Mathematics as activity

Wenceslao J. Gonzalez

pp. 113-130

in: Teoria de la acción / Action Theory, Daimon Revista Internacional de Filosofia 3, 1991.

Abstract

What is Mathematics in itself? The Action Theory can contribute to answering this question following two directions: i) looking at mathematical activity; ii) puting the touchstone in this Science as activity, a type of action among others. In the first case, Mathematics receives a "direct study": the research is carried out in order to make explicit the features of an autonomous activity; in the second case, the investigation is made in terms of an "indirect study": it requires the connection and comparison with other actions. Firstly, the task is to clarify the distinction between mathematical activity and Mathematics as activity, using the duality "act" (the inner element) and "action" (the outer component) within the field of "activity". Secondly, the character of mathematical actions is studied: a) as meaningful activity, Mathematics needs a purpose; b) the status of mathematical actions is specific, different from the activities developed in other Sciences; and c) the "internal factors" have more weight than the "external factors" in Mathematics. Thirdly, the description of mathematical actions contributes to completing the feature of this specific activity.