BETWEEN PATHOLOGY AND WELL-BEHAVIOUR – A POSSIBLE FOUNDATION FOR TAME MATHEMATICS
DOI:
https://doi.org/10.24193/subbphil.2022.sp.iss.04Keywords:
foundations of mathematics, tame mathematics, clarity-based knowledge, philosophy of mathematical practice, incompleteness theoremsAbstract
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.
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