 One possible response to Hume’s problem is to deny  premise P3,  by allowing the possibility that a priori reasoning could give rise to synthetic propositions. Kant famously argued in response to Hume that such synthetic a priori knowledge is possible (Kant 1781, 1783). He does this by a kind of reversal of the empiricist programme espoused by Hume. Whereas Hume tried to understand how the concept of a causal or necessary connection could be based on experience, Kant argued instead that experience only comes about through the concepts or “categories” of the understanding. On his view, one can gain a priori knowledge of these concepts, including the concept of causation, by a transcendental argument concerning the necessary preconditions of experience. A more detailed account of Kant’s response to Hume can be found in de Pierris and Friedman 2013.