Although Hume's analysis of geometry continues to serve as a reference point for many contemporary discussions in the philosophy of science, the fact that the first Enquiry presents a radical revision of Hume's conception of geometry in the Treatise has never been explained. The present essay closely examines Hume's early and late discussions of geometry and proposes a reconstruction of the reasons behind the change in his views on the subject. Hume's early conception of geometry as an inexact non-demonstrative science (...) is argued to be a consequence of his attempt to discredit geometrical proofs of infinite divisibility of extension by anchoring the meaning of geometrical concepts in inherently inexact qualitative measurement procedures. This measurement-based attack on the exactness and certainty of geometry is analyzed and shown to be both self-refuting and inconsistent with the general epistemological framework of the Treatise. The revised conception of geometry as a demonstrative science in the first Enquiry is then interpreted as Hume's response to the failure of his earlier attempt to discredit geometrical proofs of infinite divisibility of extension. (shrink)

There is a widespread belief, more often implied than explicitly asserted, that Hume considered all necessary propositions to be analytic.Of course Hume did not use the analytic-synthetic distinction explicitly. This only come to the forefront with Kant; and it is Kant who is probably the main source of the above-mentioned belief. Kant ascribed to Hume the view that mathematical propositions are, in his terminology, analytic. If this is correct, then since mathematics was for Hume the paradigm of a body of (...) necessary truths, it is plausible to infer that he considered necessary propositions to be one and all analytic. The absence in Hume's writings of the analytic-synthetic terminology is by no means decisive: though he did not have the terms he may well have possessed the concepts, as evidenced by his use of them. (shrink)