The argument I mean involves considerations which are exceedingly familiar, so familiar that I am afraid every one may be sick of hearing them alluded to. But, in spite of this fact, it seems to me not quite easy to put it quite precisely, in a way which will distinguish it clearly from other arguments involving the same familiar considerations, but which do not seem to me to be equally cogent. I want, therefore, to try to put it with a degree of precision, which will prevent irrelevant objections from being made to it--objections which would, I think, be relevant against some of these other arguments, but are not, I think, relevant against it.
The fact is that we all, exceedingly commonly, when, at each of two times, separated by a longer or shorter interval, we see a part of the surface of a material thing, in the sense in which I am now seeing this part of the surface of this inkstand, or when at one time we see such a surface and at another perceive one by touch, make, on the second occasion, the judgment "_This_ part of a surface is the _same_ part of the surface of the same thing, as that which I was seeing (or perceiving by touch) just now." How commonly we all do this can scarcely be exaggerated. I look at this inkstand, and then I look again, and on the second occasion I judge "This part of the surface of this inkstand is the same as, or at least contains a part which is the same as a part of, the part of its surface which I was seeing just now." Or I look at this finger and then I touch it, and I judge, on the second occasion, "This part of the surface of this finger is the same as one of those I was seeing just now." We all thus constantly identify a part of a surface of a material thing which we are perceiving at one time with a part which we _were_ perceiving at another.
Now, when we do this--when we judge "This is the _same_ part of the same thing as I was seeing or touching just now," we, of course, do not mean to exclude the possibility that the part in question may have changed during the interval; that it is really different, on the second occasion, either in shape or size or quality, or in all three, from what it was on the first. That is to say, the sense of sameness which we are here concerned with is one which clearly does not exclude change. We may even be prepared to assert, on general grounds, in all such cases, that the surface in question certainly must have changed. But nevertheless there is a great difference in one respect, between two kinds of such cases, both of which occur exceedingly commonly. If I watch somebody blowing air into a child's balloon, it constantly happens, at certain stages in the process, that I judge with regard to the part of the surface which I am seeing at that stage, not only that it _is_ larger than it was at an earlier stage, but that it is _perceptibly_ larger. Or, if I pull the face of an india-rubber doll, I may judge at a certain stage in the process that the patch of red colour on its cheek not only is different in shape from what it was at the beginning, but is _perceptibly_ so; it may, for instance, be a perceptibly flatter ellipse than it was to start with. Or, if I watch a person blushing, I may judge at a certain stage that a certain part of the surface of his face not only is different in colour from what it was, when I saw it before he began to blush, but is _perceptibly_ so--perceptibly redder. In enormous numbers of cases we do thus judge of a surface seen at a given time that it is thus _perceptibly_ different in size, or in shape, or in colour, from what it was when we saw it before. But cases are at least equally numerous in which, though we might, on general grounds be prepared to assert that it _must_ have changed in some respect, we should not be prepared to assert that it had, in any respect whatever, changed _perceptibly._ Of this part of this surface of this inkstand, for instance, I am certainly not prepared to assert that it is now perceptibly different in any respect from what it was when I saw it just now. And similar cases are so numerous that I need not give further instances. We can, therefore, divide cases, in which we judge, of a part of a surface which we are seeing, "This is the same part of the surface of the same material thing as the one I saw just now," into cases where we should also judge "But it is perceptibly different from what it was then," and cases in which, even though we might assert "It _must_ be different," we are certainly not prepared to assert that it is _perceptibly_ so.