It is only by exaggerating the difference between within and without, above and below, male and female, with and against, that a semblance of order is created... (Mary Douglas, Purity and Danger)
Mathematics imposes a semblance of order on a chaotic world through generalisation and categorisation, or what Judith Butler might describe as, ‘that dreary binary of same and other’. But to what extent does mathematical thinking lead to false categorisations, or false binaries?
Postmodernism describes a world of inherent uncertainty, of categories with permeable boundaries, which change over time. Many binary formulations have fragmented and proliferated to the point where the binaries themselves are revealed as contingent.
Fundamental constructs such as ‘gender’, previously thought as described by a set of attributes, have been found to constitute the 'identities' they were purporting to describe. We are witnessing seemingly limitless proliferation whereby certain generalisations may no longer be useful or descriptive. Could mathematical thinking be more harmful than helpful?
It is not only the mathematical tendency towards (false) generalisations that might be problematic. To what extent does the axiomatic, deductive nature of mathematical thinking affect our view of self and others? Might it lead to a belief that there are ‘natural facts’ on which our 'identities' are fixed?
In so doing, might it serve to reinforce the distinction between I and not-I, between us and them?