The rest of the argument is based upon errors of a different kind, and in it one may keep to "the one" throughout, if one choose. There is, of course, no reason to think that the speaker did this. He probably here, as before, carried over to "a one," one thought as an individual thing, distinctions drawn in view of "the one," one viewed in the abstract. As some of the statements made may be true or false as one is taken in this sense or that; and particularly as the antinomy rests upon a misconception as to the nature of sameness, I will continue the analysis. What is to be proved is, first, that one cannot be the same with itself or other, or other than itself or other; and second, that it cannot be like or unlike itself or other. The position that the one, if other than itself, would not be one, and if the same with other, would be that other, is somewhat ambiguous. If "a one" is in question, it may undoubtedly be "a one" and yet be other than any particular one; and it may be the same with other--another one--without ceasing to be one, if by same we mean similar. The play upon words in "other of other" it is not necessary to consider. The conclusion that one cannot be the same with itself is based upon the supposition that sameness is a quality superadded to the other qualities of a thing; but in its first sense the word does not even serve to indicate a relation; it is merely used to point out the absence of duality. Both "a one" and "the one" may be the same with themselves perfectly well, and in saying so we do not in thought endow them with any quality not already possessed. This last error serves also as a basis to the second paradoxical position, that one cannot be like or unlike itself or other. It assumes likeness and unlikeness to be qualities added to the other qualities of things which are like or unlike. A possible objection to my use of the term "a one" I must forestall before passing on. I have used this as synonymous with "one object." One horse is one object, and so is one part of a horse. It may be said, however, that "a one" may also be used to signify a single occurrence of oneness, as distinguished from another occurrence of oneness. That any element of consciousness may be distinguished from any similar element merely by spatial or temporal differences I have argued in the first part of my monograph. Why may not then "a one" mean the oneness of this one horse, or the oneness of this part of the horse? And if it may, can "a one" of this kind have parts any more than "the one?"