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Did Brouwer’s Intuitionistic Analysis Satisfy Its Own Epistemological Standards?

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The aim of this essay is both historical and philosophical. On the histori. level, the following remarks are intended to contribute to a better understanding of the missing reception of the more advanced parts of Luitzen E. J. Brouwer’s intuitionistic mathematics. More precisely, I want to draw attention to a crucial technical difficulty in Brouwer’s treatment of the basic theorems of intuitionistic analysis. It concerns the (intuitionistic) proof of what Brouwer viewed as one of the cornerstones of intuitionistic set theory, the “fan theorem,” as it is often called today. This difficulty most probably presented a serious obstacle to contemporary attempts to understand Brouwer’s contributions. On the philosophical level, I cannot do much more than raise the question formulated in the title of this essay. However, this question will be made more precise by focusing on the epistemology of the technical issue just mentioned. It turns out that in this discussion also the general problem of what constitutes an intuitionistic proof is at stake.