Immune Logics ain't that Immune

Da Ré and Szmuc argue that while there is a symmetry between ‘infectious’ and ‘immune’ logics, this symmetry fails w.r.t. extending an algebra with an immune or an infectious element. In this paper, I show that the symmetry also fails w.r.t. defining a new logical operation from a given set of primitive (Boolean) operations. I use the case of the material conditional to illustrate this point.