4.0411 If we tried, for example, to express what is expressed by “(x) . fx” by putting an index before fx, like: “Gen. fx”, it would not do, we should not know what was generalized. If we tried to show it by an index g, like: “f(xg)” it would not do—we should not know the scope of the generalization.

If we were to try it by introducing a mark in the argument places, like “(G, G) . F(G, G)”, it would not do—we could not determine the identity of the variables, etc.

All these ways of symbolizing are inadequate because they have not the necessary mathematical multiplicity.