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The Logical Foundations of Mathematics : Foundations and Philosophy of Science and Technology Series by William S. Hatcher, Mario Bunge is a nonfiction available to read on EtoBox.

What is The Logical Foundations of Mathematics : Foundations and Philosophy of Science and Technology Series about?

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

Who reads The Logical Foundations of Mathematics : Foundations and Philosophy of Science and Technology Series?

Author

William S. Hatcher, Mario Bunge

Publisher

Elsevier Science Netherlands

Published

1982

Language

EN

ISBN

9780080258003

Category

nonfiction

Subjects

Anthropology, Mathematics, Philosophy