The Cartesian Doubt Experiment and Mathematics :: Mathematics Math Mathematical Papers

The Cartesian Doubt Experiment and Mathematics ABSTRACT: The view that Descartes called mathematical propositions into doubt as he impugned all beliefs concerning common-sense ontology by assuming that all beliefs derive from perception seems to rest on the presupposition that the Cartesian problem of doubt concerning mathematics is an instance of the problem of doubt concerning existence of substances. I argue that the problem is not 'whether I am counting actual objects or empty images,' but 'whether I am counting what I count correctly.' Considering Descartes's early works, it is possible to see that for him, the proposition '2+3=5' and the argument 'I think, therefore I am,' were equally evident. But Descartes does not found his epistemology upon the evidence of mathematical propositions. The doubt experiment does not seem to give positive results for mathematical operations. Consciousness of carrying out a mathematical proposition, however, unlike putting forth a result of an operation, is immune to doubt. Statements of cons ciousness of mathematical or logical operations are instances of 'I think' and hence the argument 'I count, therefore I am' is equivalent to 'I think, therefore I am.' If impugning the veridicality of mathematical propositions could not pose a difficulty for Descartes's epistemology which he thought to establish on consciousness of thinking alone, then he cannot be seen to avoid the question. Discarding mathematical propositions themselves on the grounds that they are not immune to doubt evoked by a powerful agent does not generate a substantial problem for Descartes provided that he believes that he can justify them by appeal to God's benevolence. The question whether Descartes impugned veridicality of mathematical propositions via the arguments of the First Meditation is of epistemologically significance for an inquiry into the nature of Descartes' doubt experiment with a view to a plausible answer to this question may offer us clues to understand the nature of Cartesian theory of justification and the nature of foundationalistic epistemology in general. The evil genius hypothesis introduced in the last paragraph of the First Meditation does not seem to call veridicality of mathematical propositions into question: Descartes does not mention mathematical truths when he finalizes the setting of the doubt experiment. The text is ambiguous at this point and the reader is left ignorant whether simple truths of arithmetics or geometry are held exempt from doubt evoked by the evil genius hypothesis. Does this final tool of the doubt experiment put emphasis on the dubitability of judgments of common-sense ontology based on sense perception alone?