No internal or causal constraint uniquely fixes which model is the intended one, so the claim that the sentence has a determinate truth-value presupposes a metaphysicalrealism that cannot be internally justified.
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Proven or validated using only resources or evidence from within a system itself, without relying on anything external to it.
metaphysical realism(Feigl's characterization, Feigl 1956, p. 22)
Attempts to systematically employ transcendent, i.e., in principle untestable, assertions.
model(Possible worlds interpretation of S5 adapted for modal nonmonotonic logic)
A pair <I, S> where I is a set of literals (a state description / possible world) and S is a set of complete, consistent sets of literals (interpretations) with I ∈ S