Greek, Roman, Islamic, and Jewish Sources on Unequal Infinities

Abstract Chapter 1 contains a lengthy survey of the Greek, Roman, Islamic, and Jewish sources related to the existence of the actual infinite and to the topic of unequal infinities. It provides the evidence for claiming that, except for Ibn Qurra (ninth century ce), most discussions of the infinitely large in Greek, Roman, Islamic, and Jewish sources before the thirteenth century either denied the possibility of unequal infinities or were aimed, especially in some Islamic authors, at severely restricting what infinite multiplicities could be countenanced. There is no similar encompassing survey in the secondary literature which is thus already a contribution on its own. But in addition, the chapter is meant to provide the background against which to situate the medieval developments analyzed in the remaining parts of the book.