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Intuitionistic Proof Versus Classical Truth

The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics

  • Enrico Martino

Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 42)

About this book

Introduction

This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism.

The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting.

This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.



Keywords

Informal Intuitionistic Proof Creative Subject Bar Theorem Type Theory Constructivism Inductive Evidence Semantical Groundedness Impredicativity Intuitionistic Choice Sequences Beth-Models Fallible Models Brouwer realistic truth Brouwer classical truth Brouwer intuitionistic truth Brouwer creative subject Brouwer Michael Dummett Brouwer Saul Kripke Brouwer Per Martin-Löf Brouwer Arend Heyting

Authors and affiliations

  • Enrico Martino
    • 1
  1. 1.FISPPA DepartmentUniversity of PaduaPaduaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-74357-8
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Religion and Philosophy
  • Print ISBN 978-3-319-74356-1
  • Online ISBN 978-3-319-74357-8
  • Series Print ISSN 2214-9775
  • Series Online ISSN 2214-9783
  • Buy this book on publisher's site