Foundations without Foundationalism

‘In this excellent treatise Shapiro defends the use of second-order languages and logic as framework for mathematics. His coverage of the wide range of logical and philosophical topics required for understanding the controversy over second-order logic is thorough, clear, and persuasive. Shapiro recognizes that it is unlikely that he has had the last word on these controversial philosophical subjects. Nevertheless, his book is certainly an excellent place tostart work on them.‘Michael D. Resnik, University of North Carolina, History and Philosophy of Logic, 14 (1993)`Clearly written and well produced, making it a pleasure to read … Shapiro’s excellent book is for just about everyone. Logicians and philosophers of mathematics will certainly want to read it; but metaphysicians and philosophers of science and of language will greatly benefit, too.‘Dialogue

Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and Professorial Fellow in the Department of Logic and Metaphysics at the University of St Andrews, Scotland.