What’s the Point of Complete Rigour?

Abstract

Complete inferential rigour is achieved by breaking down arguments into steps that are as small as possible: inferential ‘atoms’. For example, a mathematical or philosophical argument may be made completely inferentially rigorous (‘atomized’) by decomposing its inferential steps into the type of step found in a natural deduction system. It is commonly thought that atomization, paradigmatically in mathematics but also more generally, is pro tanto epistemically valuable. The paper considers some plausible candidates for the epistemic value arising from atomization and finds that none of them fits the bill. In particular, atomized arguments do not ground the correctness of their unatomized counterparts; they are typically not credence-preserving; and they need not reveal the source of inferential disagreement. The moral this suggests is that complete rigour is not even a defeasible epistemic ideal.