Wilson Underkuffler

I provide an interpretation of Hume’s argument in Treatise 1.2 Of the Ideas of Space and Time that finite extensions are only finitely divisible (hereafter Hume’s Finite Divisibility Argument). My most general claim is that Hume intends his Finite Divisibility Argument to be a demonstration in the Early Modern sense as involving the comparison and linking of ideas based upon their intrinsic contents. It is a demonstration of relations among ideas, meant to reveal the meaningfulness or absurdity of a given supposition, and to distinguish possible states of affairs from impossible ones. It is not an argument ending in an inference to an actual matter of fact. Taking the demonstrative nature of his Finite Divisibility Argument fully into account radically alters the way we understand it. Supported by Hume’s own account of demonstration, and reinforced by relevant Early Modern texts, I follow to its logical consequences, the simple premise that the Finite Divisibility Argument is intended to be a demonstration. Clear, abstract ideas in Early Modern demonstrations represent possible objects. By contrast, suppositions that are demonstrated to be contradictory have no clear ideas annexed to them and therefore cannot represent possible objects—their ‘objects,’ instead, are “impossible and contradictory.” Employing his Conceivability Principle, Hume argues that there is a clear idea of a finite extension containing a finite number of parts and therefore, finitely divisible extensions are possible. In contrast, the supposition of an infinitely divisible finite extension is “absurd” and “contradictory” and stands for no clear idea. Consequently, Hume deems this supposition “impossible and contradictory,” that is, without meaning and therefore, descriptive of no possible object. This interpretation allays concerns found in the recent literature and helps us better understand what drives Hume’s otherwise perplexing argument in the often neglected or belittled T 1.2.

This paper considers whether elements of T 1.2 Of the Ideas of Space and Time in Hume’s Treatise is inconsistent with skepticism regarding the external world in T 1.4.2 Of Scepticism with regard to the Senses. This apparent tension vexes commentators, and efforts to resolve it drives the recent scholarship on this section of Hume’s Treatise. To highlight this tension I juxtapose Hume’s “Adequacy Principle” with what I call his “skeptical causal argument” in T 1.4.2. The Adequacy Principle appears to state that we can form conclusions about objects through the comparison of our ideas of them, while Hume’s skeptical causal argument asserts that we cannot form any conclusions about objects using ideas. Is Hume being inconsistent? I argue that he is not. My paper has three parts. First, I give a general reading of the Adequacy Principle in light of Hume’s peculiar claim that it is “the foundation of all human knowledge.” I then explain why the Adequacy Principle itself is not inconsistent with Hume’s skeptical causal argument by explaining how the term “object” should not be strictly read as “external” object but merely the “the object of inquiry” or even “the matter under consideration.” Second, I sketch Hume’s employment of the Adequacy Principle in his Divisibility Argument, explaining how this is also not at odds with his skeptical causal argument. In the third and final part I explore various interpretations in the literature and consider whether “finite extensions” need necessarily be read as external objects.