Abstract

The last two decades or so have borne witness to a modest revival of interest in the possibility that numerical relations are, at bottom, perceived properties or relations of some sort. In an earlier era writers as divergent as J. S. Mill and Edmund Husserl pursued just such a possibility, only to be swept out of the mathematical mainstream with a battery of broadsides from Gottlob Frege. Despite more recent arguments that numerical understanding is somehow derived from experience, however, no analysis of quantitative perception yet offered seems able to account adequately for the perception of arithmetical equations as simple as 1 + 2 = 3. Without a satisfactory analysis of “equality”—clearly, the pivotal relation in arithmetic—we can expect the possible empirical foundations of mathematics to continue to be generally ignored.