Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In Logicism Renewed, the author revisits this concept in light of advances in mathematical logic and the need for languages that can be understood by both humans and computers that require distinguishing between the intension and extension of predicates. Using Intensional Type Theory (ITT) the author provides a unified foundation for mathematics and computer science, yielding a much simpler foundation for recursion theory and the semantics of computer programs than that currently provided by category theory.

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The original concept of logicism, as put forward by Bertrand Russell, the belief that all of mathematics can be deduced from a very small number of fundamental logical principles, is revisited in the light of advances in mathematical logic and the need for languages that can be understood by both humans and computers which require distinguishing between the intension and extension of predicates. Using Intensional Type Theory (ITT), the author provides a unified foundation for mathematics and computer science, yielding a much simpler foundation for recursion theory and the semantics of computer programs than that currently provided by category theory.

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Logicism Renewed : Logical Foundations for Mathematics And Computer Science

Gilmore, Paul C.

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