It has been alleged that, contrary to the assumptions in Pareto's Manual, the ability to compare first-differences of utility implies cardinality. It is shown here that the validity of this theorem hinges critically on the framework of analysis. In the framework of the thirties it is valid because of the implicit use of an ‘unrestricted domain’ assumption. In the modern choice-theoretic context it is not in general true but it becomes valid if utility functions are continuous and are defined on a connected topological space.

It has been known that, in aggregating infinite utility streams, there does not exist any social welfare function, which satisfies the axioms of Pareto, intergenerational equity, and continuity. We show that the impossibility result persists even without imposing the continuity axiom, and in frameworks allowing for more general domains of utilities than those used in the existing literature.