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Mathematical Proof that Absence of Evidence *IS* Evidence of Absence

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Published on May 12, 2013

I am sick to death of Christians failing to grasp the idea that a lack of evidence really is sufficient grounds for rejecting an unlikely claim. So in frustration, I went ahead and proved it mathematically using basic probability theory. Perhaps this will be enough to end the discussion once and for all.

I think we should give this proof a name. I propose we all it the "Anticitizen Theorem." :D

Exercises for the viewer:

(1) Let's suppose that evidence can be a union of multiple events:

E = A and B.

Start with the assumption that more evidence of X makes X more likely to be true. Then prove that less evidence makes X less likely.

(2) Change assumption 1 to the following:

Assumption 1: Let P(E|X) be some number greater than zero.

In other words, the probability of E does not even have to be greater than NOT-E. It just has to be nonzero.

Under what conditions will the absence of evidence still qualify as evidence of absence?

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