Willkommen, schön sind Sie da!
Logo Ex Libris

Foundational Theories of Classical and Constructive Mathematics

  • Kartonierter Einband
  • 328 Seiten
(0) Erste Bewertung abgeben
Bewertungen
(0)
(0)
(0)
(0)
(0)
Alle Bewertungen ansehen
Focusing on the foundations, this volume explores both classical and constructive mathematics. Its great advantage is to extend th... Weiterlesen
CHF 192.00
Print on Demand - Auslieferung erfolgt in der Regel innert 4 bis 6 Wochen.
Bestellung & Lieferung in eine Filiale möglich

Beschreibung

Focusing on the foundations, this volume explores both classical and constructive mathematics. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time both subtle and more differentiated.

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.



One of the first confrontations of foundations of classical and foundations of constructive mathematics

A technical and philosophical treatment of the subject

An extensive philosophical reflection on the meaning and use of foundations in mathematics



Klappentext
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 foundations? Etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of 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.

Inhalt

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

Produktinformationen

Titel: Foundational Theories of Classical and Constructive Mathematics
Editor:
EAN: 9789400735613
ISBN: 9400735618
Format: Kartonierter Einband
Herausgeber: Springer Netherlands
Anzahl Seiten: 328
Gewicht: 499g
Größe: H235mm x B155mm x T17mm
Jahr: 2013
Auflage: 2011

Weitere Produkte aus der Reihe "The Western Ontario Series in Philosophy of Science"