
Foundations without Foundationalism. A Case for Second-order Logic PDF
Stewart ShapiroStewart 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.
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19 Sep 1991 ... The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to ...

Smoryński : Review of Stewart Shapiro, Foundations …

Foundations without Foundationalism: A Case for Second-Order Logic. Stewart Shapiro. Abstract. A language is second‐order, or higher‐order, if it has bound ...

Foundations without Foundationalism: A Case for …

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to [PDF] Foundations Without Foundationalism: A …