Foundations Without Foundationalism
Stewart Shapiro
Broschiertes Buch

Foundations Without Foundationalism

A Case for Second-Order Logic

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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-orderlogic is needed to codify many contemporary mathematical concepts. Throughout, he emphasizes philosophical and historical issues t...