Volume 25, 2008
Philosophy of Mathematics
Yvonne Raley
Pages 108-127
Jobless Objects: Mathematical Posits in Crisis
This paper focuses on an argument against the existence of mathematical objects called the “Makes No Difference Argument” (MND). Roughly, MND claims that whether or not mathematical objects exist makes no difference, and that therefore, we have no reason to believe in them. The paper analyzes four different versions of MND for their merits. It concludes that the defender of the existence of mathematical objects (the mathematical Platonist) does have some retorts to the first three versions of MND, but that no adequate reply is possible to the fourth, and most crucial, version of MND. That version argues that mathematical objects make no difference to our epistemic processes: they play no role in the process of obtaining mathematical knowledge.