Logic, Computation and Philosophy

Abstract

The great attraction of the deductive method is that it serves to «divide and conquer». By breaking a proof into minute steps, difficulty gives way to complexity the comprehension of which usually requires a lower order of intellectual capacity. In the words of Descartes, « For whenever single facts have been immediately deduced the one from the other, they have been already reduced, if the inference was evident, to a true intuition. But if we infer any single thing from various and disconnected facts, often our intellectual capacity is not so great as to embrace them all in a single intuition; in which case our mind should be content with the certitude attaching to this operation. It is in precisely similar fashion that though we cannot with one single gaze distinguish all the links of a lengthy chain, yet if we have seen the connection of each with its neighbour, we shall be entitled to say that we have seen how the first is connected with the last. »

First published in L’âge de la science,vol. 3, pp 101–115. Editions Bordas, 1971. Reproduced by permission of the author.