Hume's Philosophy of Geometry

Abstract

Hume's writings with respect to geometry represent one of the least studied and least understood parts of his philosophy. Commentators have been inclined to view Hume's analysis of geometric knowledge, particularly that in the Treatise, as confused and ill-conceived. However, as we shall see, if we take care to situate Hume's philosophy of geometry within the framework of his empiricism and familiarize ourselves with its main concerns and course of reasoning, we will be led to a much more positive view and evaluation of his efforts. As Hume saw it, the ancient view of geometry as a perfectly precise and certain science lay at the heart of the excesses which plagued both skepticism and rationalism. In the Treatise he applied his copy principle to the fundamentals of this subject and concluded that this view of geometry was based on a confusion. In one fell swoop Hume believed that he had preserved the foundations of geometry against the attack of skepticism, undermined some of the most important doctrines of rationalism, and removed what had long been viewed as an insurmountable obstacle to an empiricist epistemology. Incredibly, when we turn to the Enquiry, we find Hume embracing geometry as a perfectly precise and certain science. Little is known as to the reason behind this rather remarkable shift in view and there is considerable controversy as to just how sharp a break from the Treatise Hume intended. Hume himself is virtually silent on the topic. However, by laying the proper groundwork, we shall be able to understand why Hume found it necessary to break from the Treatise and why he pursued the direction he did. Overall, our findings will reveal that Hume's struggles with geometry, in spite of their shortcomings, clearly bear the mark of his unique genius.