# The Principles of Mathematics (1903)

## § 479

Frege's theory that assumptions are proper names for the true or the false, as the case may be, appears to me also untanble. Direct inspection seems to show that the relation of a proposition to the true or the false is quite different from that of (say) the present King of England to Edward VII. Moreover, if Frege's view were correct on this point, we should have to hold that in an asserted proposition it is the meaning, not the indication, that is asserted, for otherwise, all asserted propositions would assert the very same thing, namely the true, (for false propositions are not asserted). Thus asserted propositions would not differ from one another in any way, but would be all strictly and simply identical. Asserted propositions have no indication (FuB. p. 21), and can only differ, if at all, in some way analogous to meaning. Thus the meaning of the unasserted proposition together with its truth-value must be what is asserted, if the meaning simply is rejected. But there seems no purpose to introducing the truth-value here: it seems quite sufficient to say that an asserted proposition is one whose meaning is true, and that to say the meaning is true is the same as to say the meaning is asserted. We might then conclude that true propositions, even when they occur as parts of others, are always and essentially asserted, while false propositions are always unasserted, thus escaping the difficulty about therefore discussed above. It may also be objected to Frege that the true and the false, as opposed to truth and falsehood, do not denote single definite things, but rather the classes of true and false propositions respectively. This objection, however, would be met by his theory of ranges, which correspond approximately to my classes; these, he says, are things, and the true and the false are ranges (v. inf.).(§ 479 ¶ 1)