Ebook272 pages11 hours
The Logical Foundations of Mathematics: Foundations and Philosophy of Science and Technology Series
By William S. Hatcher and Mario Bunge
Rating: 0 out of 5 stars
()
About this ebook
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.
Related to The Logical Foundations of Mathematics
Related ebooks
Foundations of Set Theory Rating: 0 out of 5 stars0 ratingsProof Theory: Second Edition Rating: 0 out of 5 stars0 ratingsModel Theory: Third Edition Rating: 5 out of 5 stars5/5A Book of Set Theory Rating: 4 out of 5 stars4/5Introduction to Logic: and to the Methodology of Deductive Sciences Rating: 5 out of 5 stars5/5Philosophical Introduction to Set Theory Rating: 0 out of 5 stars0 ratingsSet Theory and Logic Rating: 4 out of 5 stars4/5Algebra of Proofs Rating: 5 out of 5 stars5/5Real Analysis: Measure Theory, Integration, and Hilbert Spaces Rating: 4 out of 5 stars4/5Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics Rating: 4 out of 5 stars4/5Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results Rating: 4 out of 5 stars4/5Recursive Functionals Rating: 0 out of 5 stars0 ratingsIntroduction to Logic Rating: 4 out of 5 stars4/5Lectures on Homotopy Theory Rating: 0 out of 5 stars0 ratingsFirst Course in Algebra and Number Theory Rating: 5 out of 5 stars5/5Introduction to Analysis Rating: 4 out of 5 stars4/5Introduction to the Theory of Sets Rating: 3 out of 5 stars3/5Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates Rating: 4 out of 5 stars4/5Popular Lectures on Mathematical Logic Rating: 0 out of 5 stars0 ratingsIntroduction to Real Analysis Rating: 3 out of 5 stars3/5Mathematical Logic Rating: 4 out of 5 stars4/5Introduction to Mathematical Logic (PMS-13), Volume 13 Rating: 5 out of 5 stars5/5Topoi: The Categorial Analysis of Logic Rating: 5 out of 5 stars5/5Axiomatic Set Theory Rating: 4 out of 5 stars4/5Introduction to Symbolic Logic and Its Applications Rating: 4 out of 5 stars4/5Three Views of Logic: Mathematics, Philosophy, and Computer Science Rating: 0 out of 5 stars0 ratingsPhilosophy of Mathematics Rating: 0 out of 5 stars0 ratingsSet Theory An Introduction To Independence Proofs Rating: 4 out of 5 stars4/5Topoi: The Categorial Analysis of Logic Rating: 5 out of 5 stars5/5
Mathematics For You
Algebra - The Very Basics Rating: 5 out of 5 stars5/5Basic Math Notes Rating: 5 out of 5 stars5/5Geometry For Dummies Rating: 5 out of 5 stars5/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5Calculus For Dummies Rating: 4 out of 5 stars4/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5The Elements of Euclid for the Use of Schools and Colleges (Illustrated) Rating: 0 out of 5 stars0 ratingsThe Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5See Ya Later Calculator: Simple Math Tricks You Can Do in Your Head Rating: 4 out of 5 stars4/5Calculus Made Easy Rating: 4 out of 5 stars4/5Is God a Mathematician? Rating: 4 out of 5 stars4/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsThe Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5A Mind for Numbers | Summary Rating: 4 out of 5 stars4/5GED® Math Test Tutor, 2nd Edition Rating: 0 out of 5 stars0 ratingsLogicomix: An epic search for truth Rating: 4 out of 5 stars4/5Algebra I For Dummies Rating: 4 out of 5 stars4/5
Reviews for The Logical Foundations of Mathematics
Rating: 0 out of 5 stars
0 ratings
0 ratings0 reviews
Book preview
The Logical Foundations of Mathematics - William S. Hatcher
Enjoying the preview?
Page 1 of 1