If set claims are fundamentally modal rather than referential, the inference from 'infinitely many sets share one physical base' to 'sets are a distinct object-kind' conflates structural possibility with ontological category.
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Something that could logically fit together or be arranged in a certain way, even if it doesn't actually exist in the real world.
inference(Nyāya epistemology)
A component of epistemology in Nyāya philosophy; a veritable inference yields knowledge about the world and must have premises that are themselves known
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).
referential(in philosophy of language)
Relating to how words or names point to and stand for actual things in the world.