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Preface | |
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Acknowledgments | |
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Propositional Logic | |
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Propositions and Arguments | |
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What Is Logic? | |
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Propositions | |
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Arguments | |
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Logical Consequence | |
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Soundness | |
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Connectives | |
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The Language of Propositional Logic | |
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Motivation | |
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Basic Propositions of PL | |
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Connectives of PL | |
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Wff Variables | |
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Syntax of PL | |
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Semantics of Propositional Logic | |
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Truth Tables for the Connectives | |
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Truth Values of Complex Propositions | |
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Truth Tables for Complex Propositions | |
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Truth Tables for Multiple Propositions | |
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Connectives and Truth Functions | |
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Uses of Truth Tables | |
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Arguments | |
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Single Propositions | |
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Two Propositions | |
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Sets of Propositions | |
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More on Validity | |
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Logical Form | |
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Abstracting from Content: From Propositions to Forms | |
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Instances: From Forms to Propositions | |
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Argument Forms | |
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Validity and Form | |
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Invalidity and Form | |
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Notable Argument Forms | |
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Other Logical Properties | |
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Connectives: Translation and Adequacy | |
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Assertibility and Implicature | |
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Conjunction | |
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Conditional and Biconditional | |
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Disjunction | |
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Negation | |
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Functional Completeness | |
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Trees for Propositional Logic | |
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Tree Rules | |
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Applying the Rules | |
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Uses of Trees | |
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Abbreviations | |
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Predicate Logic | |
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The Language of Monadic Predicate Logic | |
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The Limitations of Propositional Logic | |
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MPL, Part I: Names and Predicates | |
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MPL, Part II: Variables and Quantifiers | |
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Syntax of MPL | |
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Semantics of Monadic Predicate Logic | |
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Models; Truth and Falsity of Uncomplicated Propositions | |
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Connectives | |
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Quantified Propositions: The General Case | |
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Semantics of MPL: Summary | |
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Analyses and Methods | |
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Trees for Monadic Predicate Logic | |
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Tree Rules | |
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Using Trees | |
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Infinite Trees | |
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Models, Propositions, and Ways the World Could Be | |
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Translation | |
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Valuation | |
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Axiomatization | |
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Propositions | |
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Logical Consequence and NTP | |
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Postulates | |
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General Predicate Logic | |
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The Language of General Predicate Logic | |
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Semantics of GPL | |
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Trees for General Predicate Logic | |
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Postulates | |
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Moving Quantifiers | |
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Identity | |
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The Identity Relation | |
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The Identity Predicate | |
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Semantics of Identity | |
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Trees for General Predicate Logic with Identity | |
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Numerical Quantifiers | |
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Definite Descriptions | |
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Function Symbols | |
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Foundations and Variations | |
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Metatheory | |
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Soundness and Completeness | |
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Decidability and UndecidabUity | |
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Other Logical Properties | |
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Expressive Power | |
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Other Methods of Proof | |
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Axiomatic Systems | |
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Natural Deduction | |
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Sequent Calculus | |
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Set Theory | |
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Sets | |
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Ordered Pairs and Ordered n-tuples | |
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Relations | |
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Functions | |
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Sequences | |
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Multisets | |
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Syntax | |
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Notes | |
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References | |
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Index | |