Logicism, Intuitionism, and Formalism What Has Become of Them?
The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the de...
| Other Authors: | , , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2009, 2009
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| Edition: | 1st ed. 2009 |
| Series: | Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Introduction: The Three Foundational Programmes
- Introduction: The Three Foundational Programmes
- Logicism and Neo-Logicism
- Protocol Sentences for Lite Logicism
- Frege’s Context Principle and Reference to Natural Numbers
- The Measure of Scottish Neo-Logicism
- Natural Logicism via the Logic of Orderly Pairing
- Intuitionism and Constructive Mathematics
- A Constructive Version of the Lusin Separation Theorem
- Dini’s Theorem in the Light of Reverse Mathematics
- Journey into Apartness Space
- Relativization of Real Numbers to a Universe
- 100 Years of Zermelo’s Axiom of Choice: What was the Problem with It?
- Intuitionism and the Anti-Justification of Bivalence
- From Intuitionistic to Point-Free Topology: On the Foundation of Homotopy Theory
- Program Extraction in Constructive Analysis
- Brouwer’s Approximate Fixed-Point Theorem is Equivalent to Brouwer’s Fan Theorem
- Formalism
- “Gödel’s Modernism: On Set-Theoretic Incompleteness,” Revisited
- Tarski’s Practice and Philosophy: Between Formalism and Pragmatism
- The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory
- Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics
- Beyond Hilbert’s Reach?
- Hilbert and the Problem of Clarifying the Infinite