The Aprioristic Tendency and Experience

Abstract

In spite of everything, it is certain that many scientists (as we were able to verify personally during an interview with one of the most distinguished mathematicians of our time) are likely to be shocked when someone tries to demonstrate the strict analogy between the modern system and that of Descartes, an analogy we developed in Chapters 10 and 11. Is this reaction entirely unjustified? Not at all. It stems from the fact that the relativist is aware of the formidable obstacles the theory had to overcome, of the really extraordinary audacity Einstein needed to conceive the paradoxical idea of assimilating inertia and gravitation, of the wealth of ingenuity his mathematical genius had to display in order to achieve this assimilation, starting from the accumulated results of some of the most illustrious mathematicians who had preceded him and then employing dazzling feats of analysis. He knows too what a prodigious number of efforts nineteenth century physicists had to bring into play to unify what used to be called the diverse forces of nature, thus permitting Weyl and Eddington to attempt a geometrical deduction of the whole of physical reality by the reduction of electrical phenomena to space. How could Descartes, no matter how great his mathematical genius, pretend to arrive at an analogous result with only the resources of quite elementary analysis at his disposal?₁ Is it not more likely that he gloried in an altogether chimerical accomplishment, that he was, in short, the victim of a pure and simple illusion?