Reality and Truth in Mathematics

Philosophia Mathematica 6 (2):131-168 (1998)
Abstract
Brouwer's positions about existence (reality) and truth are examined in the light of ninety years of scientific progress. Relevant results in proof theory, recursion theory, set theory, relativity, and quantum mechanics are used to cast light on the following philosophical questions: What is real, and how do we know it? What does it mean to say a thing exists? Can things exist that we can't know about? Can things exist that we don't know how to find? What does it mean to say something is true? How can we know whether something is true? Can things be true that we can't ever know to be true?
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DOI 10.1093/philmat/6.2.131
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