If modal entailment sufficed, number theory and set theory would share identical commitments wherever their objects are necessarily interdefinable, which contradicts standard ontological practice.
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Dealing with possibility and necessity—questions about what could be true, what must be true, and what's merely contingent (could go either way).
modal entailment(Candidate entailment relation for the analysis of ontological commitment)
An entailment relation grounded in metaphysical necessity, where a theory entails a proposition if, necessarily, the truth of the theory implies the truth of that proposition.
ontological commitments(Quine's conception as applied to our best global theory)
The demands that the truth of our total theory imposes on the world.