Introduction

The profound transformation that mathematics underwent in the late nineteenth century led to its emergence as the abstract science we know today. This transformation was driven by the use of abstract notions and the adoption of infinitary methods. One of the most unexpected consequences of employing such powerful methods was the discovery of set-theoretic and logical paradoxes. These paradoxes revealed that abstract mathematical reasoning could lead to contradictions, indicating that infinite mathematical objects should be approached with caution. It became clear that their scope of application and existence needed to be precisely defined to avoid contradictions.