Abstract

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.
           

In this presentation, 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. Their epistemic status is similar compared to other “common” causal facts of nature that are expressible in qualitative terms, which Hume classifies as “proofs.” In conclusion, I argue that the appropriate way to understand Hume’s propositions of mixed mathematics is that they represent epistemic virtues such as precision, predictability and usefulness, not any increase of certainty compared to qualitative matter of fact propositions.