In its most general form, a diagonal argument is an argument intending to show that not all objects of a certain class C are in a certain set S, and does so by constructing a diagonal object, that is to say, an object of the class C so defined as to be other than all the objects in S. We revise three arguments inspired by the Russell paradox (an argument against Computationalism, an argument against Physicalism, and a counterargument to the Platonic One Over Many argument), extract its underlying structure, and suggest a criterion to tell the ones that end up at a paradoxical object like the old Russell set from the ones that could actually accomplish a diagonalization. We conclude with the suggestion that the use of logico-mathematical tools, which is a significant methodological contribution of the analytical tradition, opens up a promising line of research in metaphysics.