Logic and Philosophy: An Integrated Introduction

LOGIC AND PHILOSOPHY

An Integrated Introduction

Logic and Philosophy

AN INTEGRATED INTRODUCTION

WILLIAM H. BRENNER

UNIVERSITY OF NOTRE DAME PRESS

NOTRE DAME

University of Notre Dame Press

Notre Dame, Indiana 46556

www.undpress.nd.edu

All Rights Reserved

Published in the United States of America

Copyright © 1993 by University of Notre Dame

Reprinted in 2009

Library of Congress Cataloging-in-Publication Data

Brenner, William H., 1941–

Logic and philosophy : an integrated introduction / William H. Brenner.

p. cm.

Includes bibliographical references and index.

ISBN 13: 978-0-268-01299-1 (pbk. alk. paper)

ISBN 10: 0-268-01299-7 (pbk. alk. paper)

1. Logic. 2. Philosophy I. Title.

BC51.B664   1993

160—dc20

94–15464

CIP

ISBN 9780268158989

∞ This book is printed on acid-free paper.

This e-Book was converted from the original source file by a third-party vendor. Readers who notice any formatting, textual, or readability issues are encouraged to contact the publisher at [email protected].

TO MARY DEEGAN

Contents

Preface

In the Western philosophical tradition, logical investigation and general philosophical advance have gone hand in hand, each stimulating and shaping the other. The present volume contributes to an understanding of this tradition by presenting a broad range of logical concepts and methods in relation to the larger context of philosophical investigation. The philosophical depth of logic, and its relevance to philosophy generally, are thereby brought to light.

Learning philosophy, or deepening one’s understanding of it, involves developing certain skills and sensitivities. The exercises at the end of each section are designed to help make such learning possible. (When it appears after the number of an exercise, # indicates a relatively demanding question or project; * after the number means that there is an answer to the exercise at the back of the book.)

Learning philosophy also requires becoming familiar with the work of master philosophers. A few such philosophers are discussed in this book at some length. Readers unfamiliar with these philosophers will be stimulated, I hope, to read some of their works. And I hope that readers already well-versed in philosophy will find in this volume an illuminating perspective on familiar material. (I have consigned some important but less-central material to footnotes. These footnotes are best read the second time around.)

Chapter III, Modern Logic, contains most of the more technical material. Although what it covers has philosophical depth as well as (modest) technical sophistication, it may be omitted with little loss of continuity. Omitting that chapter (and supplementing what remains with readings from the classics) would tilt one’s study toward a standard introduction to philosophy; keeping it (while adding the first two appendices and subtracting sections from the last chapters) would tilt one’s study toward a standard introduction to logic. Either approach would provide an integrated introduction to logic and philosophy. Of course, the best approach, time permitting, would be to omit nothing.

It may go without saying but I will say it anyway: once past the elements of deductive and inductive reasoning, the material in this book gets less standard and more controversial.

* * *

I have profited greatly from the suggestions and corrections of many readers—Mary Deegan, Dan Devereux, Val Derlega, Cora Diamond, Rod Evans, Lynne Garris, Lewis Ford, Larry Hatab, David James, Harry K. Jones, William B. Jones, Michael J. Loux, David Loomis, John Marshall, Jr., Mary E. Marshall, Warren Matthews, Leemon McHenry, Vincent Vacarro, Steven J. Wagner, Shigeru Yonezawa, and many Old Dominion University students from several courses. Of course, none of these patient and generous readers are responsible for the deficiencies that remain.

Portions of Chapters I–V appear in my contribution to Reflections on Philosophy, a collection of essays edited by Leemon McHenry and Fred Adams (St. Martin’s Press, 1992). The editors and the publisher’s readers were most helpful.

My biggest debt is to Ludwig Wittgenstein. Most sections owe something to the influence of his logico-philosophical writings, as I understand them.

I. Introduction

Socrates (c. 469–399 B.C.)

A.  THALES TO ARISTOTLE

Western philosophy began in ancient Greece. In the sixth century B.C. Thales of Miletus claimed that everything is made of one material, namely hydor—water. His fellow Milesian Anaximander criticized this view, reasoning that nothing made of fire could be made of water, since all things made of water are essentially wet and cool, while nothing made of fire is essentially wet and cool. Anaximander proceeded to propose his own theory. Suffice it to say here that Thales and Anaximander between them initiated a tradition of systematic reasoning about the fundamental principles of nature, a tradition that, in the fifth century B.C., gave us the famous atomism of Democritus:

By convention there is sweet, by convention there is bitter, by convention hot and cold, by convention color; but in reality there are only atoms and the void.¹

Also in the fifth century B.C. an Athenian Greek by the name of Socrates argued that there is a radical difference between the physical causes put forward by the natural philosophers from Thales to Democritus and the moral ideals that can move human beings to action. And he initiated a tradition of systematic reasoning about such moral principles. Plato, in the fourth century, wrote the dialogues that were to make Socrates famous. He also founded the first university, the Academy.

