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 `ϕ``x` asserted without comment, as in

is to be taken to mean that `x` is a man implies `x` is mortal,`ϕ``x` is true for *all* values of `x` (or for *any* value), but it might equally well have been taken to mean that `ϕ``x` 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)

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.