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Modality and Probability

On p. 51 of Where the Conflict Really Lies, Plantinga says: “[T]he probability of a contingent proposition on a necessary falsehood is 1.”

So, where C = a contingent proposition and F = a necessary falsehood, Plantinga is saying P(C|F)=1.

This seems false. How are we getting our values? If we understand conditional probability to be defined as:


and we grant that a necessary falsehood has the probability of 0, then P(C|F) ≠ 1, rather, it is undefined. Shoenberg, “If P(A) = 0, then P(B|A) is undefined, just as division by zero is undefined in arithmetic. This makes sense, since if event A never happens, then it does not make much sense to discuss the frequency with which event B happens given that A also happens” (Introduction to Probability with Texas Hold’em Examples, Chapman and Hall, 2011, p.40). After some further investigation, I noticed that Tyler Wunder gives a similar objection here.

However, the above is too quick.