Aristotle studied at the Academy for twenty years. Along with (and sometimes in opposition to) his master Plato, he continued the inquiries pioneered by both Socrates and the natural philosophers. And he invented a new discipline—the systematic investigation of the principles of reasoning known as logic.

Looking back at the inquiries of his predecessors from Thales to Plato, Aristotle saw that they not only stated opinions about various subjects but also reasoned about them; he saw further that their reasoning could be analyzed into units—units of reasoning that he termed arguments. An argument is composed of at least two statements, one of which (the conclusion) is claimed to follow from the other statement or statements (the premise or premises). Thus, from the premises

No things made of water are essentially hot and dry and

All things made of fire are essentially hot and dry,

Anaximander had drawn the conclusion

Nothing made of fire is made of water.

And from the premises,

No physical ‘causes’ are reasons, and

All moral ideals are reasons,

Socrates had concluded

No moral ideals are physical ‘causes’.

The preceding arguments are deductive: in a deductive argument the conclusion is claimed to follow necessarily from its premises. The preceding arguments are also valid: in a valid deductive argument the conclusion does follow necessarily from its premises, as claimed. (Non-deductive arguments will be ignored until Chapter IV.)

Characteristically, the validity of deductive arguments is determined by logical form. Aristotle was the first to perceive and develop this point. For example, he saw that although the preceding two arguments differ radically in subject matter, they have the same logical form, namely:

No P are M.

All S are M.

∴ No S are P.

(∴ stands for therefore, thus, or consequently. M, P, and S are blanks that can be filled in with any terms [things made of water, gods, and the like].)

The preceding logical form can be represented in a diagram such as the following:

Explanation: Since nothing in M is in P, and everything in S is in M, nothing in S is in P.

Both of the preceding arguments (Anaximander’s and Socrates’) are valid because they embody this form. Any argument of the same form will be valid, no matter what terms are substituted for P, M, and S. Therefore, the following argument is valid:

No cats are meat-eaters.

All tigers are meat-eaters.

∴ No tigers are cats.

This is just as valid as the preceding cases. Of course, we do not accept both of its premises! But if we did, then (to be consistent) we would have to accept the conclusion as well. If we start with true premises, then we are bound to get a true conclusion. Valid deduction preserves truth. In other words: valid deductive reasoning rules out even the possibility of all true premises and a false conclusion.

Although the preceding argument about tigers is valid, it is not, for all that, a good argument. A good argument has to be sound. A sound argument has true premises (only true premises), as well as validity (that is, logical connection between premises and conclusion). Thus, in evaluating reasoning, we need to remember that there are two different questions to ask, one about whether the premises are true, the other about whether the conclusion follows from the premises. If the answer to both questions is yes, the argument is sound.

The distinctions sound / unsound and valid / invalid are to be applied only to arguments—not to premises, conclusions, or other statements. And the true / false distinction is to be applied only to statements, not to arguments.

EXERCISES I-A

# indicates a relatively demanding question

* means See ‘Answers to Selected Exercises’

[* answers in Appendix 4, page 179]

1.* Correct or Incorrect?—(a) Some arguments are true; (b) Some statements are valid; (c) Some statements are sound; (d) Every argument has exactly one conclusion; (e) Every argument has at least one premise; (f) Premises and conclusions are statements; (g) Statements are true or false; (h) Arguments are valid or invalid, sound or unsound.

2. For each of the following determine: Is it an argument? If so, indicate the conclusion and premise(s). If not, explain why not.

(a)* Since all Christmases are legal holidays, and no legal holidays are banking days, no Christmases are banking days.

(b) Since the First World War, America has been deeply involved in European affairs.

(c)* Today is Monday, so tomorrow is Tuesday.

(d)* If today is Monday, tomorrow is Tuesday.

(e) The streets are wet; therefore, it must have rained.

(f) When the tank is filled, we’ll be ready for our trip.

(g) If by whiskey you mean the devil’s brew, that evil concoction that lures men away from their families, ruins their health, and undermines the very structure of society, then I’m against it. On the other hand, if by whiskey you mean that warm liquid that puts some life into a gentleman on a cold winter’s day, that oil of social intercourse and good fellowship, that drink that puts much-needed tax dollars into the state treasury, then I am for it. That, sir, is my stand on whiskey.

