Emergenza, Evidenza, Conseguenza logica

This paper aims at analyzing from a philosophical point of view the concept of logical consequence, in order to highlight the connection between different kinds of consequence relations and between such relations and the intuitions in virtue of which they are introduced. The topics and theorems that are discussed are well-known. Still, their philosophical significance for the epistemological debate is not fully acknowledged. In what follows, the basic idea is developed according to which the kind of intuition that allow us to justify the introduction of the second order consequence relation is essentially different from, and emergent with respect to, the kind of intuition that allow us to justify the introduction of the first order consequence relation. In particular, this difference is based on the evidence of the existence of sets that are not definable by presenting a property shared by all their elements.