**A Priori and A Posteriori: The Case of Proof
**Timothy Williamson (University of Oxford)

08 October 2021, 16:00 (Lisbon Time – GMT+1) | Sala Mattos Romão (Departamento de Filosofia)

**Abstract:** Knowledge by mathematical proof is normally considered a paradigm of the *a priori*. However, when the process of checking a written proof is analysed, it turns out to depend on sophisticated forms of perceptual pattern recognition—indeed this is closely related to the nature of formal proof. If one checks the proof in one’s head rather than on paper, the process is similar: checking it in one’s head is the offline version of the online process of checking it on paper. Little sense can be made of the injunction to separate the content of a proof from its form. The case of mathematical proof supports the conclusion that the *a priori* and the *a posteriori* are only superficially different. This is not a form of empiricism: it does not abolish the *a priori* but accounts for it in an evolutionarily plausible way.

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