Pluralism and Together Incompatible Philosophies of Mathematics

Abstract

In this chapter, the pluralist arbitrates between two philosophical positions: the extensionalist and the constructivist. Both are anti-realists of a sort. The extensionalist position is that of Quine, and is represented by Bar-Am. The constructivist position is that of Sunholm and Martin-Löf. The two merit comparison because they both give a sensitive account of the history of logic, moreover, they give much the same account. The two positions differ on their final judgment of the modern trend. The extensionalist sees progress where the constructivist sees emptiness. To draw out the differences, we shall also meet the formalist and the realist. We shall see the accord and disaccord between these positions, especially in respect of their attitude towards logic.