The Limits of Logic

Abstract

Contents: Is Second-Order Logic Logic?: Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory, Gregory H. Moore Which logic is the right logic?, Leslie H. Tharp On second-order logic, George S. Boolos Second-order languages and mathematical practice, Stewart Shapiro What are logical notions?, Alfred Tarski A curious inference, George Boolos The rationalist conception of logic, Steven J. Wagner A critical appraisal of second-order logic, Ignacio JanA(c) Who's afraid of higher-order logic?, Peter Simons. Ontological Reduction, Intended Interpretations and the LA wenheim-Skolem Theorems: Ontological reduction, Leslie H. Tharp Intended models and the LA wenheim-Skolem theorem, Virginia Klenk Categoricity, John Corcoran Skolem's paradox and constructivism, Charles McCarty and Neil Tennant Second-order logic, foundations and rules, Stewart Shapiro. Plural Quantification: To be is to be a value of a variable (or to be some values of some variables), George Boolos Nominalist Platonism, George Boolos Second-order logic still wild, Michael D. Resnick. Philosophy of Set Theory: Kreisel, the continuum hypothesis, and second-order set theory, Thomas Weston Skolem and the LA wenheim-Skolem theorem: a case study of the philosophical significance of mathematical results, Alexander George Skolem and the skeptic, Paul Benacerraf Skolem and the skeptic, Crispin Wright Predication versus membership in the distinction between logic as language and logic as calculus, Nino B. Cocchiarella Logicism, the continuum and anti-realism, Peter Clark Name index.