The Argument from Silence, Part 1: The Bayesian Interpretation

I want to provide a Bayesian interpretation of the argument from silence.

Let S be some truth about the silence of a potential source of evidence fact and H1 and H2 be rival explanatory hypotheses.

(1) S is known to be true, i.e., Pr(S) is close to 1.

(2) H1 is not intrinsically much more probable than H2, i.e., Pr(H1 | B) is not much more probable than Pr(H2 | B).

(3) Pr(S | H2) > Pr(S | H1).

(4) Other evidence held equal, H1 is probably false, i.e., Pr(H1 | B & S) < 0.5.

Readers who have followed my series on evidential arguments against theism (and for naturalism) will immediately recognize the above as the generic form of what I have called an explanatory argument. From a Bayesian perspective, there is nothing special about the argument from silence; silence can be evidence favoring one hypothesis over another.

From a Bayesian perspective, the key question for evaluating arguments from silence is premise (3). I don’t have much to say about that in the abstract; the truth of (3) is something that must be considered on a case-by-case basis.

So is absence of evidence itself evidence of absence? As my remarks above should make clear, I think the only correct answer is, “It depends.” It would be mistake to assume that all arguments from silence are correct, but it would equally be a mistake to assume that all arguments from silence are incorrect.