Foundations without Foundationalism. A Case for Second-order Logic PDF

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.

Foundations without Foundationalism: A Case for Second-Order Logic. Stewart Shapiro. Abstract. A language is second‐order, or higher‐order, if it has bound ... Amazon.com: Foundations without Foundationalism: A Case for Second-order Logic (Oxford Logic Guides) (9780198250296): Stewart Shapiro: Books.