The hermeneutic problem in Pólya's mathematical heuristic
In my paper, I intend to reflect on Pólya's mathematical heuristic from the hermeneutic point of view of understanding and interpretation.
The essence of the hermeneutic problem: how can we understand a text - or a piece of art, a paper of philosophy... - which has its own context of meaning, while we are thinking in terms of a different context. How can we interpret it in this different context in a correct way? How does this happen? How is it possible at all?
To put it into the case of mathematics: how one understands a problem and gives a mathematical interpretation to it?
There is a tension in putting the problem into this form, because Pólya's heuristic is an inheritor of the method-oriented philosophies (e.g. Descartes's Regulae), while hermeneutic philosophers emphasized the limitations of the rational, method-based approach to finding the truth.
However, my aim is to show that there is a connection between the two approaches. There is a place for hermeneutics in Pólya's heuristic. One can dialogue with the text, face to the problem of application, and there are hermeneutic circles of understanding mathematical problems.
On the other hand, it means that Pólya's heuristic can be used to understand philosophical problems and texts as well.
