A-Logic is a new theory of formal logic based on substitution of synonyms rather than sameness of truth-values. In this book, it is contrasted, step-by-step, with today's mathematical logic. This approach reveals how A-Logic can resolve traditional logic's anomalies, such as the Liar's paradox, Hempel's Paradox of Confirmation, and Carnap's problem of dispositional predicates, while preserving all of standard logic's theorems.
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A Note on Notational Devices and Rules of Convenience
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A-logic Analytic Logic analytic truth-logic antecedent argument position assert axioms Basic Normal Forms Boolean expansion C-conditionals Chapter components concept conditional statements conjunction conjunctive normal form consequent Cont Q CONT-theorems definition disjunction domain E-valid elementary wffs entails expressions field of reference follows formal logic INC[P inconsistent individual constants instantiations logical containment logical properties logical structure logical synonymy logically valid M-logic mathematical induction Mathematical Logic meaning metatheorems MinOCNF MOCNF modes MODNF negation negation-free not-Inc occurrences predicate letter predicate schemata prefixed premisses Proof quantification theory quantifiers quasi-quotation Quine Quine's referential replacing rules of inference schema semantic sentential logic Step substitution symbols SYN Q Syn TP SYN-metatheorem SYN-theorems Syndf synonymous SynSUB T-operators T-wffs T(P v Q T(Vx)Px TAUT TAUT[P tautologous TF-conditional theorem of logic theorems TP & TQ true or false truth-functional truth-tables U-SUB Valid TP variables Vx)(Px v Qx Vx)Px Vx)Qx