Ebook: The Foundational Debate: Complexity and Constructivity in Mathematics and Physics

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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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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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.
Content:
Front Matter....Pages I-XIV
New Interpretations of Quantum Mechanics and the Theory of Knowledge....Pages 1-11
Experiment, Entanglement and the Foundations of Quantum Mechanics....Pages 13-19
Constructivism and Operationalism in the Foundations of Quantum Mechanics....Pages 21-31
Computability in Quantum Mechanics....Pages 33-46
Levels of Physical Theories....Pages 47-64
A Constructivist Manifesto for the Physical Sciences — Constructive Re-Interpretation of Physical Undecidability....Pages 65-88
How Far Can We Formalize Language Games?....Pages 89-100
What is a Random String?....Pages 101-113
Strong Determinism vs. Computability....Pages 115-131
Capturing Relativized Complexity Classes with Lindstr?m Quantifiers....Pages 133-140
Why Constructive Mathematics?....Pages 141-157
Hypothetical Extensions of Constructive Mathematics....Pages 159-174
Constructions as the Subject Matter of Mathematics....Pages 175-185
Verificationism Then and Now....Pages 187-196
Logic and Mathematics....Pages 197-210
A Connection between Leibniz’ Infinitely Small Quantities and the Analytical Hierarchy....Pages 211-218
Extensional Equality in the Classical Theory of Types....Pages 219-234
Hans Hahn and the Foundational Debate....Pages 235-245
Crisis and Return of Intuition in Hans Hahn’s Philosophy of Mathematics....Pages 247-258
How Can or Should the Recent Developments in Mathematics Influence the Philosophy of Mathematics?....Pages 259-268
On the Vienna Circle in Exile: An Eyewitness Report....Pages 269-292
Philipp Frank and the German Physical Society....Pages 293-302
Barry Smith: Austrian Philosophy. The Legacy of Franz Brentano, Chicago and La Salle, Ill.: Open Court, 1994....Pages 303-304
Gustav Bergmann:New Foundations of Ontology, edited by William Heald Foreword by Edwin B. Allaire, Madison and London: The University of Wisconsin Press, 1992....Pages 304-306
Kurt Baier: The Rational and the Moral Order. The Social Roots of Reason and Morality, Chicago and La Salle, Illinois: Open Court, 1995.....Pages 306-310
Thomas Oberdan: Protocols, Truth and Convention, Amsterdam and Atlanta, Ga.: Rodopi, 1993....Pages 310-313
Julian B. Barbour, Herbert Pfister: Mach’s Principle: From Newton’s Bucket to Quantum Gravity, Boston, Basel, Berlin: Birkh?user, 1995.....Pages 313-315
Vienna-Berlin-Prague: Centenaries Carnap, Reichenbach, Zilsel....Pages 317-342
Back Matter....Pages 343-354

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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.
Content:
Front Matter....Pages I-XIV
New Interpretations of Quantum Mechanics and the Theory of Knowledge....Pages 1-11
Experiment, Entanglement and the Foundations of Quantum Mechanics....Pages 13-19
Constructivism and Operationalism in the Foundations of Quantum Mechanics....Pages 21-31
Computability in Quantum Mechanics....Pages 33-46
Levels of Physical Theories....Pages 47-64
A Constructivist Manifesto for the Physical Sciences — Constructive Re-Interpretation of Physical Undecidability....Pages 65-88
How Far Can We Formalize Language Games?....Pages 89-100
What is a Random String?....Pages 101-113
Strong Determinism vs. Computability....Pages 115-131
Capturing Relativized Complexity Classes with Lindstr?m Quantifiers....Pages 133-140
Why Constructive Mathematics?....Pages 141-157
Hypothetical Extensions of Constructive Mathematics....Pages 159-174
Constructions as the Subject Matter of Mathematics....Pages 175-185
Verificationism Then and Now....Pages 187-196
Logic and Mathematics....Pages 197-210
A Connection between Leibniz’ Infinitely Small Quantities and the Analytical Hierarchy....Pages 211-218
Extensional Equality in the Classical Theory of Types....Pages 219-234
Hans Hahn and the Foundational Debate....Pages 235-245
Crisis and Return of Intuition in Hans Hahn’s Philosophy of Mathematics....Pages 247-258
How Can or Should the Recent Developments in Mathematics Influence the Philosophy of Mathematics?....Pages 259-268
On the Vienna Circle in Exile: An Eyewitness Report....Pages 269-292
Philipp Frank and the German Physical Society....Pages 293-302
Barry Smith: Austrian Philosophy. The Legacy of Franz Brentano, Chicago and La Salle, Ill.: Open Court, 1994....Pages 303-304
Gustav Bergmann:New Foundations of Ontology, edited by William Heald Foreword by Edwin B. Allaire, Madison and London: The University of Wisconsin Press, 1992....Pages 304-306
Kurt Baier: The Rational and the Moral Order. The Social Roots of Reason and Morality, Chicago and La Salle, Illinois: Open Court, 1995.....Pages 306-310
Thomas Oberdan: Protocols, Truth and Convention, Amsterdam and Atlanta, Ga.: Rodopi, 1993....Pages 310-313
Julian B. Barbour, Herbert Pfister: Mach’s Principle: From Newton’s Bucket to Quantum Gravity, Boston, Basel, Berlin: Birkh?user, 1995.....Pages 313-315
Vienna-Berlin-Prague: Centenaries Carnap, Reichenbach, Zilsel....Pages 317-342
Back Matter....Pages 343-354
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