A performative interpretation of mathematics - Skovsmose, Ole [UNESP] (Springer Nature, 2023)
Inspired by a performative interpretation of language, a performative interpretation of mathematics is suggested. According to this interpretation, any form of mathematics is intrinsically linked to potential or actual actions. This interpretation is elaborated upon with respect to both advanced mathematics and school mathematics. It is highlighted that any kind of mathematics exercises a symbolic power, which brings to the forefront the ethical dimension of a philosophy for mathematics. Any kind of action is in need of ethical reflections and so specifically are mathematics-based actions. The ethical reflections concern the possible impact of mathematics, the different groups of people that might be affected by such actions, the possible acting subjects that might be hidden behind the curtain of mathematics, and the possible intentions behind the action and the ethical reflections themselves. Taken together, ethical reflections concern how symbolic acts rooted in mathematics might form our life-worlds.
Keywords: Ethical reflection; Formalism; Intuitionism; Life-world; Logicism; Mathematics in action; Performative interpretation of language; Performative interpretation of mathematics; Philosophy of mathematical practice; Symbolic power