in our sense, it seems equally clear that every property of the form "is a spatial part of this whole" is _not_ internal, but purely external. Yet this last, according to me, is one of the things which the dogma of internal relations denies. It implies that it is just as necessary that anything, which is in fact a part of a particular whole, should be a part of that whole, as that any whole, which has a particular thing for a part, should have that thing for a part. It implies, in fact, quite generally, that any term which does in fact have a particular relational property, could not have existed without having that property. And in saying this it obviously flies in the face of common sense. It seems quite obvious that in the case of many relational properties which things have, the fact that they have them is _a mere matter of fact:_ that the things in question _might_ have existed without having them. That this, which seems obvious, is true, seems to me to be the most important thing that can be meant by saying that some relations are purely external. And the difficulty is to see how any philosopher could have supposed that it was not true: that, for instance, the relation of part to whole is no more external than that of whole to part. I will give at once one main reason which seems to me to have led to the view, that _all_ relational properties are internal in this sense. What I am maintaining is the common-sense view, which seems obviously true, that it may be true that A has in fact got P and yet also true that A might have existed without having P. And I say that this is equivalent to saying that it may be true that A has P, and yet _not_ true that from the proposition that a thing has _not_ got P it _follows_ that that thing is _other_ than A--numerically different from it. And one reason why this is disputed is, I think, simply because it is in fact true that if A has P, and _x_ has _not_, it _does_ follow that _x_ is other than A. These two propositions, the one which I admit to be true (1) that if A has P, and _x_ has not, it _does_ follow that _x_ is other than A, and the one which I maintain to be false (2) that if A has P, then from the proposition with regard to any term _x_ that it has not got P, it _follows_ that _x_ is other than A, are, I think, easily confused with one another. And it is in fact the case that if they are not different, or if (2) follows from (1), then no relational properties are external. For (1) is certainly true, and (2) is certainly equivalent to asserting that none are. It is therefore absolutely essential, if we are to maintain external relations, to maintain that (2) does _not_ follow from (1). These two propositions (1) and (2), with regard to which I maintain that (1) is true, and (2) is false, can be put in another way, as follows: (1) asserts that if A has P, then any term which has not, _must_ be other than A. (2) asserts that if A has P, then any term which had not, _would necessarily be_