**Topic:**

**Interconnections**

## The Concept of Mathematical Elucidation:

theory and problems

By José SeoaneThere is a contrast between concepts which may be treated in accordance with the criteria of mathematical rigor and concepts which are not susceptible of such a treatment. We will call theoretical concepts to the former and pre-theoretical to the latter. In mathematical world, sentences which relate theoretical and pre-theoretical concepts (in a determinated way) are denominated thesis; sentences which relate only theoretical concepts (in a determinated way) are denominated theorems. Elucidatory processes in mathematics have thesis as their principal output. I intend to establish in this paper that the introduction of the concept of mathematical elucidation has an important theoretical value to the effects of studying a certain special type of intended conceptual relation and a certain type of justificatory argumentation for it. The analysis of the contrast between thesis and theorems will allow us to construct a context where the interest for those conceptual relations and their supporting justificatory mechanisms arises naturally. Then, I will attempt to offer some structural features of mathematical elucidation qua conceptual relation and their impact on the strategies of elucidatory justification. This is what I grandiloquently call theory in the heading. I will suggest also a classification of the problems which a theoretical reflexion as the one proposed may contribute to clarify and I will make some brief observations on some paradigmatic examples of each one of the categories of the classification constructed. This work should be considered as a modest definition of a sort of research program.

Source: CLE e-prints