If background knowledge inductively entails God's existence with probability approaching 1, then P(~God | background knowledge) converges to zero without requiring strict logical entailment.
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A guarantee that something must be true based purely on the rules of logic alone, with no exceptions or uncertainty.
background knowledge(Popper's philosophy of science)
Items that must be taken for granted during scientific criticism, but which are not conclusively established and may be challenged at any time, especially if their uncritical acceptance is suspected of causing subsequent difficulties.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.