1st Edition

Logicism Renewed Logical Foundations for Mathematics and Computer Science, Lecture Notes in Logic 23

By Paul C. Gilmore Copyright 2005
    252 Pages
    by A K Peters/CRC Press

    252 Pages
    by A K Peters/CRC Press

    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.

    Preface, Chapter 1: Elementary Logic, Chapter 2: Type Theory, Chapter 3: An Intensional Type Theory, Chapter 4: Recursions, Chapter 5: Choice and Function Terms, Chapter 6: Intuitionist Logic, Chapter 7: Logic and Mathematics, Chapter 8: Logic and Computer Science, References, Index

    Biography

    Paul C. Gilmore