Cartesian Logic by Stephen Gaukroger

By Stephen Gaukroger

This publication offers with a formerly missed episode within the historical past of good judgment and theories of cognition: the way conceptions of inference replaced in the course of the seventeenth century. Gaukroger specializes in the paintings of Descartes, contrasting his rationalization of inference as a right away seize in accord with the traditional gentle of cause with the Aristotelian view of inference as a discursive procedure. He bargains a brand new interpretation of Descartes' contribution to the query, revealing it to be an important enhance over humanist and overdue Scholastic conceptions, and argues that the Cartesian account performed a pivotal function within the improvement of our figuring out of the character of inference.

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355-356: "Having shown that the proposition saying that a generated thing is indestructible implies that that thing has the capacity of contraries' belonging to it at the same time, he goes on immediately to raise the objection that can be brought against this line of reasoning. That which is both generated and indestructible has the capacity of not being in the direction of the past, since it was non-existent before being, and the capacity of being in the direction of the future, since it is supposed indestructible.

7, note 10). , I, 23, 41"23-30. This example is used by Aristotle in the De Caelo, I 11 281°7. Mp). Since T contains L(p D q) D (Lp 3 Lq) and the rule of necessitation, it is normal. Hence given p 3 Mp (Hughes & Cresswell TH1), it follows that p = p • Mp, and since T is normal, Mp = M(p • Mp) (Note of B. Graham). 8 This latter illegitimate conclusion would be stronger than the premise. It would result in a sophism in the distribution of the modalities. Consequently, whenever a reasoning by realization is employed to demonstrate not the intrinsic impossibility of a thing, but rather the logical incompatibility between the possibility of one thing and the reality of another, simple application of the principle that the impossible does not logically follow from the possible is not enough.

Themistius, in a subtle passage of his Commentary, lays down the principle and shows the absurdities that its denial would entail. To allow perishable substances to transgress their essence and accede to immortality and indestructibility would be to destroy the very limits that define the nature of things and to make contrary capacities persist indefinitely. "As the generable and the perishable are not so by chance and by fortune, it is seen that they are so by nature. Indeed, all that there is is either by nature or by chance-for we leave aside here that which art produces; but all natural things maintain (custodiunt) the capacities that are proper to them.

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