There were arguments in the late 19th century as to the "existential import" of the quantifier  . The question was, if you say "all men are mortals," are you at the same time saying that there are in fact some men? Eventually it was decided that the most useful choice would be to say that, no, you are making no such claim. For example, the statement "all moon men are green" would actually be considered a true statement, since there is no example of a moon man who is not green to serve as a counterexample. We say then that the statement is vacuously true. This is related to the meaning of implication: If "M" = "is a moon man" and "G" = "is green," then our statement is x[Mx Gx]. Since, for every x, Mx is false, the statement MxGx is always true. Thus, x[MxGx] is a true statement.
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