Forall x: Calgary. An Introduction to Formal Logic

forallx CALGARY An Introduction to Formal Logic

P. D. Magnus Tim Button

with additions by J. Robert Loftis Robert Trueman remixed and revised by Aaron Thomas-Bolduc

Richard Zach Fall 2021+

forall x: Calgary

An Introduction to Formal Logic

By P. D. Magnus Tim Button

with additions by J. Robert Loftis Robert Trueman remixed and revised by Aaron Thomas-Bolduc

Richard Zach

Fall 2021+

This book is based on forallx: Cambridge, by Tim Button (University College London), used under a CC BY 4.0 license, which is based in turn on forallx, by P.D. Magnus (University at Albany, State University of New York), used under a CC BY 4.0 license, and was remixed, revised, & expanded by Aaron Thomas-Bolduc & Richard Zach (University of Calgary). It includes additional material from forallx by P. D. Magnus and Metatheory by Tim Button, used under a CC BY 4.0 license, from forallx: Lorain County Remix, by Cathal Woods and J. Robert Loftis, and from A Modal Logic Primer by Robert Trueman, used with permission.

This work is licensed under a Creative Commons Attribution 4.0 license. You are free to copy and redistribute the material in any medium or format, and remix, transform, and build upon the material for any purpose, even commercially, under the following terms:

You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

The LATEX source for this book is available on GitHub and PDFs at forallx.. This version is revision 9cc9765 (2022-08-11).

The preparation of this textbook was made possible by a grant from the Taylor Institute for Teaching and Learning.

Cover design by Mark Lyall.

Contents

Preface

vi

I Key notions of logic

1

1 Arguments

2

2 The scope of logic

7

3 Other logical notions

18

II Truth-functional logic

26

4 First steps to symbolization

27

5 Connectives

32

6 Sentences of TFL

49

7 Ambiguity

56

8 Use and mention

62

III Truth tables

68

9 Characteristic truth tables

69

10 Truth-functional connectives

72

11 Complete truth tables

77

12 Semantic concepts

85

iii

CONTENTS

iv

13 Truth table shortcuts

96

14 Partial truth tables

101

IV Natural deduction for TFL

108

15 The very idea of natural deduction

109

16 Basic rules for TFL

112

17 Constructing proofs

141

18 Additional rules for TFL

161

19 Proof-theoretic concepts

169

20 Derived rules

173

21 Soundness and completeness

181

V First-order logic

190

22 Building blocks of FOL

191

23 Sentences with one quantifier

200

24 Multiple generality

214

25 Identity

229

26 Sentences of FOL

236

27 Definite descriptions

244

28 Ambiguity

254

VI Interpretations

258

29 Extensionality

259

30 Truth in FOL

267

31 Semantic concepts

278

32 Using interpretations

280

33 Reasoning about interpretations

288

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