Volume 5, Issue 1, 2005
Motivations for Realism in the Light of Mathematical Practice
The aim of this paper is to identify some of the motivations that can be found for taking a realist position concerning mathematical entities and to examine these motivations in the light of a case study in contemporary mathematics. The motivations that are found are as follows: (some) mathematicians are realists, mathematical statements are true, and finally, mathematical statements have a special certainty. These claims are compared with a result in algebraic topology stating that a certain sequence, the so-called Mayer-Vietoris sequence, has different properties when placed in different categories. The conclusion is that the before mentioned motivations should be modified and it is suggested that they could also be explained by a position claiming that mathematical entities are introduced by mathematicians.