If 'Ex' is false at w for all values of 'x', then the existentialproposition '∃xEx' is false at w, yielding an incorrect truth value for intuitively true quantified modal propositions.
Whether a statement is true or false—it's the truth property that any claim possesses.
modal(in logic and metaphysics)
Dealing with possibility and necessity—questions about what could be true, what must be true, and what's merely contingent (could go either way).
w (possible world)(as used in modal logic)
A hypothetical scenario or state of affairs — philosophers use this to talk about what *could* be true in different situations, not just what's actually true right now.
∃x (the existential quantifier symbol)(as used in symbolic logic)
A shorthand symbol meaning 'there exists at least one' — so '∃xEx' means 'there exists at least one thing that has property E.'
By contrast, “no-trace”, or strict, actualists like Prior (1957), Adams (1981), and Fitch (1996) hew closely to the intuition that, had a contingent individual a failed to exist, there would have been absolutely no trace, no metaphysical vestige, of a — neither a itself in some non-concrete state nor any abstract proxy for a. Hence, unlike trace actualism, there are no such vestiges in the actual world of objects that are not actual but only could have been. The logical consequences for no