolic, logic as a kind of new language system for deductive logic. (It is not a new logic; logical principles are unchangeable, like the principles of algebra. It is more like changing from Roman numerals to Arabic numerals.) There are at least three reasons for this change: (1) The first and most important one is that the new logic really is superior to the old in efficiency for expressing many long and complex arguments, as Arabic numerals are to Roman numerals, or a digital computer to an analog computer, or writing in shorthand to writing in longhand. However, longhand is superior to shorthand in other ways: e.g. it has more beauty and elegance, it is intelligible to more people, and it gives a more per- sonal touch. That is why most people prefer longhand most of the time - as most beginners prefer simpler computers (or even pens). It is somewhat similar in logic: most people "argue in longhand," i.e. ordinary language; and Aristotelian logic stays close to ordinary language. That is why Aristotelian logic is more practical for beginners. Even though symbolic language is superior in sophistication, it depends on commonsense logic as its foundation and root. Thus you will have a firmer foun- dation for all advanced logics if you first master this most basic logic. Strong roots arc the key to healthy branches and leaves for any tree. Any farmer knows that the way to get better fruit is to tend the roots, not the fruits. (This is only an analogy. Analogies do not prove anything - that is a common fallacy - they only illuminate and illustrate. But it is an illuminating analogy.) Modern symbolic logic is mathematical logic. "Modern symbolic logic has been developed primarily by mathematicians with mathematical applications in mind." This from one of its defenders, not one of its critics (Henry C. Baycrly, in A Primer of Logic. N.Y.: Harper & Row, 1973, p.4). Mathematics is a wonderful invention for saving time and empowering sci- ence, but it is not very useful in most ordinary conversations, especially philo- sophical conversations. The more important the subject matter, the less relevant The two logics 17 mathematics seems. Its forte is quantity, not quality. Mathematics is the only totally clear, utterly unambiguous language in the world; yet it cannot say any- thing very interesting about anything very important Compare the exercises in a symbolic logic text with those in this text How many are taken from the Great Books? How many are from conversations you could have had in real life? (2) A second reason for the popularity of symbolic logic is probably its more scientific and exact form. The very artificiality of its language is a plus for its defenders. But it is a minus for ordinary people. In fact, Ludwig Wittgenstein, probably the most influential philosophical logician of the 20th century, admit- ted, in Philosophical Investigations, that "because of the basic differences between natural and artificial languages, often such translations [between natu- ral-language sentences and artificial symbolic language] are not even possible in principle." "Many logicians now agree that the methods of symbolic logic are of little practical usefulness in dealing with much reasoning encountered in real- life situations" (Stephen N. Thomas, Practical Reasoning in Natural Language, Prentice-Hall, 1973). - And in philosophy! "However helpful symbolic logic may be as a tool of t h e... sciences, it is [relatively] useless as a tool of philosophy. Philosophy aims at insight into principles and into the relationship of conclusions to the princi- ples from which they are derived. Symbolic logic, however, does not aim at giv- ing such insight" (Andrew Bachhuber, Introduction to Logic (New York: Appleton-Century Crofts, 1957), p. 318). (3) But there is a third reason for the popularity of symbolic logic among philosophers, which is more substantial, for it involves a very important differ- ence in philosophical belief. The old, Aristotelian logic was often scorned by 20th-century philosophers because it rests on two commonsensical but unfash- ionable philosophical presuppositions. The technical names for them arc "epis- temological realism" and "metaphysical realism." These two positions were held by the vast majority of all philosophers for over 2000 years (roughly, from Socrates to the 18th century) and are still held by most ordinary people today, since they seem so commonsensical, but they were not held by many of the influential philosophers of the past three centuries. (The following summary should not scare off beginners; it is much more abstract and theoretical than most of the rest of this book.) The first of these two presuppositions, "epistemological realism," is the belief that the object of human reason, when reason is working naturally and rightly, is objective reality as it really