Hermeneutyka intuicji matematycznej
Hermeneutics of Mathematical Intuition

Summary/Abstract: In this article, we propose a hermeneutic analysis and approach to mathematical intuition, briefly highlighting differences from strictly phenomeno- logical approaches (Husserl, Ingarden). We analyse various ways in which math- ematical intuition manifests itself, including the use of intuitive concepts—which are informal yet active in the creation of mathematical knowledge—and back- ground knowledge. Furthermore, we contrast intuitive actions with those strictly determined by the rules of formalised theories, and we point to the use of intui- tive models. Mathematicians operate within a horizon of implicit and unspoken assumptions that form a hermeneutic horizon, even when they attempt to codify mathematical theories in a strictly formalised manner, and hermeneutics methodi- cally reconstructs this background knowledge. An analysis of historical case stud- ies reveals that such horizontal implicit components of mathematical knowledge are always present in the development of mathematics. They usually take the form of ontological and structural presuppositions that influence the shape of the formalisation employed.

• Details
• Contents