(h) From St. Augustine (fifth century), On the Teacher:

To be opinionated is most shameful for two reasons: Not only can a person not learn what he is convinced he already knows, but also the very rashness itself is a mark of a mind that is not properly disposed.

(i) From St. Augustine, Soliloquies:

I have decided that there is nothing I must more carefully avoid than the marriage-bed. I find that there is nothing which more certainly casts a man’s mind out of its citadel than female blandishments and bodily contacts, which are essential to marriage. The danger of attempting it is greater than the happiness of achieving it.

(j)* From St. Augustine’s Confessions: Lord, make me chaste and continent, but not yet.

3.* Correct or Incorrect?—(a) Every argument with true premises and a true conclusion is valid; (b) Every argument with true premises and a true conclusion is sound; (c) All valid arguments are sound; (d) All sound arguments are valid; (e) A valid argument has to have a true conclusion; (f) A valid argument has to have true premises.

4. Which of the following deductive arguments are sound, which unsound? In each case, explain why.

(a)* All animals are mammals; all dolphins are animals; therefore, all dolphins are mammals.

(b)* All mammals are animals; all dolphins are animals; therefore, all dolphins are mammals.

(c) No protein-rich meals are meatless; thus, no meatless meals are protein-rich.

(d) No flames are moist and cool; thus, nothing moist and cool is a flame.

5.* Explain the difference in logical form between (a) and (b) in the preceding exercise.

6. How is a valid argument like a good food freezer?²

7.# Make some notes on Greek atomism. Begin by looking up the etymology of atom in a dictionary, then consult a history of philosophy or an encyclopedia on Democritus or atomism. Based on your reading, what arguments were given by ancient atomists in support of their position and in opposition to earlier views? Can you state an argument against their theory?

B.  LOGIC AND PHILOSOPHY

Logic focuses on the validity component of soundness. The principles governing the validity of categorical syllogisms—the sort of arguments used as examples in the preceding section—are dealt with in the next chapter. Chapter III is about the principles governing the validity of truth-functional inferences, a class of arguments investigated by the Stoic philosophers of late Greek antiquity and by European logicians early in the twentieth century. In the present section we shall be looking at four sample truth-functional arguments, using them to reinforce what we learned in the previous section about the very important distinction between valid and invalid deductive reasoning.

The following two arguments are valid:

If that’s a metal, it conducts electricity.

That’s a metal.

Therefore, it conducts electricity.

If that’s a metal, it conducts electricity.

It does not conduct electricity.

Therefore, it’s not a metal.

The first is an instance of the modus ponens ("mode of affirming") pattern, namely:

The second is an instance of the modus tollens ("mode of denying") pattern, namely:

Whatever statements we substitute for the p’s and q’s of these argument patterns or formulas, the resulting arguments will be valid. (Think of a p or q as a blank that can be filled in with any statement or assertion.)*

Modus ponens and modus tollens are among the commonest forms of reasoning. Two corresponding invalid forms are nearly as common. The first is fallacy of denying the antecedent:

The second is fallacy of affirming the consequent:

(Antecedent and consequent refer to the if and then component of an if / then statement, respectively.)

The two preceding forms are invalid because they fail to guarantee that true conclusions will result from true premises. You can demonstrate their invalidity by producing clear examples of them in which false statements are concluded from true premises. Thus, the following example demonstrates the invalidity of affirming the consequent:

If she’s a senator, she’s a citizen.

She’s a citizen.

Therefore, she’s a senator.

(Madonna is a citizen but not a senator.)

And the following shows the invalidity of denying the antecedent:

If it’s purple, it’s a mixed color.

It’s not purple.

Thus, it’s not a mixed color.

(Orange is not purple but is a mixed color.)

Compare that instance of denying the antecedent with the following:

If Ted Kennedy is President, then he lives in the White House.

Ted Kennedy is not President.

Consequently, he doesn’t live in the White House.

The first instance of denying the antecedent had true premises and a false conclusion; this one has true premises and a true conclusion. An invalid form of reasoning may indeed happen to have true premises and a true conclusion; what makes it invalid is that it is also possible for it to have true premises but a false conclusion. You demonstrate invalidity by producing a clear illustration of that possibility.

* * *

Formal techniques for determining the validity or invalidity of a wide range of deductive arguments are presented in the next two chapters. Chapter IV takes up two informal varieties of reasoning: induction and non-deductive reasoning by analogy. Chapter V explains a system of classifying and detecting logical errors (fallacies).

