15.4. EXISTS() and Quantifiers
Formal logic makes use of quantifiers that can be applied to propositions. The two forms are “For all x, P(x)” and “For some x, P(x)”. The first is written as {{inverted uppercase A }} and the second is written as {{reversed uppercase E}}, if you want to look up formulas in a textbook. The quantifiers put into symbols such statements as “all men are mortal” or “some Cretans are liars” so they can be manipulated.
The big question more than 100 years ago was that of existential import in formal logic. Everyone agreed that saying “all men are mortal” implies that “no men are not mortal,” but does it also imply that “some men are mortal”—that we have to have at least one man who is mortal?
Existential import lost the ...
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