 Instead of introducing certainty into natural philosophy as Newton claimed, mathematics, albeit a useful device “in almost every art and profession” (THN 2.3.3.2), is thus grounded in natural fictions. It has a limited contribution to the advancement of knowledge. Mathematics in Hume’s eyes is only another human cognitive enterprise that has no potential to make other fields of knowledge immune to human fallibility. This is in sharp contrast with the cognitive optimism Newton expresses in the Preface to the Principia and several other passages about the role of mathematics in natural inquiry (see Guicciardini 2009, esp. ch. 13 &amp; 14; Zemplén &amp; Demeter 2010). Newton is confident that by making the method of inquiry mathematical, natural philosophy can be infused with certainty and demonstrativity. This confidence is undermined by Hume’s account of how mathematical knowledge is possible at all.