McGrew (2013) decomposes the argument from silence into a product of three probabilities — would the author notice, record, and would the record survive — so the inference is only as strong as its weakest term

The argument from silence (argumentum ex silentio) — inferring that some fact is false, or some event did not occur, because a source that would be expected to mention it does not — is an old historiographical method with a formal literature. Timothy McGrew's 2013 treatment (Acta Analytica) gives it a Bayesian structure. The evidential force of a silence turns on three questions: if the hypothesis were true, how probable is it that the author "would have noticed it (N)," would "record it (R)," and that "this record would have survived and that contemporary historians would be aware of it (S)?" McGrew approximates the critical value by the product P(N|H) × P(R|H & N) × P(S|H & N & R).

Because the force is a product, the inference is only as strong as its weakest term: if any one of notice, record, or survival is low, the argument is near-worthless even when the other two are near-certain. A silence is decisive only when all three terms sit close to 1 — the author would surely have known the fact, surely have written it down, and that writing would surely have reached us.

The survival/record terms carry an explicit corollary. McGrew stresses that "all that we are entitled to say is that there is no reference to it in any of that writer's surviving works," and that "the more of a writer's works we know or can reasonably suppose to have been lost, the less weight we are entitled to place on mere omission in the remainder." Silence in a partial corpus is weak; silence in the one document that would define the matter is strong.

This framework grades the vault's own recurring negative findings, which reach conclusions by a cited party's own silence — see claim-bjork-desirable-difficulties-not-prediction-error (silence in the defining text) and claim-dreyfus-1973-lineage-link-uncorroborated (silence in the author's other retrospectives). The two sit at different strengths of this same product; that grading is drawn in observation-bjork-dreyfus-same-argument-from-silence-graded-differently. The companion lesson — that humans systematically over-trust these inferences — is claim-mcgrew-humans-systematically-over-trust-arguments-from-silence. The whole cluster is indexed at moc-argument-from-silence.