 However far his understanding of complex mathematics reached, he advanced a radical sceptical challenge for mathematics, and thereby he also undermined knowledge claims associated with demonstrative reasoning (Meeker 2007). The sceptical problem arises from the inexactness of geometrical ideas and the fallibility of our reasoning processes. Geometry for Hume is about actual figures and shapes whose ideas cannot be perfectly exact because our perceptual abilities are limited, and reasoning based on these ideas inherits this inexactness. Ideas relevant for arithmetic, i.e., numbers, do not suffer from this imprecision, but arithmetical reasoning is just as fallible as human reasoning in general. The outcome of our demonstrative reasoning must be judged by a probabilistic judgment on the reliability of our reasoning faculties, which in turn must be judged by a further probabilistic judgment on the probabilistic judgment on the reliability of our faculties. The apparent demonstrative certainty of our mathematical reasoning degenerates into probability, and we are left with fallible and uncertain conclusions even in our demonstrative sciences (THN 1.4.1.2–6).