<logic> Quantified statements have existential import iff (in the standard interpretation) they are taken to assert the existence of their subjects. Aristotle held that all quantified propositions have existential import. The modern view, due to George Boole, is that existentially quantified statements do and that universally quantified statements do not. Hence in the modern view, (x)(Ax => Bx) ("All A's are B's") is non-committal on the existence of any A's; it may be true even for an interpretation whose domain contains no objects to instantiate x, or none that happen to be A's. By contrast, ( Ex)(AxoBx) ("Some A's are B's") asserts the existence of at least one A, and it would be false for any interpretation whose domain contained no such values for x.
See predicate logic, quantifier
[Glossary of First-Order Logic]
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