By Stephen Gaukroger (ed.)
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Extra resources for Descartes: Philosophy, Mathematics and Physics
It had been subordinated to the method, but could be read into any, and all, technical successes in mathematics and natural philosophy. And such success there certainly had been since 1619. Sometime between that date and 1625 Descartes had produced his construction for all the ‘solid’ problems of the ancients using only a circle and parabola. ^^ Working in the mathematical circles around Marin Mersenne, he was very much a rising star in the emerging community of French mathematical savants. ^^ One is led to suspect that Descartes could have continued on with his special studies, resting content in the apparent knowledge that his triumphs confirmed the method and instantiated his universal math ematics.
T h e retina, a sense organ receiving two-dimensional patterns of disturbance from the external world, would then have provided the model for the parallel construal of all senses. The removal of retinal patterns via the optic nerve to the brain would very plausibly be the model for the generalized account of the transmission of ‘figures’ ‘without the passage of any real entity’. The central metaphor of spiritual eyes applying themselves to patterns lodged in the brain substance would merely have generalized to all the senses the sort of account that would probably have had to be given of the psychology of vision, once the physical process had been rigorously mechanized.
Beyond all this there is a striking methodological unity in the vision of universal mathematics. The solution of any problem in any properly mathematical field is held to consist essentially in an unfolding in the imagination of relations holding among extensional measures of dimen sions. The art of unfolding those relations, to be given in an algebraic theory of equations, presumably holds for every properly mathematical field. To summarize, then, we may say that in rule 14 Descartes shows how straight lines and rectangular figures may function as symbols to be used in signifying any and all magnitudes which enter into a problem to be solved within universal mathematics.
Descartes: Philosophy, Mathematics and Physics by Stephen Gaukroger (ed.)