The Principles of Mathematics (1903)

§ 90

Although some may be replaced by its equivalent in terms of any, it is plain that this does not give the meaning of some. There is, in fact, a kind of duality of any and some: given a certain propositional function, if all terms belonging to the propositional function are asserted, we have any, while if one at least is asserted (which gives what is called an existence-theorem), we get some. The proposition ϕx asserted without comment, as in x is a man implies x is mortal, is to be taken to mean that ϕx is true for all values of x (or for any value), but it might equally well have been taken to mean that ϕx is true for some value of x. In this way we might construct a calculus with two kinds of variable, the conjunctive and the disjunctive, in which the latter would occur wherever an existence-theorem was to be stated. But this method does not appear to possess any practical advantages.(§ 90 ¶ 1)