A matemática, os princípios lógicos e o cogito: dúvida e certeza nas Meditações Metafísicas de Descartes - Rolim, Diógenes Rodrigues Moura (2021)
The development of doubt in Descartes' Meditations reaches its most radical level by undermining even the simplest truths in mathematics. Despite being a method based on reason, there were those who saw in cartesian doubt an insurmountable path, insofar as it would have compromised their own rational operations. Indeed, to doubt even the intuitive truths of mathematics would be to doubt intuition in general, which is the privileged form of reason. In our work, we propose a reflection on the limit of cartesian doubt based on the comparison between mathematical truths and logical truths. Why would it not be possible, due to the method's own conditions, to doubt the logical principles, whose guarantee is the intuitive evidence itself? Why is reason not at all compromised by the strength of a method that calls into question the exemplary product of reason, which is mathematics? To answer these questions, we analyze the development and the meaning of doubt in the Meditations, the clarifications made by Descartes mainly in the Replies to the Objections and Principles of Philosophy, as well as the meaning of the cartesian conception of mathematics and his understanding of the so-called common notions , which involve part of the truths considered undoubted.