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Article ID: CBB479319966

Proof vs Provability: On Brouwer’s Time Problem (2020)

Yourgrau, Palle (Author)

History and Philosophy of Logic
Volume: 41
Issue: 2
Pages: 140-153
Publication date: 2020

URI: https://doi.org/10.1080/01445340.2019.1702264

DOI: 10.1080/01445340.2019.1702264

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Proof Intuitionistic mathematics Temporality Philosophy of mathematics 20th century Brouwer, Luitzen E. J.

Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies that Brouwer has invited us to introduce into mathematics.

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