Skepticism, Math and Memory

Descartes thinks to himself “I’ve done plenty of math in my time, and though most of the time I do it very well, I have often made mistakes, miscalculations. Sometimes I’ve even been sure, upon reviewing my work, that I had done it all correctly, only later, upon reviewing it anew, to find that I had made mistakes which were now open and obvious to me. Perhaps even, on the rare occasion, I returned to review the matter a third time and became convinced once again that I had been right the first time around. All of this makes me think that I can in principle be wrong about even seemingly self-evident mathematical propositions like that 2+3=5. Therefore, I cannot take any mathematical proposition, even though it is clearly analytic, as indubitable.” At the present time, 2+2=4 is self-evident to me. Perhaps I remember doing a mathematical calculation wrong in the past. Should this lead me to conclude that I can be wrong about mathematical truths, or truths of logic? No, perhaps not. Perhaps at best what I can be skeptical of is my memory of ever having miscalculated anything. The evil demon, however powerful, cannot efface from my mind the self-evidence of analytic propositions under my immediate comprehension. Descartes thinks we could logically possibly be mistaken about a mathematical proposition even if it were fully understood (not mis-understood). I think that kind of universal possibilism is incoherent and literally unthinkable.

This analysis may just push the skeptical question back one step, though. After all, how do I know right now that I understand with full comprehension that Pv~P self-evidently? The same answer can be given though: it may just be self-evident to me that it is self-evident. It may be rational to doubt whether I have ever misunderstood an apparently self-evident proposition (i.e., taken a proposition as self-evident without it being so), but not rational to doubt what is now presented to my mind as a clear and distinct self-evident truth. Descartes thinks that it is because we have memories of experiences in which we recall encountering what seemed to us a self-evident proposition which turned out to be false, that we must concede the possibility of being wrong about any proposition which appears to us to be self-evidently true, but this more easily licenses skepticism with respect to those memories and experiences, however recent, than it does skepticism with respect to logical, mathematical, and analytic propositions.

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About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
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