The Foundational Debate: Complexity and Constructivity in Mathematics and Physics

by Werner DePauli-Schimanovich (Editor), Eckehart Köhler (Editor), F. Stadler (Editor)

Overview

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics.
This ‘foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics.

Product Details

ISBN-13:	9789048146178
Publisher:	Springer Netherlands
Publication date:	12/04/2010
Series:	Vienna Circle Institute Yearbook , #3
Edition description:	Softcover reprint of hardcover 1st ed. 1995
Pages:	354
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

New Interpretations of Quantum Mechanics and the Theory of Knowledge.- Experiment, Entanglement and the Foundations of Quantum Mechanics.- Constructivism and Operationalism in the Foundations of Quantum Mechanics.- Computability in Quantum Mechanics.- Levels of Physical Theories.- A Constructivist Manifesto for the Physical Sciences — Constructive Re-Interpretation of Physical Undecidability.- How Far Can We Formalize Language Games?.- What is a Random String?.- Strong Determinism vs. Computability.- Capturing Relativized Complexity Classes with Lindström Quantifiers.- Why Constructive Mathematics?.- Hypothetical Extensions of Constructive Mathematics.- Constructions as the Subject Matter of Mathematics.- Verificationism Then and Now.- Logic and Mathematics.- A Connection between Leibniz’ Infinitely Small Quantities and the Analytical Hierarchy.- Extensional Equality in the Classical Theory of Types.- Hans Hahn and the Foundational Debate.- Crisis and Return of Intuition in Hans Hahn’s Philosophy of Mathematics.- How Can or Should the Recent Developments in Mathematics Influence the Philosophy of Mathematics?.- On the Vienna Circle in Exile: An Eyewitness Report.- Philipp Frank and the German Physical Society.- Reviews.- Vienna-Berlin-Prague: Centenaries Carnap, Reichenbach, Zilsel.- Activities of the Institute Vienna Circle.- Survey 1995.- Preview 1996.- Index of Names.