Limits of Logic

Stewart Shapiro, University of St. Andrews, UK and The Ohio State University at Newark, USA Gregory H. Moore, Leslie H. Tharp, George S. Boolos, Stewart Shapiro, Alfred Tarski, Steven J. Wagner, Ignacio Jane, Peter Simons, Virginia Klenk, John Corcoran, Charles McCarty, Neil Tennant, Michael D. Resnick, Thomas Weston, Alexander George, Paul Benacerraf, Crispin Wright, Nino B. Cocchiarella, Peter Clark.

• 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 Jané; Who's afraid of higher-order logic?, Peter Simons. Ontological Reduction, Intended Interpretations and the Löwenheim-Skolem Theorems: Ontological reduction, Leslie H. Tharp; Intended models and the Löwenheim-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 Löwenheim-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.

’Almost every significant paper on second-order logic and the philosophical importance of the Löwenheim-Skolem theorems is here in this collection...a useful addition to the library of anyone interested in the nature of logic in general and in the function of second-order methods in particular.’ Studia Logica