Can there be an alternative mathematics, really?
pp. 349-359
in: Michael H. G. Hoffmann, Johannes Lenhard, Falk Seeger (eds), Activity and sign, Berlin, Springer, 2005Abstract
David Bloor, already in 1976, asked the question whether an alternative mathematics is possible. Although he presented a number of examples, I do not consider these really convincing. To support Bloor's view I present three examples that to my mind should be considered as genuine alternative: (a) vague mathematics, i. e., a mathematics wherein notions such as 'small", "large" and "few" can be used, (b) random mathematics where mathematics consists (almost) solely of a practice, and (c) a mathematics where infinitesimals can be used without any problem, on the assumption that one is willing to work with local models only and to resist looking for global models. Finally, I argue that these examples support Otte's thesis that an ontology is constituted by a practice and not vice-versa.
