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It is not the case that One can derive a formula giving the probability that God does not exist relative to information about the number of apparent evils in the world.
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Logical probability requires a prior probability space over possible worlds, but no non-arbitrary such space exists for theistic hypotheses.
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2.
Carnap's inductive logic programs collapsed precisely because assigning logical probabilities across metaphysical hypotheses requires substantive commitments that cannot be derived from logic alone.
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3.
Without a principled prior for divine existence, any formula purporting to calculate P(~God | evil) smuggles in empirical or theological assumptions, rendering it non-logical.
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Reason for 2 of 2
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1.
The reference class of 'apparent evils' is theory-laden: whether an event counts as evil depends on background moral and theological commitments that are themselves contested.
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2.
Alston argued that our cognitive faculties are demonstrably unreliable for assessing whether God has sufficient reasons for permitting specific evils, undermining the evidential weight assigned to each counted instance.
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Reasons Against
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Reason against
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1.
A substantive theory of inductive logic, or logical probability, can be brought to bear upon the argument from evil.
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2.
When this is done, the probability that God does not exist can be calculated relative to the number of apparent evils found in the world.
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