Bergson on number. Issue 1 (2nd January 2021) - Watt, Robert
ABSTRACT: This article reconstructs Henri Bergson's argument at the beginning of the second chapter of his Essai sur les données immédiates de la conscience for his view that every idea of number involves space. It begins by criticizing previous interpretations of this view. Most controversially, it argues that Bergson's view specifically relates to our ideas of what Bertrand Russell calls 'pluralities', i.e. particular trios, quadruples, etc., and not to our ideas of 'abstract numbers' such as 3 and 4. The article goes on to elucidate the premises of Bergson's argument. It concludes that the first step in the argument is either invalid, or it turns on a premise that is plainly false, depending on how a particular scope ambiguity is resolved. It suggests that the second step in Bergson's argument turns on the assumption that space and time differ in the following respect: while it is impossible for the same thing to be wholly present at different spatial locations, it is perfectly possible for the same thing to be wholly present at different temporal locations.