Truth in Mathematics: The Question of Pluralism

摘要: The discovery of non-Euclidean geometries (in the nineteenth century) undermined claim that Euclidean geometry is one true and instead led to a plurality no which could be said (without qualification) “truer” than others. In similar spirit many have claimed independence results for arithmetic set theory twentieth has there or we are left with systems can this chapter I will investigate such pluralist conceptions theory. begin an examination what perhaps most sophisticated developed version view date—namely, Carnap in Logical Syntax Language—and argue approach problematic pluralism involved too radical. remainder question it would take establish more reasonable pluralism. This involve mapping out some mathematical scenarios (using recent proved jointly Hugh Woodin) arguably maintain been secured.