is; that human reason can know objective reality, and can sometimes know it with certainty; that when we say "two apples plus two apples must always be four apples," or that "apples grow on trees," we are saying something true about the universe, not just about how we think or about how we choose to use symbols and words. Today many philosophers arc 18 INTRODUCTION skeptical of this belief, and call it naive, largely because of two 18th-century "Enlightenment" philosophers, Hume and Kant. Hume inherited from his predecessor Locke the fatal assumption that the immediate object of human knowledge is our own ideas rather than objective reality. Locke naively assumed that we could know that these ideas "corre- sponded" to objective reality, somewhat like photographs; but it is difficult to see how we can be sure any photograph accurately corresponds to the real object of which it is a photograph if the only things we can ever know directly are pho- tographs and not real objects. Hume drew the logical conclusion of skepticism from Locke s premise. Once he limited the objects of knowledge to our own ideas, Hume then dis- tinguished two kinds of propositions expressing these ideas: what he called "matters of fact" and "relations of ideas." What Hume called "relations of ideas" are essentially what Kant later called "analytic propositions" and what logicians now call "tautologies": propositions that are true by definition, true only because their predicate merely repeats all or part of their subject (e.g. "Trees are trees" or "Unicorns are not non-unicorns" or "Unmarried men are men"). What Hume called "matters of fact" are essentially what Kant called "syn- thetic propositions," propositions whose predicate adds some new information to the subject (like "No Englishman is 25 feet tall" or "Some trees never shed their leaves"); and these "matters of fact," according to Hume, could be known only by sense observation. Thus they were always particular (e.g. "These two men are bald") rather than universal (e.g. "All men are mortal"), for we do not sense universals (like "all men"), only particulars (like "these two men"). Common sense says that we can be certain of some universal truths, e.g. that all men are mortal, and therefore that Socrates is mortal because he is a man. But according to Hume we cannot be certain of universal truths like "all men are mortal" because the only way we can come to know them is by gener- alizing from particular sense experiences (this man is mortal, and that man is mortal, etc.); and we cannot sense all men, only some, so our generalization can only be probable. Hume argued that particular facts deduced from these only- probable general principles could never be known or predicted with certainty. If it is only probably true that all men are mortal, then it is only probably true that Socrates is mortal. The fact that we have seen the sun rise millions of times does not prove that it will necessarily rise tomorrow. Hume's "bottom line" conclusion from this analysis is skepticism: there is no certain knowledge of objective reality ("matters of fact"), only of our own ideas ("relations of ideas"). We have only probable knowledge of objective real- ity. Even scientific knowledge, Hume thought, was only probable, not certain, because science assumes the principle of causality, and this principle, according to Hume, is only a subjective association of ideas in our minds. Because we have seen a "constant conjunction" of birds and eggs, because we have seen eggs The two logics 19 follow birds so often, we naturally assume that the bird is the cause of the egg. But we do not see causality itself, the causal relation itself between the bird and the egg. And we certainly do not see (with our eyes) the universal "principle of causality." So Hume concluded that we do not really have the knowledge of objective reality that we naturally think we have. We must be skeptics, if we are only Humean beings. Kant accepted most of Hume's analysis but said, in effect, "I Kant accept your skeptical conclusion." He avoided this conclusion by claiming that human knowledge does not fail to do its job because its job is not to conform to objec- tive reality (or "things-in-themselves," as he called it), i.e. to correspond to it or copy it. Rather, knowledge constructs or forms reality as an artist constructs or forms a work of art. The knowing subject determines the known object rather than vice versa. Human knowledge does its job very well, but its job is not to learn what is, but to make what is, to form it and structure it and impose mean- ings on it. (Kant distinguished three such levels of imposed meanings: the two "forms of apperception": time and space; twelve abstract logical "categories" such as causality, necessity, and relation; and the three "ideas of pure reason": God, self, and