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    That conjunction is necessarily false only if God's exist... — Carmelics
    Home/Problem of Evil
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    Supports→There is at least some non-zero probability that God does not exist, given our background knowledge (premise 2 holds).

    That conjunction is necessarily false only if God's existence is a necessary truth or background knowledge entails God's existence.

    Problem of Evil
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    Problem of Evil

    Key Terms

    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.

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    Neither God's existence being a necessary truth nor background knowledge entaili...

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    Related propositions within the same area of thought.
    Only necessarily false propositions have a probability equal to zero.
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    The conjunction ¬P & G & k is necessarily false only if either ¬P is n...90%Neither God's existence being a necessary truth nor background knowled...85%The existence of God is neither a logically necessary truth nor entail...83%Theism is very probably false, even when the evidence for God's existe...81%

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    As regards (2), it certainly seems plausible, assuming that the existence of God is not logically necessary, that there is at least some non-zero probability that God does not exist, given our background knowledge. But one can derive (2), provided that one is willing to accept the (not uncontroversial) principle that only necessarily false propositions have a probability equal to zero. (This principle is very plausible if one accepts the idea of infinitesimals. If one does not, one may hold that some contingent propositions have a probability equal to zero.) Given this assumption, the reasonin...

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