258. In the passage from part II. of the Treatise, already referred to, he distinctly tells us that the unity to which existence belongs excludes multiplicity. ‘Existence itself belongs to unity, and is never applicable to number but on account of the unites of which the number is composed. Twenty men may be said to exist, but ’tis only because one, two, three, four, &c., are existent. ... A unite, consisting of a number of fractions, is merely a fictitious denomination, which the mind may apply to any quantity of objects it collects together; nor can such an unity any more exist alone than number can, as being in reality a true number. But the unity which can exist alone, and whose existence is necessary to that of all number, is of another kind and must be perfectly indivisible and incapable of being resolved into any lesser unity’. [1] What then is the ‘unity which can exist alone’? The answer, according to Hume, must be that it is an impression separately felt and not resoluble into any other impressions. But then the question arises, how a succession of such impressions can form a number or sum; and if they cannot, how the so-called real unity or separate impression can in any sense be a unite, since a unite is only so as one of a sum. To put the question otherwise, Is it not the case that a unite has no more meaning without number than number without unites, and that every number is not only just such a ‘fictitious denomination,’ as Hume pronounces a ‘unite consisting of a number of fractions’ to be, but a fiction impossible for our consciousness according to Hume’s account of it? It will not do to say that such a question touches only the fiction of ‘abstract number,’ but not the existence of numbered objects; that (to take Hume’s instance) twenty men exist with the existence of each individual man, each real unit, of the lot. It is precisely the numerability of objects--not indeed their existence, if that only means their successive appearance, but their existence _as a sum_--that is in question. If such numerability is possible for such a consciousness as Hume makes ours to be; in other words, if he can explain the fact that we count; ‘abstract number’ may no doubt be left to take care of itself. Is it then possible? ‘Separate impressions’ mean impressions felt at different times, which accordingly can no more co-exist than, to use Hume’s expression, ‘the year 1737 can concur with the year 1738;’ whereas the constituents of a sum must, as such, co-exist. Thus when we are told that ‘twenty may be said to exist because one, two, three, &c., are existent,’ the alleged reason, understood as Hume was bound to understand it, is incompatible with the supposed consequence. The existence of an object would, to him, mean no more than the occurrence of an impression; but that one impression should occur, and then another and then another, is the exact opposite of their coexistence as a sum of impressions, and it is such co-existence that