world.) Thus the world of experience is formed by our knowing it rather than our knowledge being formed by the world. Kant called this idea his "Copernican Revolution in philosophy." It is sometimes called "epistemological idealism" or "Kantian idealism," to distinguish it from epistemological realism. ("Epistemology" is that division of philosophy which studies human know- ing. The term "epistemological idealism" is sometimes is used in a different way, to mean the belief that ideas rather than objective reality are the objects of our knowledge; in that sense, Locke and Hume are epistemological idealists too. But if we use "epistemological idealism" to mean the belief that the human idea (or knowing, or consciousness) determines its object rather than being determined by it, then Kant is the first epistemological idealist.) The "bottom line" for logic is that if you agree with either Hume or Kant, logic becomes the mere manipulation of our symbols, not the principles for a true orderly knowledge of an ordered world. For instance, according to episte- mological idealism, general "categories" like "relation" or "quality" or "cause" or "time" are only mental classifications we make, not real features of the world that we discover. In such a logic, "genus" and "species" mean something very different than in Aristotelian logic: they mean only any larger class and smaller sub-class that we mentally construct. But for Aristotle a "genus" is the general or common part of a thing's real essential nature (e.g. "animal" is man's genus), and a "species" is the whole essence (e.g. "rational animal" is man's species). (See Chapter III, Sections 2 and 3.) Another place where modern symbolic logic merely manipulates mental symbols while traditional Aristotelian logic expresses insight into objective real- ity is the interpretation of a conditional (or "hypothetical") proposition such as 20 INTRODUCTION "If it rains, I will get wet." Aristotelian logic, like common sense, interprets this proposition as an insight into real causality: the rain causes me to get wet. I am predicting the effect from the cause. But symbolic logic does not allow this com- monsensical, realistic interpretation. It is skeptical of the "naive" assumption of epistemological realism, that we can know real things like real causality; and this produces the radically anti-commonsensical (or, as they say so euphemisti- cally, "counter-intuitive") "problem of material implication" (see page 23). Besides epistemological realism, Aristotelian logic also implicitly assumes metaphysical realism. (Metaphysics is that division of philosophy which inves- tigates what reality is; epistemology is that division of philosophy which inves- tigates what knowing is.) Epistemological realism contends that the object of intelligence is reality. Metaphysical realism contends that reality is intelligible; that it includes a real order; that when we say "man is a rational animal," e.g. we are not imposing an order on a reality that is really random or chaotic or unknowable; that we are expressing our discovery of order, not our creation of order; that "categories" like "man" or "animal" or "thing" or "attribute" are taken from reality into our language and thought, not imposed on reality from our language and thought. Metaphysical realism naturally goes with epistemological realism. Technically, metaphysical realism is the belief that universal concepts corre- spond to reality; that things really have common natures; that "universals" such as "human nature" are real and that we can know them. There are two forms of metaphysical realism: Plato thought that these uni- versals were real things in themselves, while Aristotle thought, more common- sensically, that they were real aspects of things which we mentally abstracted from things. (See Chapter II, Section 3, "The Problem of Universals") The opposite of realism is "nominalism " the belief that universals are only man-made nomini (names). William of Ockham (1285-1349) is the philosopher who is usually credited (or debited) with being the founder of nominalism. Aristotelian logic assumes both epistemological realism and metaphysical realism because it begins with the "first act of the mind," the act of understand- ing a universal, or a nature, or an essence (such as the nature of "apple" or "man"). These universals, or essences, are known by concepts and expressed by what logic calls "terms." Then two of these universal terms are related as sub- jects and predicates of propositions (e.g. "Apples are fruits," or "Man is mor- tal"). "Aristotle never intended his logic to be a merely formal calculus [like mathematics]. He tied logic to his ontology [metaphysics]: thinking in concepts presupposes that the world is formed of stable species" (J. Lenoble, La notion de /'experience, Paris, 1930, p. 