Concluding remarks at the Cerisy conference

Abstract

The great philosopher Ludwig Wittgenstein once wrote, ‘Philosophy leaves everything as it is’. That is, philosophy does not change anything, and can never change anything. We may think — I indeed think — that that was a foolish remark; doubtless all philosophers, even great ones, make foolish remarks sometimes. There are many people who would vehemently repudiate Wittgenstein’s observation — followers of Karl Marx, for example. We know, and have been celebrating, how greatly Brouwer’s philosophy changed mathematics — not, alas, for all mathematicians, but for a select band, so well represented here, able to understand and appreciate Brouwer’s insights.