In Gillian Russell & Greg Restall (eds.), New Waves in Philosophy of Science. pp. 112-141 (2012)
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Less discussed than Hume’s skepticism about what grounds there could be for projecting empirical hypotheses is his concern with a skeptical regress that he thought threatened to extinguish any belief when we reflect that our reasoning is not perfect. The root of the problem is the fact that a reflection about our reasoning is itself a piece of reasoning. If each reflection is negative and undermining, does that not give us a diminution of our original belief to nothing? It requires much attention to detail, we argue, to determine whether or not there is a skeptical problem in this neighborhood. Consider that if we subsequently doubt a doubt we had about our reasoning, that would suggest a restoration of some of the force of our original belief. We would then have instead of runaway skepticism an alternating sequence of pieces of skeptical reasoning that cancel each others’ effects on our justification in the original proposition, at least to some degree. We will argue that the outcome of the sequence of reflections Hume is imagining depends on information about a given case that is not known a priori. We conclude this from the fact that under three precise, explanatory, and viable contemporary reconstructions of what this kind of reasoning about reasoning could be like and how it has the potential to affect our original beliefs, a belief-extinguishing regress is not automatic or necessary
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