35). Symbolic logic is a set of symbols and rules for manipulating them, with- out needing to know their meaning and content, or their relationship to the real world, their "truth" in the traditional, commonsensical sense of "truth." A The two logics 21 computer can do symbolic logic. It is quantitative (digital), not qualitative. It is reducible to mathematics. The new logic is sometimes called "prepositional logic" as well as "mathe- matical logic" or "symbolic logic" because it begins with propositions, not terms. For terms (like "man" or "apple") express universals, or essences, or natures; and this implicitly assumes metaphysical realism (that universals are real) and epistemological realism (that we can know them as they really are). Typically modern philosophers criticize this assumption as naive, but it seems to me that this is a very reasonable assumption, and not naive at all. Is it too naive to assume that we know what an apple is? The new logic has no means of saying, and even prevents us from saying, what anything is! And if we cease to say it, we will soon cease to think it, for there will be no holding-places in our language for the thought. Language is the house of thought, and homelessness is as life-threatening for thoughts as it is for people. If we should begin to speak and think only in nominalist terms, this would be a monumental historic change. It would reverse the evolutionary event by which man rose above the animal in gaining the ability to know abstract universals. It would be the mental equivalent of going naked on all fours, living in trees, and eating bugs and bananas. (Could monkeys have evolved by natural selection from nominalists?) While it may be "extremist" to suggest it, such a mental "devolution" is not intrinsically impossible. And changes in logic are not wholly unrelated to it. Already, "internet logic," or the logic of spontaneous association by "keywords," is replacing "genus and species logic," or the logic of an ordered hierarchy of objectively real categories. To most modern minds, those last seven words sound almost as archaic as alchemy or feudalism. Many criticize them as ideological- ly dangerous. These critics dislike categories because they "feel that" (that phrase is a category confusion, by the way) classifications, and universal state- ments about classes such as "Hittites could not read Hebrew," constitute "preju- dice," "judgmentalism," "oppression," or even "hate speech." Logic and social change are not unrelated. Not only our logicians but also our society no longer thinks primarily about the fundamental metaphysical ques- tion, the question of what things are, the question of the nature of things. Instead, we think about how we feel about things, about how we can use them, how we see them behave, how they work, how we can change them, or how we can predict and control their behavior by technology. But all this does not raise us above the animal level in kind, only in degree. The higher animals too have feelings, and things to use, and sight, and action, and even a kind of technology of behavior prediction and control. For the art of hunting is an art of predicting and controlling the behavior of other animals. What do we have that no mere ani- mal has? The thing that many modern philosophers vilify: abstraction. We have the power to abstract and understand universals. This is the thing traditional logic is founded on, and this is the thing symbolic logic ignores or denies. 22 INTRODUCTION Logic is deeply related to moral and ethical changes in both thought and practice. All previous societies had a strong, nearly universal, and rarely ques- tioned consensus about at least some basic aspects of a "natural moral law," about what was "natural" and what was "unnatural." There may not have been a greater obedience to this law, but there was a much greater knowledge of it, or agreement about it. Today, especially in the realm of sex (by far the most radi- cally changed area of human life in both belief and practice), our more "advanced" minds find the old language about "unnatural acts" not only "polit- ically incorrect" but literally incomprehensible, because they no longer accept the legitimacy of the very question of the "nature" of a thing. Issues like homo- sexuality, contraception, masturbation, pedophilia, incest, divorce, adultery, abortion, and even bestiality are increasingly debated in other terms than the "nature" of sexuality, or the "nature" of femininity and masculinity. It is not an unthinkable suspicion that one of the most powerful forces driving the new logic is more social than philosophical, and more sexual than logical. Symbolic logic naturally fosters utilitarian ethics, which is essentially an ethic of consequences. The fundamental principle of utilitarianism is that an act is good if its probable consequences