The Foundational Debate: Complexity and Constructivity in Mathematics and PhysicsWerner DePauli-Schimanovich, Eckehart Köhler, F. Stadler Springer Science & Business Media, 14.03.2013 - 354 Seiten 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. |
Inhalt
| 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 |
PAVEL TICHÝ Constructions as the Subject Matter | 175 |
PER MARTINLÖF Verificationism Then and Now 187 | 197 |
KAREL ČUDA 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 |
MICHAEL STÖLTZNER Philipp Frank | 293 |
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 |
Reviews | 303 |
The Rational and the Moral Order | 306 |
Activities of the Institute Vienna Circle | 343 |
Andere Ausgaben - Alle anzeigen
The Foundational Debate: Complexity and Constructivity in Mathematics and ... Werner DePauli-Schimanovich,Eckehart Köhler,Friedrich Stadler Keine Leseprobe verfügbar - 2010 |
The Foundational Debate: Complexity and Constructivity in Mathematics and ... Werner DePauli-Schimanovich,Eckehart Köhler,Friedrich Stadler Keine Leseprobe verfügbar - 1995 |
The Foundational Debate: Complexity and Constructivity in Mathematics and ... Werner DePauli-Schimanovich,Eckehart Köhler,Friedrich Stadler Keine Leseprobe verfügbar - 2013 |
Häufige Begriffe und Wortgruppen
algorithms alternative set theory analysis argument axiom of choice axioms Berlin Brouwer Calude Cambridge Carnap Chaitin classical mathematics complexity computable functions computable sequence concept consider constructive mathematics constructivism defined definition DePauli-Schimanovich discussion effectively Einstein empirical empiricism equation equivalent Ernst Mach example existence experimental extensional equality fact finite first-order logic formal formula Foundational Debate foundations of mathematics Gödel Hahn Hans Hahn Harvard Hilbert infinite interpretation intuition intuitionism intuitionistic judgement Kurt Gödel language laws Mach math mathematicians means natural numbers Neurath notion objects observation operator oracle particle Philipp Frank philosophy of mathematics physical possible predictions principle problem proof properties proposition quantifiers quantum mechanics question random strings rational real numbers reason Reichenbach relation Schlick scientific semantics sense set theory structure theorem thesis tion true truth Turing machines undecidable Unity of Science University Vienna Circle Wittgenstein