If every apparent counterexample to substitutional sufficiency resolves into an enthymeme, the additional criterion tracks background assumptions rather than a genuinely distinct validity relation.

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Substitutional sufficiency(as used in logic and semantics): The idea that if you can swap one thing for another without changing the truth of a statement, then that one thing is enough (sufficient) to explain or define the other.
Validity relation(as used in logic): A logical connection between statements or ideas that determines whether one correctly follows from or supports another.
background assumptions(Davies 2003a, p. 43): Assumptions an externalist must hold in order to rationally grant that the *premises are warranted, which already imply the conclusion (3)
counterexample([IHT] arg. 2): A possible obligational situation (casus possibilis positus) that verifies the antecedent and falsifies the consequent of an inference
criterion(as used in philosophy to describe a test for whether an idea works): A standard or rule used to decide whether something counts as true or valid.
enthymeme(Used to describe Xia Ge's argument, which relies on an unstated law about the permanence of existence across time.): An argument in which one or more premises are left implicit (hidden), requiring the audience to supply the unstated assumption.

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