result in "the greatest happiness for the greatest number" of people. It is an " i f... then..." ethics of calculating con- sequences - essentially, "the end justifies the means" (though that formula is somewhat ambiguous). Symbolic logic fits this perfectly because it is essential- ly an " i f... then... " logic, a calculation of logical consequences. Its basic unit is the proposition (p or q) and its basic judgment is "if p then q." In contrast, Aristotelian logic naturally fosters a "natural law ethic," an ethic of universal principles, based on the nature of things, especially the nature of man. For its basic unit is the term, a subject (S) or a predicate (P) within a proposition (p); and its basic judgment is "all S is P" - a statement of universal truth about the nature of S and P. The very nature of reason itself is understood differently by the new sym- bolic logic than it was by the traditional Aristotelian logic. "Reason" used to mean essentially "all that distinguishes man from the beasts," including intu- ition, understanding, wisdom, moral conscience, and aesthetic appreciation, as well as calculation. "Reason" now usually means only the last of those powers. That is why many thinkers today who seem at first quite sane in other ways actu- ally believe that there is no fundamental difference between "natural intelli- gence" and "artificial intelligence" - in other words, you are nothing but a com- puter plus an ape. (Having met some of these people at MIT, I must admit that their self-description sometimes seems quite accurate.) Aristotelian logic is not exact enough for the nominalistic mathematical logi- cian, and it is too exact for the pop psychology subjectivist or New Age mystic. Out at sea there between Scylla and Charybdis, it reveals by contrast the double tragedy of modern thought in its alienation between form and matter, structure The two logics 23 and content, validity and meaning. This alienated mind was described memo- rably by C.S. Lewis: "the two hemispheres of my brain stood in sharpest con- trast. On the one hand, a glib and shallow rationalism. On the other, a many- islanded sea of myth and poetry. Nearly all that I loved, I believed subjective. Nearly all that was real, I thought grim and meaningless" (Surprised by Joy). Neither mathematical logic nor "experience" can heal this gap; but Aristotelian logic can. It is thought's soul and body together, yet not confused. Mathematical logic alone is abstract and "angelistic," and sense experience and feeling alone is concrete and "animalistic," but Aristotelian logic is a human instrument for human beings. Aristotelian logic is also easier, simpler, and therefore time-saving. For example, in a logic text book misleadingly entitled Practical Reasoning in Natural Language, the author takes six full pages of symbolic logic to analyze a simple syllogism from Plato's Republic that proves that justice is not rightly defined as "telling the truth and paying back what is owed" because returning a weapon to a madman is not justice but it is telling the truth and paying back what is owed. (pp. 224-30). Another single syllogism of Hume's takes eight pages to analyze (pp. 278-86). I have found that students who are well trained in Aristotelian logic are much better at arguing, and at understanding arguments, than students who are trained only in symbolic logic. For Aristotelian logic is the logic of the four most basic verbal communication arts: reading, writing, listening, and speaking. It is the logic of Socrates. If you want to be a Socrates, this is the logic you should begin with. The old logic is like the old classic movies: strong on substance rather than sophistication. The new logic is like typically modern movies: strong on "spe- cial effects" but weak on substance (theme, character, plot); strong on the tech- nological "bells and whistles" but weak on the human side. But logic should be a human instrument; logic was made for man, not man for logic. The Problem of "Material Implication" The following issue is quite abstract and difficult, though I shall try to make it as simple as possible. It is included because I believe it shows that "something is rotten in the state of Denmark" at the very heart of the new logic. (For a fuller treatment of the new logic see the Appendix, p. 364.) Logic is most especially about reasoning, or inference: the process of think- ing by which we draw conclusions from evidence, moving from one proposition to another. The proposition we begin with is called a "premise" and the propo- sition we move to, or infer, or reason to, is called a "conclusion." The simplest and most straightforward kind of reasoning is to move from a true premise (or, more usually, from a number of true premises together) to a 24 INTRODUCTION true conclusion. But we can also use false propositions in