eBook - PDF

The Logical Foundations of Mathematics

Name: The Logical Foundations of Mathematics
ISBN: 9781483189635

Foundations and Philosophy of Science and Technology Series

William S. Hatcher,

Mario Bunge,

330 pages
English
PDF
Available on iOS & Android

eBook - PDF

The Logical Foundations of Mathematics

Foundations and Philosophy of Science and Technology Series

William S. Hatcher,

Mario Bunge,

About this book

The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.

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Yes, you can access The Logical Foundations of Mathematics by William S. Hatcher, Mario Bunge in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics Reference. We have over one million books available in our catalogue for you to explore.