Now in a way we can dispute about the rules of logic, or about the validity of certain inferences. Consider the following immediate inferences [sic]: "all men are mortal. Therefore some men are mortal." Logicians used to dispute about the validity of this inference, but it was a purely verbal dispute about the meaning of "all." If "all men are mortal" is taken to mean the same as "There are some men and if anything is a man it is mortal," the inference is valid. If "all men are mortal" is taken to mean merely "if anything is a man it is mortal," the inference is not valid. The ordinary use of "all" is vague, and either interpretation accords with some of the uses of the word. The example is instructive in spite of its triviality, for it shows how disputes about the validity of inferences are disputes about the meanings of words. Formal logic of the Quine sort may be regarded as a systematization of certain suggested rules (not the actual ones) for the use of the words "and," "not," "all," and "some."
(J. J. C. Smart, "Reason and Conduct," Philosophy 25 [July 1950]: 209-24, at 219)
Note from KBJ: Smart is describing the so-called problem of existential import, about which Aristotle and George Boole famously disagree. Aristotle interprets "all men are mortal" as "there are some men and if anything is a man it is mortal," while Boole interprets it as "if anything is a man it is mortal." In other words, for Aristotle, universal propositions (both affirmative and negative) have existential import. For Boole, universal propositions do not have existential import. (Aristotle and Boole agree that particular propositions have existential import.) The inferences from "All S are P" to "Some S are P" and from "No S are P" to "Some S are not P" are therefore valid for Aristotle but invalid for Boole. (These inferences are known as subalternation.)
Keith Burgess-Jackson, J.D., Ph.D. 