Descartes is (in)famous for his apparent skepticism. While he was merely rehearsing the common Pyrrhonist skepticism, most famously being advocated by Michel de Montaigne and Mersenne, before criticizing it. In doing so he asks us to doubt two categories of beliefs: that of the extramental world (I refrain from using the word “physical” for separate reasons) and of mathematical facts. His reasons for doubting both categories were different. But first, let us look at why do we find these beliefs to be self-evident.
I believe that my dog is sitting in front of me because my sense tells me that he is. But my senses do, from time to time, deceive me, for example in the case of optical illusion and under the influence of psychoactive drugs. So this method of acquiring belief is generally put into doubt – although many individual believes might still be true but the senses generally lose their credibility as a source of self-evident believes. And in the case of mathematical facts, we find them to be true because they are tautologies – i.e. they are true by virtue of their definition, or at least because they are true by demonstration of proves. Also, these are not claims about the external world, Pythagoras theorem will still be true even if there is no external world and no physical triangles. Descarte gives two reasons to doubt these mathematical beliefs (Point 5, Part 1, Principles of Philosophy and Book 1, Meditations.) First, he merely states and in my opinion without giving any convincing examples to the effect that we often err while forming mathematical beliefs, and second, that God has created us in such a way that we err sometimes so it is possible that he might have created us in a way that we err all the time, even in things mathematical. The second argument can be made without invoking God as evolution might as easily have organized our cognitive faculties in such a way that we systematically err.
While to doubt the first source of beliefs seems reasonable, the second looks less convincing as it is on the one hand a general claim about all cognitive faculties and not merely about the method of acquiring mathematical claims, and on the other, we have no examples that lead us to doubt the specific source of such believes. Whatever their merit, it is clear that the epistemological value of the reasons to doubt both categories is very different.
