The assessment of changing in mathematical ends in Maddy’s philosophy

Abstract

In Maddy’s philosophy, mathematics is autonomous, i.e., it is not subordinated to either science or philosophy. Mathematics establishes and pursues its own goals and must be judged on its own terms. This leads Maddy to admit, in Naturalism in Mathematics (1997) and also in Second Philosophy (2007), that, even if mathematicians choose to pursue a goal that could seem improper from the philosophical or scientific point of view, there is nothing to be done except accepting the new state of affairs. In Defending the Axioms (2011), nevertheless, Maddy changes her position regarding this issue. She claims to have found the basis from which to assess the adequacy of mathematical goals. From this basis, if mathematicians choose to pursue what seems to be an improper goal, the philosopher could claim that they are going astray. In this paper, I will review Maddy’s positions in these books; and, especially regarding Defending the Axioms, I will sustain that the institution of a permanent parameter for the judgment of mathematical goals goes against the alleged autonomy of mathematics and other important traits of her philosophy.

Keywords: Penelope Maddy, autonomy of mathematics, mathematical ends.