Hume’s Fork and Mixed Mathematics
Slavov, M. (2017). Hume’s Fork and Mixed Mathematics. Archiv für Geschichte der Philosophie, 99(1), 102-119. https://doi.org/10.1515/agph-2017-0004
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Archiv für Geschichte der PhilosophieTekijät
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2017Tekijänoikeudet
© Walter de Gruyter GmbH & Co. This is a final draft version of an article whose final and definitive form has been published by de Gryuter. Published in this repository with the kind permission of the publisher.
Given the sharp distinction that follows from Hume’s Fork, the proper epistemic status of propositions of mixed mathematics seems to be a mystery. On the one hand, mathematical propositions concern the relation of ideas. They are intuitive and demonstratively certain. On the other hand, propositions of mixed mathematics, such as in Hume’s own example, the law of conservation of momentum, are also matter of fact propositions. They concern causal relations between species of objects, and, in this sense, they are not intuitive or demonstratively certain, but probable or provable. In this article, I argue that the epistemic status of propositions of mixed mathematics is that of matters of fact. I wish to show that their epistemic status is not a mystery. The reason for this is that the propositions of mixed mathematics are dependent on the Uniformity Principle, unlike the propositions of pure mathematics.
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