I'm learning a bit about the predicate calculus from various online sources so I have a better chance of selecting a good text for a thorough (self-)study.(adsbygoogle = window.adsbygoogle || []).push({});

By "subject class" I mean "x" in [itex]\forall x[/itex]. Is it true that the subject class of the universal quantifier can be empty, while the subject class of the existential quantifier cannot be empty?

If so, [tex](\forall x [Px \implies (\exists y [whatever])]\ \wedge \neg \exists x [Px]) \implies (\forall x [Px \implies (\exists y [whatever])]\ \mbox{is vacuously true})[/tex]?

Edit: IOW, I'd like to know if I understand how PC handles the problems involving existential import so I can judge how well different texts address the issue. Well, that and I find the issue interesting.

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# Quantifiers, emptiness, and vacuous truth

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