At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...) over the correlation between the logical moments of quantity (universal, particular, singular) and the categorial ones (unity, plurality, totality). (shrink)

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. (shrink)