Logicism Renewed
Logical Foundations for Mathematics and Computer Science
Published on 9. April 2020
978-1-108-67693-9 (ISBN)
Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. 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 this volume, the twenty-third publication in the Lecture Notes in Logic series, Paul C. Gilmore revisits logicism in light of recent advances in mathematical logic and theoretical computer science. Gilmore addresses the need for languages which can be understood by both humans and computers and, using Intensional Type Theory (ITT), provides a unified basis for mathematics and computer science. This yields much simpler foundations for recursion theory and the semantics of computer programs than those currently provided by category theory.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
0,00 MB
ISBN-13
978-1-108-67693-9 (9781108676939)
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Schweitzer Classification
Person
Paul C. Gilmore is Professor Emeritus in the Computer Science Department at the University of British Columbia, Vancouver. His research interests include logical foundations of mathematics and computer science, applications of logic in computer science, and databases.
Content
Preface; 1. Elementary logic; 2. Type theory; 3. An intensional type theory; 4. Recursions; 5. choice and function terms; 6. Intuitionist logic; 7. Logic and mathematics; 8. Logic and computer science.
