A Performative Interpretation of Mathematics
摘要
My performative interpretation of mathematics is inspired by a performative interpretation of language. I elaborate on this interpretation by discussing language as description, mathematics as description, language as performance, and mathematics as performance. The descriptive interpretation of language reflects a conception of reality as being “out there” waiting to be depicted. This interpretation has been expressed by the picture theory of language turning into a descriptive interpretation of mathematics, as formulated by Wittgenstein. Originally, the performative interpretation of language was elaborated within analytic philosophy, but it developed profoundly through discourse theory. A discourse forms our experiences, knowledge, ideas, assumptions, preconceptions, superstitions, and ideologies. It forms categories for understanding as well as for misunderstanding. Like discourse, mathematics forms our experiences, knowledge, ideas, assumptions, preconceptions, superstitions, and ideologies. It also forms categories for understanding and misunderstanding. Mathematics forms our worldviews, and also our life-worlds.