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2nd Edition

# Logic: The Basics

By

,

## Shay Allen Logan

ISBN 9781138852273
Published March 5, 2017 by Routledge
288 Pages

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## Book Description

Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as:

· mathematical preliminaries

· propositional logic

· English and standard ‘symbolic translations’

· tableau procedures.

Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of how they can take their knowledge further. With its wealth of exercises (solutions available in the encyclopedic online supplement), Logic: The Basics is a useful textbook for courses ranging from the introductory level to the early graduate level, and also as a reference for students and researchers in philosophical logic.

I BACKGROUND IDEAS

1 Consequences

1.1 Relations of support

1.2 Logical consequence: the basic recipe

1.3 Valid arguments and truth

2 Models, Modeled, and Modeling

2.1 Models

2.2 Models in science

2.3 Logic as modeling

2.4 A note on notation, metalanguages, etc.

3 Language, Form, and Logical Theories

3.1 Language and formal languages

3.2 Languages: syntax and semantics

3.3 Atoms, connectives, and molecules

3.4 Connectives and form

3.5 Validity and form

3.6 Logical theories: rivalry

4 Set-theoretic Tools

4.1 Sets

4.2 Ordered sets: pairs and n-tuples

4.3 Relations

4.4 Functions

4.5 Sets as tools

II THE BASIC CLASSICAL THEORY

5 Basic Classical Syntax and Semantics

5.1 Cases: complete and consistent

5.2 Classical ‘truth conditions’

5.3 Basic classical consequence

5.4 Motivation: precision

5.5 Formal picture

5.6 Defined connectives

5.7 Some notable valid forms

6 Basic Classical Tableaux

6.1 What are tableaux?

6.2 Tableaux for the Basic Classical Theory

7 Basic Classical Translations

7.1 Atoms, Punctuation, and Connectives

7.2 Syntax, altogether

7.3 Semantics

7.4 Consequence

III FIRST-ORDER CLASSICAL THEORY

8 Atomic Innards: Unary

8.1 Atomic innards: names and predicates

8.2 Truth and falsity conditions for atomics

8.3 Cases, domains, and interpretation functions

8.4 Classicality

8.5 A formal picture

9 Everything and Something

9.1 Validity involving quantifiers

9.2 Quantifiers: an informal sketch

9.3 Truth and falsity conditions

9.4 A formal picture

10 First-Order Language with Any-Arity Innards

10.1 Truth and falsity conditions for atomics

10.2 Cases, domains, and interpretation functions

10.3 Classicality

10.4 A formal picture

11 Identity

11.1 Logical expressions, forms, sentential forms

11.2 Validity involving identity

11.3 Identity: informal sketch

11.4 Truth conditions: informal sketch

11.5 Formal picture

12 Tableaux for First-Order Logic with Identity

12.1 A Few Reminders

12.2 Tableaux for Polyadic First-Order Logic

13 First-Order Translations

13.1 Basic Classical Theory with Innards

13.2 First-Order Classical Theory

13.4 Examples in the polyadic language

IV NONCLASSICAL THEORIES

14 Alternative Logical Theories

14.1 Apparent unsettledness

14.2 Apparent overdeterminacy

14.3 Options

14.4 Cases

14.5 Truth and falsity conditions

14.6 Logical Consequence

15 Nonclassical Sentential Logics

15.1 Syntax

15.3 Defined connectives

15.4 Some notable forms

16 Nonclassical First-order Theories

16.1 An Informal Gloss

16.2 A formal picture

17 Nonclassical Tableaux

17.1 Closure Conditions

17.2 Tableaux for Nonclassical First-Order Logics

18 Nonclassical Translations

18.1 Syntax and Semantics

18.2 Consequence

V FREEDOM, NECESSITY AND BEYOND

19 Speaking Freely

19.1 Speaking of non-existent ‘things’

19.2 Existential import

19.3 Freeing our terms, expanding our domains

19.4 Truth conditions: an informal sketch

19.5 Formal picture

20 Possibilities

20.1 Possibility and necessity

20.2 Towards truth and falsity conditions

20.3 Cases and consequence

20.4 Formal picture

20.5 Remark on going beyond possibility

21 Free and Modal Tableaux

21.1 Free Tableaux

21.2 Modal Tableaux

22.1 Other conditionals

22.2 Other negations

22.3 Other alethic modalities: actuality

22.4 Same connectives, different truth conditions

22.5 Another road to difference: consequence

22.6 Summary and looking behind and ahead

References

...

## Author(s)

### Biography

Jc Beall is Board of Trustees Distinguished Professor of Philosophy at the University of Connecticut, Storrs, USA; and Professor of Philosophy at the University of Tasmania, Hobart, Australia.

Shay Allen Logan is a Postdoctoral Scholar in Logic at North Carolina State University, USA.

## Reviews

This work is an excellent and easily accessible resource material, especially for those interested to pursue further studies in advanced logic. It is a roadmap that tells you how to navigate your way in the forest of different logical theories. It serves as a gateway to the "plurality of logics". Jeremiah Joven Joaquin, De La Salle University, Manila.

With this new edition, Logic the basics is the best introductory textbook for non-classical logic. It clearly introduces each new topic and shows how it connects to earlier chapters. It is a fantastic choice for introducing undergraduates to exciting developments in logic. Tracy Lupher, Co-director of the Logic and Reasoning Institute, James Madison University, USA