good reasoning. Since a false conclusion cannot be logically proved from true premises, we can know that if the conclusion is false then one of the premises must also be false, in a logically valid argument. A logically valid argument is one in which the conclusion necessarily fol- lows from its premises. In a logically valid argument, if the premises are true, then the conclusion must be true. In an invalid argument this is not so. "All men are mortal, and Socrates is a man, therefore Socrates is mortal" is a valid argu- ment. "Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog" is not a valid argument. The conclusion ("Lassie is a dog") may be true, but it has not been proved by this argument. It does not "follow" from the premises. Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument according to Aristotelian logic. Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees. However, modern symbolic logic dis- agrees. One of its principles is that "if a statement is true, then that statement is implied by any statement whatever." Since it is true that Lassie is a dog, "dogs have four legs" implies that Lassie is a dog. In fact, "dogs do not have four legs" also implies that Lassie is a dog! Even false statements, even statements that are self-contradictory, like "Grass is not grass," validly imply any true conclusion in symbolic logic. And a second strange principle is that "if a statement is false, then it implies any statement whatever." "Dogs do not have four legs" implies that Lassie is a dog, and also that Lassie is not a dog, and that 2 plus 2 are 4, and that 2 plus 2 are not 4. This principle is often called "the paradox of material implication." Ironically, "material implication" means exactly the opposite of what it seems to mean. It means that the matter, or content, of a statement is totally irrelevant to its logically implying or being implied by other statements. Common sense says that Lassie being a dog or not being a dog has nothing to do with 2+2 being 4 or not being 4, but that Lassie being a collie and collies being dogs does have something to do with Lassie being a dog. But not in the new logic, which departs from common sense here by totally sundering the rules for logical implication from the matter, or content, of the propositions involved. Thus, the paradox ought to be called "the paradox of wort-material implication." The paradox can be seen in the following imaginary conversation: Logician: So, class, you see, if you begin with a false premise, anything fol- lows. Student: I just can't understand that. Logician: Are you sure you don't understand that? Student: If I understand that, I'm a monkey's uncle. Logician: My point exactly. (Snickers.) Student: Whats so funny? The two logics 25 Logician: You just can't understand that. The relationship between a premise and a conclusion is called "implica- tion," and the process of reasoning from the premise to the conclusion is called "inference" In symbolic logic, the relation of implication is called "a tnith-func- tional connective," which means that the only factor that makes the inference valid or invalid, the only thing that makes it true or false to say that the premise or premises validly imply the conclusion, is not at all dependent on the content or matter of any of those propositions, but only whether the premise or premis- es are true or false and whether the conclusion is true or false. That last paragraph was cruelly abstract. Let's try to be a little more specif- ic. In symbolic logic, (1) If the premise or premises (let's just say "the premise" for short) are true and the conclusion is true, then the " i f... then" proposition summariz- ing the implication is true. If p is true and q is true, then "if p then q" is true. So "if grass is green, then Mars is red" is true. (2) If the premise is true and the conclusion is false, then the " i f... then" proposition summarizing the implication is false. If p is true and q is false, then "if p then q" is false. So "if grass is green, then Mars is not red" is false. (3) If the premise is false and the conclusion is true, then the " i f... then" proposition summarizing the implication is true. If p is false and q is true, then "if p then q" is true. So "if grass is purple, then Mars is red" is true. (4) If the premise is false and the conclusion is false, then the " i f... then" proposition summarizing the implication is true. If p is false and q is false, then "if p then q" is true. So "if grass is purple, then Mars is pur- ple" is also true! In this logic, if the premise and the conclusion are both false, the premise implies the conclusion (this is #4), and if the premise is false and the conclusion is true, the premise also implies the conclusion (this is #3). So if the moon is blue, then the moon is red (#4); and if the moon is blue, then the moon is not blue (#3)! This may make some defensible sense mathematically, but it certain- ly does not make sense commonsensically, for it does not seem to make sense in the real world. Logicians have an answer to the above charge, and the answer is perfectly tight and logically consistent. That is part of the problem! Consistency is not enough. Logic should be not just a mathematically consistent system but a human instrument for understanding reality, for dealing with real people and things and real arguments about the real world. That is the basic assumption of the old logic. If that assumption is naive and uncritical, unfashionable and unin- telligent - well, welcome to Logic for Dummies. 