GENERICITY AND ARBITRARINESS

We compare the notions of genericity and arbitrariness on the basis of the realist import of the method of forcing. We argue that Cohen's Theorem, similarly to Cantor's Theorem, can be considered a meta-theoretical argument in favor of the existence of uncountable collections. Then we discuss the effects of this metatheoretical perspective on Skolem's Paradox. We conclude discussing how the connection between arbitrariness and genericity can offer arguments in favor of Forcing Axioms.