The Generalised Tarski Thesis (GTT) yields classical consequence when its cases are taken to be possible worlds, where possible worlds are complete and consistent with respect to negation. That (classical) precisification of ‘follows from’ is familiar and useful, however, it is not the only sense of ‘follows from’ apparent in English. Another strongly apparent sense of ‘follows from’ takes ‘from’ seriously. There is a sense of ‘follows from’ that is more restrictive than the classical sense; it demands that premises be ‘relevant’ to conclusions. That sense of ‘follows from’ is more restrictive than the classical one: it imposes constraints that go beyond truth-preservation over possible worlds. The constraints, in effect, concern the behaviour of negation. What is required is not only truth-preservation over possible worlds, but truth-preservation over cases that go beyond the constraints of worlds, beyond the constraints of completeness and consistency. The task is to specify such cases, thereby cashing out relevant consequence.
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