Logicism, Intuitionism, and Formalism
What Has Become of Them?
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Beschreibung
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 development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in the famous Hilbert-Brouwer controversy in the 1920s.
The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics.
The volume will be of interest primarily to researchers and graduate students of philosophy, logic, mathematics and theoretical computer science. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.
Contains essays by world-leading experts in the philosophy and foundations of mathematics, describing current developments in the foundations of mathematics in a historical perspective Analyses the classical philosophical and foundational views of Frege, Brouwer, Hilbert, Gödel and Tarski and examines their relevance for current developments Provides an in-depth analysis of various kinds of neologicist philosophies of mathematics Contains a comprehensive section on mathematical intuitionism and constructive mathematics Offers extensive discussions, by several authors, of the proof-theoretic programme of Hilbert and Bernays
Autor*in
Sten Lindström
Themen in »Logicism, Intuitionism, and Formalism«
Bertrand Russell Formalism Foundations of mathematics Gottlob Frege Intuitionism Logicism Philosophy of mathematics Topology Variable calculus mathematics proof theorem type theory