Abstract

© 2013 The Editors of The Philosophical QuarterlyWhy did matter matter for Descartes and Leibniz? The answer, Kurt Smith argues in this thought‐provoking book, is that without it mathematics would be unintelligible. A world without matter is insufficient for mathematics because the immaterial cannot be divided into discrete quantities. Without a divisible material structure, the determinate unities necessary for the additive quantities in turn necessary for mathematics are unactualisable. God needs matter to institute mathematics. However, with the creation of matter, mathematical intelligibility necessarily follows. Smith's main aim, therefore, is to show that Descartes and Leibniz believed the biconditional: ‘Mathematics is intelligible if, and only if, matter exists’.The bulk of the book is dedicated to ‘analysis’ and ‘synthesis’. For Smith, analysis is a kind of transcendental process by which one discovers the basic conceptual categories necessary for the possibility of any object under investigation. A triangle's...