Abstract

In this chapter, we look at how philosophical standpoints widely held by mathematicians, conventionalism, and logical positivism were brought about through works of mathematicians. Starting from Poincaré’s philosophical ideas, we try to understand philosophical ideas of two mathematicians in the Vienna Circle, Hans Hahn and Karl Menger, through their mathematical works. After that, we also touch upon a problem about the relationship between natural science and mathematics, which the Vienna Circle left unsolved.