Existential Import

A statement has existential import if its truth depends on the existence of objects of a certain type.

For modern predicate logic, universal statements necessarily lack existential import. Because they are conditionals, they do not assert the existence of any Ss; all they say is that if any x is an S, then it is (or is not) a P.

If there are no Ss, then any statement of the form (x) (Sx ...) is true by default, regardless of the consequent, because the antecedent is not true of anything. That follows from the nature of conditionals as defined by the truth table.

By contrast, particular statements do have existential import. By the nature of conjunction, any statement of the form (x) (Sx . ...) is true only if some x is S.

Relations and Multiple Quantification

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