David Hume and John Keill and the Structure of Continua

Abstract

In Part II of Book I of the Treatise of Human Nature David Hume discusses the alleged possibility of infinite divisibility of a continuum (extension). Hume's discussion is part of his examination of our ideas of space and time. The few scholars who have bothered to deal with Hume's discussion have generally followed the lines set out in the essential study of Kemp Smith.1 Hume's discussion of continuity is considered to be unsatisfactory to say the least, and it has become regarded as an answer to Bayle's treatment of the subject in the Zeno article in his Dictionnaire critique et historique.2 As a matter of fact, however, Pierre Bayle is nowhere mentioned by name in the Treatise, nor is it as clear as some scholars would like us to believe that Hume's account of continuity is formulated explicitly as an answer to Bayle's skeptical arguments.3 This is not to say that it is totally inconceivable that Bayle has been a source for Hume. It only means that one would have to state one's case more carefully than has been done in the past and that one should also certainly wish to take into account Bayle's Systeme de philosophie, in which one section is explicitly devoted to the