Abstract

Pierre Gassendi, who did not like nonsense, said of the idea of infinity: ‘if someone calls something "infinite" he attributes to a thing which he does not grasp a label which he does not understand’. Gassendi’s is a harsh judgement for, surely, we all do quite cheerfully and successfully use the concept of infinity, and in a variety of contexts. Yet if Gassendi’s judgement is too hard it is easy enough to have sympathy with his claim. For it is a perennial fact that we never, in Descartes’s phrase, seem to have an ‘adequate idea’ of infinity. Nor is this just because it is an abstract noun like friendship or strength, for it retains this familiar lack of adequacy when it appears in its adjectival or adverbial forms: infinite space, infinite power, infinitely large, infinitely good. It is not my intention in this paper to offer a philosophical account of this familiar state of affairs, though perhaps what I shall have to say will throw some little light on the matter. It is rather to explore how discussions of such questions take us into issues at the heart of the foundations of modern philosophy, and specifically, into the great debate which I will refer to by the usual title as that between the Rationalists and the Empiricists, of whom the protagonists are traditionally identified as Descartes on the one side and Locke on the other. It would not be out of place for somebody to say in response to that famous contrast that either it is hackneyed or else it is mistaken. It is hackneyed because we all know that Descartes and Locke represent contrasting traditions in modern philosophy and there is nothing new to be said about it. It is mistaken because, as a matter of fact, it is simplistic to set them up as dogmatic exponents of their respective schools. There are rationalist elements in Locke’s Essay, especially in Book IV, and there is a strong empiricist element in Descartes, especially in his science. Those emphasizing the former, Webb for example in the last century and Aaron in this, have underlined the place of intuition and demonstration in Locke’s account of knowledge. Descartes’s empirical leanings have been noted in his account of the role of experiment in the natural sciences. There is of course no denying these aspects of their philosophies. But my path will be more revisionist than supportive of such readings of their work. I shall argue that the dominant (though not the only) strain in Descartes is a rationalist one and that Locke was keenly aware of this and strongly hostile to it. On the other side, whilst Locke was impressed by much of Descartes’s presentation of knowledge, and borrowed heavily from it, he never looks tike subscribing at all to the central rationalist doctrines, and indeed saw his work as a major refutation of them. In all of this his account of our idea of infinity plays an exemplary role. But before we reach Locke we should go back to Descartes.