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Epistemology versus Ontology

Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf

  • Book
  • © 2012

Overview

Editors:
  1. P. Dybjer

    1. Goteborg, Sweden

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  2. Sten Lindström

    1. Dept. Philosophy & Linguistics, University of Umea, Umea, Sweden

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  3. Erik Palmgren

    1. Dept. Mathematics, Uppsala University, Uppsala, Sweden

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  4. G. Sundholm

    1. Leiden, Netherlands

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  • Comprehensive overview of the philosophical problems of the foundational framework in current mathematics
  • Demonstrates the impact of the work of the eminent academic: Per Martin-Löf
  • Contains contributions from mathematicians and philosophers

Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 27)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Philosophy of Logic and Mathematics

    1. Front Matter

      Pages 1-1
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  4. Foundations

    1. Front Matter

      Pages 181-181
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About this book

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?

Editors and Affiliations

  • Goteborg, Sweden

    P. Dybjer

  • Dept. Philosophy & Linguistics, University of Umea, Umea, Sweden

    Sten Lindström

  • Dept. Mathematics, Uppsala University, Uppsala, Sweden

    Erik Palmgren

  • Leiden, Netherlands

    G. Sundholm

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