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Foundational Theories of Classical and Constuctive Mathematics

Giovanni Sommaruga, editor
Publisher: 
Springer
Publication Date: 
2011
Number of Pages: 
314
Format: 
Hardcover
Series: 
The Western Ontario Series in Philosophy of Science 76
Price: 
139.00
ISBN: 
9789400704305
Category: 
Anthology
We do not plan to review this book.

Introduction : Giovanni Sommaruga
Part I: Senses of ‚foundations of mathematics’
Bob Hale, The Problem of Mathematical Objects
Goeffrey Hellman, Foundational Frameworks
Penelope Maddy, Set Theory as a Foundation
Stewart Shapiro, Foundations, Foundationalism, and Category Theory

Part II: Foundations of classical mathematics
Steve Awodey, From Sets to Types, to Categories, to Sets
Solomon Feferman, Enriched Stratified Systems for the Foundations of Category TheoryColin McLarty, Recent Debate over Categorical Foundations

Part III: Between foundations of classical and foundations of constructive mathematics
John Bell, The Axiom of Choice in the Foundations of Mathematics
Jim Lambek and Phil Scott, Reflections on a Categorical Foundations of Mathematics

Part IV: Foundations of constructive mathematics
Peter Aczel, Local Constructive Set Theory and Inductive Definitions
David McCarty, Proofs and Constructions
John Mayberry, Euclidean Arithmetic: The Finitary Theory of Finite Sets
Paul Taylor, Foundations for Computable Topology
Richard Tieszen, Intentionality, Intuition, and Proof in Mathematics

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