Mathematical Variables as Indigenous Concepts

Abstract

This paper explores the semiotic status of algebraic variables. To do that we build on a structuralist and post‐structuralist train of thought going from Mauss and Lévi‐Strauss to Baudrillard and Derrida. We import these authors’ semiotic thinking from the register of indigenous concepts (such as mana), and apply it to the register of algebra via a concrete case study of generating functions. The purpose of this experiment is to provide a philosophical language that can explore the openness of mathematical signs to reinterpretation, and bridge some barriers between philosophy of mathematics and critical approaches to knowledge.

Acknowledgements

Part of this work was done while I was visiting at Boston University’s Center for the Philosophy of Science, and an early draft was presented in the Eighteenth Novembertagung at the University of Bonn. I would like to thank the institutions involved for supporting my research.

The anonymous reviewer of this paper raised, among various useful remarks for which I’m grateful, the following questions: ‘Is there a certain particular mathematical specificity to the working of Derrida’s “secrecy” in mathematics? In other words, how are the workings of Derrida’s “secrecy” different in mathematics than in other domains? And how does this specificity affect and make possible the technical aspects of mathematics? … is mathematics a special field, which might, for example, prevent the possibility of metaphors in the strict sense, or would distinguish the way structures work in algebra as opposed to the case of indigenous magic concepts?’ I could not consider these questions in this text, but I would like to highlight them as important questions for future research.

Notes

[1] One example is the replica trick, used by statistical physicists, which, in a sense, takes an integer valued variable, and then makes it converge to zero; see Mezard, Parisi, and Virasoro (1987) and Talagrand (2003).

[2] For a different discussion of productive ambiguities in mathematics see Grosholz (2007).

[3] I use this term in the sense of Deleuze and Guattari (1987).

[4] Derrida comments on Lévi‐Strauss in Derrida (1976), where he also remarks on algebraic writing. The not necessarily fulfilled potential of algebraic writing to undermine logocentrism is also mentioned in Derrida (1981, 35). For the path I’m following here, however, I found it best to draw on Derrida’s later work, where his notion of writing ‘springs off the page’ into a less obviously textual world.

[5] For a comparison between Derridean indecision and the mathematical/logical concept related to the work of Gödel and Turing see Plotnitsky (1994, 214–223). For an analysis of the semiotic undecidability enabling Gödel’s incompleteness theorems see Wagner (2007; 2008).