Suppose we say that a Malin génie is causing us to have the experience of thinking that we are correct when we calculate that three times three is thirteen. Descartes in this way wishes to cast doubt on our confidence with respect to even apprehending mathematical truths which appear tautological. I want to suggest, however, that, in rethinking it, it is not logically possible that somebody be fooled into thinking that ‘3×3=13’ is true, since all that is required to understand that it is false is an understanding of the terms (three and thirteen) and connectives (times and equals) in the sentence. Thus, no demon can fool us into thinking that 3×3=13, but rather can only fool us into thinking that our miscalculation is a proper apprehension of the terms and connectives in the proposition. Once a proposition of this nature is grasped clearly and distinctly it is literally not logically possible for us to be wrong about it.
Consider alternatively a logical truth such as ~~(Pv~P); it is pretty clear that all which is required for a knowledge that this proposition is true is an understanding of the terms and the connectives. Is it logically possible that we are wrong to think that ~~(Pv~P) is true? No, it is not. It is only logically possible that we can mis-apprehend the terms and connectives in such a way as to literally mis-understand the proposition itself. Some propositions, therefore, once grasped, have to be recognized as self-evidently true, and we can even say contra the skeptic that we know them with deductive closure because it is not logically possible that we be wrong about them – only it is logically possible that we do not have them in mind. Once we do have them in mind, however, it follows that we cannot be wrong about them.
Even an evil Demon cannot fool us into thinking that ‘2+2=4’ is false, but can only confuse our apprehension of the terms and connectives.
Maybe it is worth noting that my presumed model of mind is not a composite computing object (like the brain), but a simple substance with fundamentally simple apprehension.