26 INTRODUCTION Section 4. All of logic in two pages: an overview (B) This is one of the shortest and simplest sections in this book, but it is also one of the most important, for it is the foundation for everything else in logic. If you do not understand it clearly, you will be hopelessly confused later on. (It is explained in more detail in the next section, Section 5.) The ancient philosophers defined Man as the "rational animal." To be human is (among other things) to reason, to give reasons for believing things to be true. We can see common forms, or structures, in all human reasoning, no mat- ter what the contents, or objects, that we reason about. Logic studies those structures. The fundamental structure of all reasoning is the movement of the mind from premises to a conclusion. The conclusion is what you are trying to prove to be true; the premises are the reasons or evidence for the truth of the conclu- sion. The two basic kinds of reasoning are inductive and deductive. Inductive reasoning reasons from particular premises (e.g. "I'm mortal" and "You're mortal" and "He's mortal" and "She's mortal"), usually to a more general or universal conclusion (e.g. "All men are mortal"). Deductive reasoning reasons from at least one general, or universal premise (e.g. "All men are mortal") usu- ally to a more particular conclusion (e.g. "I am mortal"). Inductive reasoning yields only probability, not certainty. (It is not certain that all men are mortal merely on the basis that four men, or 4 million, are.) Deductive reasoning, when correct, yields certainty. (It is certain that if all men are mortal, and if I am a man, then I am mortal.) A deductive argument succeeds in proving its conclusion to be true if and only if three conditions are met. These are the three check points of any deductive argument. (1) First, all the terms must be clear and unambiguous. If a term is ambiguous, it should be defined, to make it clear. Otherwise, the two parties to the argument may think they are talking about the same thing when they are not. (2) Second, all the premises must be true. You can (seem to) "prove" any- thing from false premises: e.g. "All Martians are infallible, and I am a Martian, therefore I am infallible." (3) Third, the argument must be logically valid. That is, the conclusion must necessarily follow from the premises, so that if the premises are true, then the conclusion must be true. All of logic in two pages: an overview 27 (1) A "term" in logic is the subject or the predicate of a proposition (a declarative sentence). Terms are either clear or unclear. Terms cannot be either true or false. E.g. "mortal" is neither true nor false. The proposition "All men are mortal" is true, and the proposition "Some men are not mortal" is false. (2) Propositions are declarative sentences. They are either true or false. "True," in commonsense usage, means "corresponding to reality," and "false" means the opposite. There is no one simple and infallible way of telling whether any proposition is true or false. (3) There is, however, a fairly simple and truly infallible way of telling whether an argument is valid or invalid: the laws of logic, which you will learn in this book. A deductive argument is logically valid if its conclusion necessarily fol- lows from its premises, invalid if it does not. There are various forms of argu- ment, and each form has its own inherent rules for validity. All the rules for each form of argument are natural to that form of argu- ment and to the human mind. If at any point in this book you think that any of its logical laws contradict what you already implicitly know by innate common sense, please stop and check; for you must be misunderstanding either the laws of logic or what you think common sense tells you, for logic does nothing more than make explicit the rules everyone knows innately by common sense. Arguments are made up of propositions (premises and a conclusion), and propositions are made up of terms (subject and predicate). Terms are either clear or unclear. Propositions (whether premises or the conclusion) are either true or false. Arguments are either logically