José Ferreirós: Arbitrary collections — a matter of logic?

Invitation pdf

José Ferreirós (Institute of Philosophy, CAS):
Arbitrary collections — a matter of logic?

Abstract
There is a long tradition of incorporating arbitrary collections into logic, by assuming that the 'standard' semantics of second-order logic comprises the full powerset of the domain. Similar ideas have been recently incorporated into plural logic. However, we will argue that such notions do not properly belong in logic strictly understood, originating as they do in the Cantor-Dedekind conception of the continuum. A proper understanding of second-order logic should thus be restricted.