AnIntroduction toLogicand Its Philosophy

? .. an Introduction ~- to Logic and

, Its Philosophy

Raymond Bradley / Norman Swartz

AN INTRODUCTION TO LOGIC AND ITS PHILOSOPHY

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RAYMOND BRADLEY NORMAN SWARTZ

Department of Philosophy Simon Fraser University

HACKETT PUBLISHING COMPANY

Published inn thhee United States of America by HACKETT PUBLISHING COMPANY, IINNC.

Copyriigghhtt?? 1979 byy Raymond Bradley anndd Norman Swartz

All rights rreesserved

Published inn Great Britain by Basil Blackwell PPublisher

Printed inn thhee United States of America Fouurrtthh printing 119988

Library of Congress Catalog Card Numberr 7799--551037 ISBN 00--991155114444--6600-3

0- 91 55114444--5599--xx ((ppbbk)

Cover design byy Richard L.. LLiisstenberger Art forr cover byy James Felter, Centre for thhee Arts,

Simon Fraserr UUniversity

Interiorr design byy James NN.. Rogers

For further information, please address HHaacckkeetttt PPuubblliisshhiinngg CCoommppaannyy,, IInncc.. P.O. BBooxx 44937 Indianapolis, Indiana 46204

To the members of our families, of whose company we were too oftteenn deprived during the years spenntt writingg this book

Contents

P R E F A C E xv

T O T H E T E A C H E R xvii

T O T H E S T U D E N T xxi

POSSIBLE WORLDS 1

1. T H I S A N D O T H E R POSSIBLE W O R L D S 1 The realm of possibilities 1 What are the limits to the possible? 2 Possibility is not the same as conceivability 3 Possible worlds: actual and non-actual 4 Logical possibility distinguished from other kinds 6 The constituents of possible worlds 7

2. PROPOSITIONS, T R U T H , A N D F A L S I T Y 9 Truth and falsity defined 9 Truth in a possible world 11 Truth in the actual world 12 The myth of degrees of truth 12

3. P R O P E R T I E S O F P R O P O S I T I O N S 13 Possibly true propositions 13 Possibly false propositions 13 Contingent propositions 14 Contradictories of propositions 14 Noncontingent propositions 15 Necessarily true propositions 16 Necessarily false propositions 17 More about contradictory propositions 18 Some main kinds of noncontingent propositions 19 Summary 24 Symbolization 25

4. R E L A T I O N S B E T W E E N P R O P O S I T I O N S 28 Inconsistency 28 Consistency 30 Implication 31 Equivalence 35 Symbolization 41

vii

CONTENTS

5. S E T S O F P R O P O S I T I O N S 42 Truth-values of proposition-sets 42 Modal properties of proposition-sets 42 Modal relations between proposition-sets 44 Minding our "P's and "Q"s 47

6. M O D A L P R O P E R T I E S A N D R E L A T I O N S P I C T U R E D O N W O R L D S - D I A G R A M S 48 Worlds-diagrams for modal properties 49 Worlds-diagrams for modal relations 50 Interpretation of worlds-diagrams 50 A note on history and nomenclature 53 Capsule descriptions of modal relations 54 Appendix to section 6 57

7. IS A S I N G L E T H E O R Y O F T R U T H A D E Q U A T E F O R B O T H C O N T I N G E N T A N D N O N C O N T I N G E N T PROPOSITIONS? 58

8. T H E " P O S S I B L E W O R L D S " I D I O M 62

PROPOSITIONS 65

1. I N T R O D U C T I O N 65

2. T H E B E A R E R S O F T R U T H - V A L U E S 65 Thesis 1: Such things as beliefs, statements, assertions, remarks, hypotheses, and theories are the bearers of truth and falsity. 68 Thesis 2: Acts of believing (stating, asserting, etc.) are the bearers of truth-values. 68 Thesis 3: That which is believed, stated, etc., is what is true or false. 71 Thesis 4: Sentences are the bearers of truth-values. 71 Thesis 5: Sentence-tokens are the bearers of truth-values. 73 Thesis 6: Sentence-types are the bearers of truth-values. 74 Thesis 7: Context-free sentences are the bearers of truth-values. 75 Thesis 8: Context-free sentence-tokens are those things to which truth and falsity may be attributed. 76 Thesis 9: Context-free sentence-types are those things to which truth and falsity may be attributed. 76 Thesis 10: Propositions are those things to which truth and falsity may be attributed. 79 Thesis 11: Propositions are to be identified with the meanings of sentences. 80 Thesis 12: Propositions are to be identified with sets of possible worlds. 82

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