quantities, they certainly must have. Having thus seemingly disposed of the purely intelligible character of quantity in its application to space and time, he can more safely ignore what he could not so plausibly dispose of--its pure intelligibility as number. In order to seem to do so, he must get rid of ‘Infinite Divisibility’. 264. The condition of such a method being acquiesced in is, that quantity in all its forms should be found reducible to ultimate unites or indivisible parts in the shape of separate impressions. Should it be found so, the whole question indeed, how ideas of relation are possible for a merely feeling consciousness, would still remain, but mathematics would stand on the same footing with the experimental sciences, as a science of relations between impressions. Upon this reducibility, then, we find Hume constantly insisting. In regard to number indeed he could not ignore the fact that the science which deals with it recognizes no ultimate unite, but only such a one as ‘is itself a true number.’ But he passes lightly over this difficulty with the remark that the divisible unite of actual arithmetic is a ‘fictitious denomination’--leaving his reader to guess how the fiction can be possible if the real unite is a separate indivisible impression--and proceeds with the more hopeful task of resolving space into such impressions. He is well aware that the constitution of space by impressions and its constitution by indivisible parts stand or fall together. If space is a compound impression, it is made up of indivisible parts, for there is a ‘minimum visibile’ and by consequence a minimum of imagination; and conversely, if its parts are indivisible, they can be nothing but impressions; for, being indivisible, they cannot be extended, and, not being extended, they must be either simple impressions or nothing. With that instinct of literary strategy which never fails him, Hume feels that the case against infinite divisibility, from its apparent implication of an infinite capacity in the mind, is more effective than that in favour of space being a compound impression, and accordingly puts that to the front in the Second Part of the Treatise, in order, having found credit for establishing it, to argue back to the constitution of space by impressions. In fact, however, it is on the supposed composition of all quantity from separate impressions that his argument against its infinite divisibility rests. Quantity made up of impressions, and there must be a least possible impression.