| Description |
1 online resource (xv, 385 pages) |
| Series |
Logic, epistemology, and the unity of science ; v. 27 |
|
Logic, epistemology and the unity of science ; v. 27.
|
| Contents |
Part 1. PHILOSOPHY OF LOGIC AND MATHEMATICS -- Kant and Real Numbers / Mark van Atten -- Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing / Juliet Floyd -- Truth and Proof in Intuitionism / Dag Prawitz -- Real and Ideal in Constructive Mathematics / Giovanni Sambin -- In the Shadow of Incompleteness: Hilbert and Gentzen / Wilfried Sieg -- Evolution and Logic / Jan M. Smith -- The "Middle Wittgenstein" and Modern Mathematics / Sören Stenlund -- Primitive Recursive Arithmetic and Its Role in the Foundations of Arithmetic: Historical and Philosophical Reflections: In Honor of Per Martin-Löf on the Occasion of His Retirement / William W. Tait -- Part 2. FOUNDATIONS -- Type Theory and Homotopy / Steve Awodey -- A Computational Interpretation of Forcing in Type Theory / Thierry Coquand and Guilhem Jaber -- Program Testing and the Meaning Explanations of Intuitionistic Type Theory / Peter Dybjer -- Normativity in Logic / Jean-Yves Girard -- Constructivist Versus Structuralist Foundations / Erik Palmgren -- Machine Translation and Type Theory / Aarne Ranta -- Constructive Zermelo-Fraenkel Set Theory, Power Set, and the Calculus of Constructions / Michael Rathjen -- Coalgebras as Types Determined by Their Elimination Rules / Anton Setzer -- Second Order Logic, Set Theory and Foundations of Mathematics / Jouko Väänänen |
| Summary |
This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? |
| Analysis |
Philosophy (General) |
|
Genetic epistemology |
|
Ontology |
|
Logic, Symbolic and mathematical |
|
Philosophy |
|
Mathematical Logic and Foundations |
|
Epistemology |
|
History of Mathematical Sciences |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
|
Print version record |
| Subject |
Martin-Löf, Per, 1942-
|
| SUBJECT |
Martin-Löf, Per, 1942- fast |
| Subject |
Mathematics -- Philosophy.
|
|
Mathematics -- Philosophy -- History
|
|
MATHEMATICS -- Essays.
|
|
MATHEMATICS -- Pre-Calculus.
|
|
MATHEMATICS -- Reference.
|
|
Sciences sociales.
|
|
Sciences humaines.
|
|
Mathematics -- Philosophy
|
| Genre/Form |
Festschriften
|
|
History
|
|
Festschriften.
|
| Form |
Electronic book
|
| Author |
Dybjer, Peter.
|
| ISBN |
9789400744356 |
|
9400744358 |
|
