Cartesian Deduction

Abstract
The objective of the article is twofold: to advance an interpretation of Descartes’ position on the problem of explaining how deduction from universal propositions to their particular instances can be both legitimate and useful for discovery of truth; and to argue that his position is a valuable contribution to the philosophy of logic. In Descartes’ view. the problem in question is that syllogistic deductions from universal propositions to their particular instances is circular and hence useless as a means for discovery of truth. Descartes’ solution to the problem is to claim that noncircular, useful deduction from the universal to the particular must first be based on deduction from particular truths to particular truths. I examine previous interpretations of Cartesian deduction given by E.M. Curley, Bernard Williams, and Andre Gombay. None of these interpretations fit with all of Descartes’ criticisms of syllogistic deduction and his characterization of useful and legitimate deduction (such as the cogito). I argue that the key to a correct interpretation is Descartes’ claim that implicit knowledge of universal propositions plays a crucial role in useful and legitimate deduction, and I explain how we may cash in his talk of implicit knowledge through Ryle’s notion of knowing how. Having set out a fuller explication of Descartes’ theory of deduction, I argue that it is consistent with the way people actually reason, that it helps us with problems in the philosophy of logic that have been raised by John Stuart Mill, Hilary Putnam, and Michael Dummett
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