Hume and Descartes on skepticism with regard to demonstrative reasoning

Abstract

Commentaries on Hume's Treatise 1.4.1, "Of scepticism with regard to reason," have focused on the argument that an initial lack of certainty concerning the conclusion of an inference gradually diminishes to zero. In my view, Hume offers this famous argument only after, and as corollary to, a far more interesting skeptical argument concerning demonstrative reasoning, which occurs at the very beginning of Treatise 1.4.1. I focus on this neglected argument, point to its Cartesian roots, and draw a distinction between ordinary doubts and a radical skeptical doubt about the inevitable interference of fallible faculties in our demonstrative inferences. Hume suggests that, in common life and science, solutions to ordinary doubts concerning human fallibility themselves rely on causal reasoning-that we have applied inferential rules correctly in any given instance is a "matters of fact" conclusion, thus it is supported by the only kind of evidence that such a conclusion can have. Hume's argument brilliantly reverses the force of the increased confidence normally acquired on the basis of such causal reasoning. Once we have realized, in the radically skeptical frame of mind, that in our attempts to improve and evaluate demonstrative reasoning we use merely causal reasoning, there is no longer the hope of a progressive adjustment of the exercise of our faculties to an assumed objective validity of our demonstrative rules. The increase in assurance by causal methods only amounts to "the addition of new probabilities," and there is no gradual transition from probability to demonstratively certain knowledge. Hume thereby reaches a radical skeptical doubt regarding the possibility of our ever attaining genuinely certain demonstrative knowledge - and, unlike Descartes, he reaches this doubt without the external device of an all-powerful deceiver.