Mathematics and values

Abstract

There is a widespread perception that mathematics is objective and value-free and that values only enter into mathematics subjectively in the personal preferences of mathematicians. In this paper I argue that, on the contrary, mathematics itself is value-laden; imbued with epistemological, ontological, aesthetic and ethical values. I identify a range of values including truth, universalism, objectivism, rationalism, objectism and ethics, including utility, and purity, that permeate mathematics. Although some of these are accepted there is controversy both as to whether these are indeed values of mathematics, or whether, such as in the case of truth, universalism and objectivism, these are simply necessary concerns or properties of mathematics. I argue that values are indicated by preferences expressed and choices made in terms of beliefs and underlying frameworks. The initial choice of the framework of absolutism and its underlying assumptions is not forced upon us by necessity. Once this choice is made a consequence is that mathematics is ethics-free and largely values-free. However, other choices of more humanistic philosophies of mathematics lead to the conclusion that mathematics is imbued with ethical values, including openness, fairness, democracy and that even pure mathematics is implicated in human well-being and is therefore imbued with ethical values.