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(1)
- Giovanni Sommaruga ed. Foundational Theories of Classical and Constructive Mathematics, Springer, The Western Ontario Series in Philosophy of Science, vol. 76, Due in January, 2011
Discription
The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.
Contents
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 Theory
Colin 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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- Volker Halbach Axiomatic Theories of Truth, Cambridge University Press, Due in December 2010
Description
At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth.
Contents
Preface
1. Foundations
2. Typed truth
3. Type-free truth
4. Ways to the truth
5. Index of systems
Bibliography
Index.
