Logic: The Basics

Jc BeallisBoard 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.

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

• I BACKGROUND IDEAS1 Consequences 1.1 Relations of support 1.2 Logical consequence: the basic recipe 1.3 Valid arguments and truth 1.4 Summary, looking ahead, and reading 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. 2.5 Summary, looking ahead, and reading 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 3.7 Summary, looking ahead, and reading 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 4.6 Summary and looking ahead II THE BASIC CLASSICAL THEORY5 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 5.8 Summary and looking ahead 6 Basic Classical Tableaux 6.1 What are tableaux? 6.2 Tableaux for the Basic Classical Theory 6.3 Summary and looking ahead 7 Basic Classical Translations 7.1 Atoms, Punctuation, and Connectives 7.2 Syntax, altogether 7.3 Semantics 7.4 Consequence 7.5 Summary and Looking Ahead III FIRST-ORDER CLASSICAL THEORY8 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 8.6 Summary and looking ahead 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 9.5 Summary and looking ahead. 10 First-Order Language with Any-Arity Innards10.1 Truth and falsity conditions for atomics 10.2 Cases, domains, and interpretation functions 10.3 Classicality 10.4 A formal picture 10.5 Summary and looking ahead 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 11.6 Summary and looking ahead 12 Tableaux for First-Order Logic with Identity 12.1 A Few Reminders 12.2 Tableaux for Polyadic First-Order Logic 12.3 Summary and looking ahead 13 First-Order Translations 13.1 Basic Classical Theory with Innards 13.2 First-Order Classical Theory 13.3 Polyadic Innards13.4 Examples in the polyadic language 13.5 Adding Identity 13.6 Summary and Looking Ahead IV NONCLASSICAL THEORIES14 Alternative Logical Theories 14.1 Apparent unsettledness 14.2 Apparent overdeterminacy 14.3 Options14.4 Cases 14.5 Truth and falsity conditions 14.6 Logical Consequence 14.7 Summary, looking ahead, and reading 15 Nonclassical Sentential Logics 15.1 Syntax 15.2 Semantics, Broadly 15.3 Defined connectives 15.4 Some notable forms 15.5 Summary and looking ahead 16 Nonclassical First-order Theories 16.1 An Informal Gloss 16.2 A formal picture 16.3 Summary and looking ahead 17 Nonclassical Tableaux 17.1 Closure Conditions 17.2 Tableaux for Nonclassical First-Order Logics 17.3 Summary and looking ahead 18 Nonclassical Translations 18.1 Syntax and Semantics 18.2 Consequence 18.3 Summary and looking ahead V FREEDOM, NECESSITY AND BEYOND19 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 sketch19.5 Formal picture 19.6 Summary and looking ahead 20 Possibilities20.1 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 20.6 Summary and looking ahead 21 Free and Modal Tableaux 21.1 Free Tableaux 21.2 Modal Tableaux 21.3 Summary and looking ahead 22 Glimpsing Different Logical Roads 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