The Foundational Debate: Complexity and Constructivity in Mathematics and Physics

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Werner DePauli-Schimanovich, Eckehart Köhler, F. Stadler
Springer Science & Business Media, 14.03.2013 - 354 Seiten
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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.
 

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Inhalt

ROLAND OMNES New Interpretations of Quantum
1
ANTON ZEILINGER Experiment Entanglement
12
G CATTANEO M L DALLA CHIARA R GIUNTINI
21
MYRVOLD Computability in Quantum Mechanics 33
32
MICHAEL STöLTZNER Levels of Physical Theories
47
KARL SVOZIL A Constructivist Manifesto for the Physical Sciences
65
ROHIT PARIKH How Far Can We Formalize Language Games?
89
CRISTIAN CALUDE What is a Random String?
101
PAVELTICHY Constructions as the Subject Matter
175
PER MARTINLôF Verificationism Then and Now 187
186
JAN WOLENSKI Logic and Mathematics
197
KAREL CUDA A Connection between Leibniz Infinitely Small
211
WILLIAM W TAIT Extensional Equality in the Classical Theory of Types
219
Hans Hahn
235
ERHARD OESER Crisis and Return of Intuition
247
HANSCHRISTIAN REICHEL How Can or Should the Recent Developments
259

CRISTIAN CALUDE DOUGLAS I CAMPBELL
115
JANOS A MAKOWSKY Capturing Relativized Complexity Classes
132
DIRK VAN DALEN Why Constructive Mathematics?
141
PETER H KRAUSS Hypothetical Extensions of Constructive
159
MICHAEL STöLTZNER Philipp Frank
293
Reviews
303
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