Sub specie aeternitatis

Abstract

The formalization of pre-theoretical notions is not a science, but an art. This becomes evident when we have to decide what is indispensable and what is essential in the transition from the intuitive to the formal. I exemplify this type of difficulty with the formalization of an intuitive notion of a finite collection of objects. The observance of greater fidelity to the pre-theoretical notion, even if unnecessary from a formal perspective, resulted in two new definitions of finite set.