‘Powerless to separate from the clouds’: Badiou, mathematics and geography

ABSTRACT

Alain Badiou’s work provides an important opportunity for critical human geographers to enhance our grasp of a range of abstract mathematical concepts while clarifying that toward which we must remain critical. Yet the geographical encounter with Badiou thus far has been needlessly hampered by, and has itself reinforced, a certain pessimism about the ability of qualitatively-trained geographers to deal in any meaningful way with his mathematical arguments. Challenging this pessimism, the present paper argues that if we trust ourselves a bit more to think through, with, and against mathematical concepts, we can in fact learn a great deal from Badiou. To illustrate this claim, the paper draws upon mathematical dimensions of Badiou’s arguments – as well as some ideas from Gestalt theory – to highlight failures both of his ontological and of his phenomenological projects. In light of the latter failure, however, Badiou’s mathematical concepts suggest the possibility of an analysis of qualitative geographical phenomena that both retains a place for subjectivity and leaves space for the recognition of ‘proto-quantitative relations’. The paper closes by suggesting how Badiou’s abstract mathematical concept of the ‘transcendental’ can help to understand the manipulative production of space in twenty-first century capitalism.

KEYWORDS:

• Badiou
• mathematics
• Gestalt theory
• transcendental
• subjectivity
• proto-quantitative relations

Acknowledgments

The author would like to thank two reviewers and especially Chris Philo for transformative and insightful suggestions. Thanks also to Lucas Pohl for the original impetus to write an earlier version of this paper. All errors and omissions are my own.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Badiou’s analysis of this landscape in terms of its ‘transcendental’ is examined in detail, though for different purposes, in Hannah, 2021. The account offered here closely parallels this earlier account in parts, and relies (unavoidably) upon some of the same passages in Badiou. However the distribution of emphasis is somewhat different.

2 As of this writing, the third and final volume of the trilogy, translated into English as The Immanence of Truths (Badiou, forthcoming 2022), has not yet appeared.

3 I am grateful to Chris Philo for alerting me to the central role of William Kirk in introducing geographers to Gestalt theory.