BETWEEN PATHOLOGY AND WELL-BEHAVIOUR -- A POSSIBLE FOUNDATION FOR TAME MATHEMATICS.

An in-depth examination of the foundations of mathematics reveals how its treatment is centered around the topic of "unique foundation vs. no need for a foundation" in a traditional setting. In this paper, I show that by applying Shelah's stability procedures to mathematics, we confine ourselves to a certain section that manages to escape the Gödel phenomenon and can be classified. We concentrate our attention on this mainly because of its tame nature. This result makes way for a new approach in foundations through model-theoretic methods. We then cover Penelope Maddy's "foundational virtues" and what it means for a theory to be foundational. Having explored what a tame foundation can amount to, we argue that it can fulfil some of Maddy's foundational qualities. In the last part, we will examine the consequences of this new paradigm -- some philosophical in nature -- on topics like philosophy of mathematical practice, the incompleteness theorems and others. [ABSTRACT FROM AUTHOR]