There is then, I think, a difficulty in being sure that _any_ relational properties are internal in this first sense. But, if what we want to do is to show that some are _not,_ and that therefore the dogma that all relations are internal is false, I think the most conclusive reason for saying this is that if _all_ were internal in this first sense, all would necessarily be internal in the second, and that this is plainly false. I think, in fact, the most important consequence of the dogma that all relations are internal, is that it follows from it that all relational properties are internal in this second sense. I propose, therefore, at once to consider this proposition, with a view to bringing out quite clearly what it means and involves, and what are the main reasons for saying that it is false. The proposition in question is that, if P be a relational property and A a term to which it does in fact belong, then, no matter what P and A may be, it may always be truly asserted of them, that any term which had _not_ possessed P would necessarily have been other than--numerically different from--A: or in other words, that A would necessarily, in all conceivable circumstances, have possessed P. And with this sense of "internal," as distinguished from that which says _qualitatively different,_ it is quite easy to point out some relational properties which certainly are internal in this sense. Let us take as an example the relational property which we assert to belong to a visual sense-datum when we say of it that it has another visual sense-datum as a spatial part: the assertion, for instance, with regard to a coloured patch half of which is red and half yellow. "This whole patch contains this patch" (where "this patch" is a proper name for the red half). It is here, I think, quite plain that, in a perfectly clear and intelligible sense, we can say that any whole, which had not contained that red patch, could not have been identical with the whole in question: that from the proposition with regard to any term whatever that it does not contain _that_ particular patch it _follows_ that that term is _other_ than the whole in question--though _not_ necessarily that it is qualitatively different from it. _That_ particular whole could not have existed without having that particular patch for a part. But it seems no less clear, at first sight, that there are many other relational properties of which this is not true. In order to get an example, we have only to consider the relation which the red patch has to the whole patch, instead of considering as before that which the whole has to it. It seems quite clear that, though the whole could not have existed without having the red patch for a part, the red patch might perfectly well have existed without being part of that particular whole. In other words, though every relational property of the form "having _this_ for a spatial part" is "internal"