Sheep without SOL. The Case of Second-Order Logic

According to Quine, second-order logic (SOL) is set-theory in disguise. This claim has been disputed on solid grounds, in particular in the work by George Boolos on plural quantification. Nevertheless, since plural logic (PL) and SOL are equi-interpretable, they seem to provide equal alternatives. The picking of one over the other seems to rely merely on ontological (or at least broadly philosophical) preferences. In the present article, I am going to address a non-ontological argument for a distinction between PL and SOL. This argument will be grounded on the different mathematical applicability to set-theory that PL and SOL respectively show to have.