can be truly asserted of every relational property." This is a proposition which is again quite certainly true; and, in order to compare it with (2), there is, I think, no need to adopt any further convention for expressing it, since the questions whether it is or is not different from (2), and whether (2) does or does not follow from it, will obviously depend on the same questions with regard to the two propositions, with regard to the particular relational property, P,
xP entails {yP * (y = x)}
and
xP * {yP entails (y = x)}
Now what I maintain with regard to (1) and (2) is that, whereas (1) is true, (2) is false. I maintain, that is to say, that the proposition "What we assert of P, when we say
xP * {yP entails (y = x)}.
is true of every relational property" is false, though I admit that what we here assert of P is true of some relational properties. Those of which it is true, I propose to call internal relational properties, those of which it is false external relational properties. The dogma of internal relations, on the other hand, implies that (2) is true; that is to say, that every relational property is internal and that there are no external relational properties. And what I suggest is that the dogma of internal relations has been held only because (2) has been falsely thought to follow from (1).
And that (2) does not follow from (1), can, I think, be easily seen as follows. It can follow from (1) only if from any proposition of the form
p entails (q * r)