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Logicism, Intuitionism, and Formalism, Springer Netherlands, Libro Tedesco | Libreria Universitaria

C- structive mathematics may also be characterized as mathematics based on intuiti- isticlogicand,thus,beviewedasadirectdescendant ofBrouwer'sintuitionism. It saw the development of three major foundational programmes: In this period, there were also lively exchanges between the various schools culminating in the famous Hilbert-Brouwer controversy in the s.

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.

Logicism, Intuitionism, and Formalism

A special section is concerned with constructive mathematics and its foundations. This active branch of mathematics is a direct legacy of Brouwer's intuitionism. Today one often views it more abstractly as mathematics based on intuitionistic logic. It can then be regarded as a generalisation of classical mathematics in that it may be given, firstly, the standard set-theoretic interpretation, secondly, algorithmic meaning, and thirdly, nonstandard interpretations in terms of variable sets sheaves over topological spaces.

The volume will be of interest primarily to researchers and graduate students of philosophy, logic, mathematics and theoretical computer science.

Formalism and Intuitionism

The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. The present anthology has its origin in two international conferences that were arranged at Uppsala University in August Logicism, Intuitionism and F- malism: What has become of them? The rst conference concerned the three major programmes in the foundations of mathematics during the classical period from Frege s Begrif- schrift in to the publication of Godel ] s two incompleteness theorems in The three foundational programmes, pp.

B urgess , Protocol sentences for lite logicism, pp. S tewart S hapiro , The measure of Scottish neo-logicism, pp.

Categories

N eil T ennant , Natural logicism via the logic of orderly pairing, pp. Intuitionism and Constructive Mathematics.

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P eter A czel , A constructive version of the Lusin separation theorem, pp. H ajime I shihara , Relativization of real Most users should sign in with their email address.


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