Foundations without Foundationalism : A Case for Second-Order Logic

Stewart Shapiro presents a distinctive original view of the foundations of mathematics, arguing that second-order logic has a central role to play in laying these foundations. He gives an accessible account of second-order and higher-order logic, paying special attention to philosophical and historical issues. 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 frameworks for mathematics. His coverage of the wide range of logical and philosophical . . . is thorough, clear, and persuasive.' Michael D. Resnik, History and Philosophy of Logic