The chief overall purpose of Chapters I–V is to promote a working knowledge of a variety of widely applicable ways of analyzing and assessing arguments. Chapters VI–VIII highlight some other related areas of philosophical concern.

Philosophy is reasoning about fundamental concepts and principles. Logic is the branch of philosophy in which Reason reasons about itself. In reasoning about itself, Reason reflects on the concept of valid argument. It also reflects on related topics such as statement, truth and falsity, sense and nonsense. Chapters VI and following deal with those topics, and (more extensively) with topics usually associated with the three other main branches of philosophy: ethics, epistemology, and metaphysics. Value is the key concept of ethics; knowledge, of epistemology; and reality, of metaphysics.* While material relating to topics in ethics, epistemology, and (most of all) metaphysics can be found throughout this book, the bulk of it is in Chapters VI–VIII.

Philosophy began with the water metaphysics of Thales. About a century later, Democritus formulated a still-influential form of materialism according to which reality is fundamentally atoms moving around in empty space. Considerable portions of the book from Chapter VI on deal with ideas and arguments from several important critics of materialistic metaphysics, starting with Plato.

EXERCISES I-B

[* answers in Appendix 4, page 180]

1. Can there be an invalid argument with true premises and a true conclusion? Can there be a valid argument with false premises and a false conclusion? If so, give an example; if not, say why not.

2.* (a) Is every deductive argument with true premises and a false conclusion invalid? (b) Is every invalid deductive argument an argument with true premises and a false conclusion? Be sure to explain your answers.

3. Give an original example of each of the following: modus ponens, fallacy of affirming the consequent, modus tollens, fallacy of denying the antecedent.

4. State an example that clearly demonstrates the invalidity of affirming the consequent.

5. For each of the following, state an example that clearly demonstrates its invalidity.

(a)* All religious people are believers in a higher power; therefore, all believers in a higher power are religious people. (Hint: Formulate an obviously invalid parallel argument—namely, an argument of the form All so-and-so are such-and-such; therefore, all such-and-such are so-and-so with an obviously true premise and an obviously false conclusion.)

(b) We never get both steak and lobster. We’re not getting steak. So we must be getting lobster.

(c) Some dogs are not fierce animals. Thus, some fierce animals are not dogs.

6. Using material from this chapter and from the glossary at the back of the book, define philosophy, ethics, epistemology, metaphysics, and logic.

7.# Collect some cartoon strips that strike you as philosophical. For each, explain why you call it philosophical.

*Modus ponens and modus tollens are related to the concepts of sufficient condition and necessary condition, respectively:

If the mouse in the jar is alive (A), then there is oxygen in the jar (O) says that A is sufficient for O. Thus the validity of modus ponens:

If A,O (given what is sufficient for O, you get O)

If the mouse is alive, then there is oxygen is equivalent to "O is necessary for A." Thus the validity of modus tollens:

If A, O (remove what is necessary for A and you remove A)

*The line between logic and the other fields of philosophy is not a sharp one. In discussing philosophical questions that relate to these concepts, we will also in the process be extending our knowledge of logic. For logic, broadly understood, is about special as well as about general principles of valid reasoning: it is about principles of inference (and fallacies) that relate uniquely to special topics (value, knowledge, reality, and so on), as well as to principles of inference such as modus ponens that apply to any topic whatsoever.

II. Traditional Logic

Aristotle (384–322 B.C.)

A.  TERMS, STATEMENTS, SYLLOGISMS

Traditional logic refers to the teachings of Aristotle’s collected logical treatises, The Organon,* along with some later additions, mainly from the Middle Ages. We shall focus in this chapter on the less technical parts of traditional logic. (The first two appendices contain some slightly more technical material.)

It is helpful to relate traditional logic to the development of an argumentative essay. First you choose a subject, then you think of something to say about your subject. Something said about a subject is, in the jargon of logicians, a predicate. Let the subject be abortions and the predicate be morally permissible acts. Do we want to affirm that abortions are morally permissible, or to deny it? And do we want to make our claim about every abortion, or about some (at least one) abortion? Aristotle set out four ways of answering such questions, namely the following standard forms of categorical statements:

All abortions are morally permissible is universal affirmative; Some abortions are morally permissible, particular affirmative; No abortions are morally permissible, universal negative; and Some abortions are not morally permissible, particular negative. (Note that there are other, non-standard ways of making the same statements. For example:

Note also that some always means at least one in