This essay addresses the question of when evidence for a stronger claim H1 also constitutes evidence for a weaker claim H2. Although the answer “Always” is tempting, it is false on a natural Bayesian conception of evidence. This essay first describes some prima facie counterexamples to this answer and surveys some weaker answers and rejects them. Next, it proposes an answer, which appeals to the “Dragging Condition.” After explaining and arguing for its use of the Dragging Condition, the essay argues that the Dragging Condition provides a general account of, and solution to, the counterexamples with which the essay began. The essay briefly discusses the relevance of the Dragging Condition to the recently much-discussed topic of “transmission failure” in epistemology, applies the Dragging Condition to the problem of “bootstrapping” in epistemology, and discusses three important objections to the view defended in the essay.

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