Social and material conditions for mathematics

Studiekreds i videnskabsteori. Ved adjunkt Mikkel Willum Johansen, IND.

Abstract

Mathematical knowledge has traditionally been taken to be absolutely objective, i.e. completely independent of contingent facts about the agents who discover the results. Today, this absolutistic view of mathematics has been challenged by a number of different theories. Most noticeably, social constructivists such as David Bloor and Donald MacKenzie have stressed the influence social factors have had on the development of mathematics, and Bloor simply describes mathematics as a social institution. Other theorists such as Rafael Núñez and George Lakoff have claimed mathematics to be embodied and fundamentally shaped by sensory-motor experience and certain particularly human cognitive strategies. I this paper we will report from a qualitative study of the practice of working mathematicians. The study shows that the production of mathematical knowledge is clearly conditioned both by social factors and by our experience of and ability to actively use the material world. Thus, the study confirms some of the basic ideas of the two approaches mentioned above. However, the study also gives reason to questions the reductionism inherent in both the social constructivistic and the embodiment approach. Mathematics cannot be reduced either to the social or to sensory-motor experience.

Nærmere information om seminaret kan fås ved henvendelse til centerleder Claus Emmeche.