thus we avoid is, and keep to are. But, seriously, that does not look like the explanation of a difficulty; it looks more like trifling with phrases. For, if you mean that and , taken each severally, even “have” this relation, you are asserting what is false. But if you mean that and in such a relation are so related, you appear to mean nothing. For here, as before, if the predicate makes no difference, it is idle; but, if it makes the subject other than it is, it is false.
But let us attempt another exit from this bewildering circle. Let us abstain from making the relation an attribute of the related, and let us make it more or less independent. “There is a relation , in which and stand; and it appears with both of them.” But here again we have made no progress. The relation has been admitted different from and , and no longer is predicated of them. Something, however, seems to be said of this relation , and said, again, of and . And this something is not to be the ascription of one to the other. If so, it would appear to be another relation, , in which , on one side, and, on the other side, and , stand. But such a makeshift leads at once to the infinite process. The new relation can be predicated in no way of , or of and ; and hence we must have recourse to a fresh relation, , which comes between and whatever we had before. But this must lead to another, ; and so on, indefinitely. Thus the problem is not solved by taking relations as independently real. For, if so, the qualities and their relation fall entirely apart, and then we have said nothing. Or we have to make a new relation between the old relation and the terms; which, when it is made, does not help us. It either itself demands a new relation, and so on without end, or it leaves us where we were, entangled in difficulties.
The attempt to resolve the thing into properties, each a real thing, taken somehow together with in-