valid or invalid. Only terms can be clear or unclear; only propositions can be true or false; only arguments can be logically valid or invalid. So the three questions you should habitually ask of yourself when writ- ing or speaking, and of others when you are reading or listening to them, are: (1) Are the terms all clear and unambiguous? (2) Are the premises all true? (3) Is the reasoning all logically valid? If the answer to all three of these questions is Yes, then the conclusion of the argument must be true. So in order to disagree with any conclusion, you must show that there is either (1) an ambiguous term, or (2) a false premise, or (3) a logical fal- lacy in the argument such that the conclusion does not necessarily follow from the premises. (You will soon learn the rules forjudging that.) If you cannot do any of these three things, then honesty demands that you admit that the con- clusion has been proved to be true. (All this applies to deductive arguments only; inductive arguments do not claim certainty.) 28 INTRODUC1TON Section 5. The three acts of the mind (B) This section gives you the outline for all of logic. It is an expansion of the pre- vious section (Section 4) and a summary of the rest of the book. The basis for the science and art of logic is two facts: the fact that human beings think, and the fact that thought has a structure. That structure can be clas- sified from various points of view and for various purposes. For instance, a physiologist or physician might distinguish brain activity of the autonomic nerv- ous system (e.g. breathing) from activity of the frontal lobes (self-conscious thought). A moralist might distinguish thoughts that are voluntary, and under our control, from those that are involuntary, since we are responsible only for what is under our control. A Marxist would distinguish thoughts supposedly produced by a Capitalist system from those produced by a Communist system. But from the viewpoint of logic, we distinguish three kinds of thoughts, three "acts of the mind": 1. Simple apprehension 2. Judging 3. Reasoning "Simple apprehension" is a technical term. It means basically "conceiving," "understanding," or "comprehending" one object of thought, one concept, such as 'mortal* or 'man' or 'triangle' or 'triangle with unequal angles.' Animals apparently cannot perform this act of understanding; if they can, they do not express it in words. Computers certainly cannot do this; a computer no more understands what you program into it than a library building understands the information in the books you put into it. Judging is more complex than simple apprehension. Instead of just thinking one concept, like 'man,' it relates two concepts, like "man" and "mortal," to each other by predicating one term (the predicate) of the other (the subject) in judg- ing that, e.g. "Man is mortal" or "Man is not a triangle." As judging is more complex than simple apprehension, reasoning is more complex than judging. As judging moves from one act of simple apprehension (the subject) to another (the predicate), reasoning moves from two or more judg- ments (the premises, or assumptions) to another (the conclusion) in arguing that if the premises are true, then the conclusion must be true. E.g. "All men are mor- tal, and I am a man, therefore I am mortal," or "A man is not a triangle, and that is a triangle, therefore that is not a man." The mental products produced in the mind by the three acts of the mind are: 1. Concepts (the products of conceiving) 2. Judgments (the products of judging) 3. Arguments (the products of reasoning, or arguing) Distinguishing between the acts and their objects is not crucial for logic. What is crucial is distinguishing the three acts, and the three objects. The three acts of the mind 29 These three mental entities (concepts, judgments, and arguments) are expressed in logic as: 1. Terms 2. Propositions 3. Arguments (the most usual form of which is the syllogism) They are expressed in language as: 1. Words or phrases (less than a complete sentence) 2. Declarative sentences 3. Paragraphs, or at least two or more declarative sentences connected by a word like 'therefore' which indicates an argument Examples: 1. "Man" 2. "Socrates is a man." 3. "All men are mortal, and Socrates is a man, therefore Socrates is mortal." (Logic does not deal with interrogative sentences (questions, like "What time is it?"), imperative sentences (commands or requests, like "Pass the mus- tard, please"), exclamatory sentences (like "Oh! Wow! What a hit!"), or perfor- mative sentences (like "I dub thee knight"), but only with declarative sentences, sentences that claim to state a truth.) Non-declarative sentences are not proposi- tions. The difference between logic and language is (1) that languages are man- made

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