Mathematics in Philosophy: Selected Essays

Description

This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point of view, that mathematical thought is central to our thought in general, underlies the essays. In his introduction, Parsons articulates that point of view and relates it to past and recent discussions of the foundations of mathematics. Mathematics in Philosophy is divided into three parts. Ontology―the question of the nature and extent of existence assumptions in mathematics―is the subject of Part One and recurs elsewhere. Part Two consists of essays on two important historical figures, Kant and Frege, and one contemporary, W. V. Quine. Part Three contains essays on the three interrelated notions of set, class, and truth. Charles Parsons is Edgar Pierce Professor of Philosophy at Harvard University. He is the author of Mathematics in Philosophy: Selected Essays from Cornell and On Constructive Interpretation of Predicative Mathematics. Cover Title Page Contents Preface Preface to the Cornell Paperbacks Edition Introduction Part one. Mathematics, Logic, and Ontology 1. Ontology and Mathematics 2. A Plea for Substitutional Quantification 3. Informal Axiomatization, Formalization, and the Concept of Truth Part two. Interpretations 4. Infinity and Kant’s Conception of the “Possibility of Experience” 5. Kant’s Philosophy of Arithmetic 6. Frege’s Theory of Number 7. Quine on the Philosophy of Mathematics Part three. Sets, Classes, and Truth 8. Sets and Classes 9. The Liar Paradox 10. What Is the Iterative Conception of Set? 11. Sets and Modality Bibliography Index