Logic for philosophy
Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.
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What is Logic?
Beyond Standard Prepositional Logic
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accessibility relation antecedent assignment g assumption axiomatic proofs axiomatic system axioms bachelor Barcan formula canonical model clause conditional proof construct containing contradiction counterfactual countermodel deduction theorem defined definition denotation deontic domain example Exercise exists fact false formal language formula function symbols given identity induction inference instance interpretation function intuitionistic intuitively invalid lemma logical consequence logical constants logical truth logically implies mathematical means metalanguage metalogic metaphysical modal logic modal systems MPL-model natural numbers natural-language necessarily notion object PL-interpretation possible worlds predicate logic premises prepositional logic provable prove quantifiers rational number real number reflexive represent result rule S-consistent semantic consequence sentence letters sequent sequent proof set of wffs supervaluational Suppose for reductio T-model T-schema tautology things trivalent interpretation truth condition truth function truth tables truth values validity and semantic valuation function variable assignment wff f