Stewart Shapiro presents a distinctive and persuasive view of the foundations of mathematics, arguing controversially that second-order logic has a central role to play in laying these foundations. To support this contention, he first gives a detailed development of second-order and higher-order logic, in a way that will be accessible to graduate students. He then demonstrates that second-order notions are prevalent in mathematics as practised, and that higher-order logic is needed to codify many contemporary mathematical concepts. Throughout, he emphasizes philosophical and historical issues that the subject raises. Foundations without Foundationalism is a key contribution both to philosophy of mathematics and to mathematical logic. '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 to start work on them.' Michael D. Resnik, History and Philosophy of Logic

About the Author
Stewart Shapiro is Professor of Philosophy at Ohio State University.

Reviews
Contains more on second-order logic than is readily available in any other textbook or survey. Philosophically, the book also contains many words of wisdom. * Journal of Symbolic Logic *



Book Information
ISBN 9780198250296
Author Stewart Shapiro
Format Paperback
Page Count 300
Imprint Oxford University Press
Publisher Oxford University Press
Weight(grams) 441g
Dimensions(mm) 235mm * 156mm * 18mm