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Mills says that utilitarianism cannot be proven because it is impossible to prove first principles. First principles are the foundation of arguments. They are not fact that can be tested, but rather represent the system in which those facts make sense. Thus, since utilitarianism is an argument for utility as a first principle, it cannot be proven in the traditional sense. However, Mill also argues that utilitarianism can be proven in a broader sense; we do not have to arbitrarily choose first principles. Rather, it is possible to deliberate on reasons in favor and in opposition to given principles. Thus, in his essay Mill attempts to provide considerations (as opposed to proofs) in favor of utilitarianism. Mill argues that we desire the things we do because they are a means to happiness or are included in our definition of happiness.
Happiness must be understood broadly, as including such general concepts as the flourishing of human culture, and the acquisition of those things that we desire. Mill says that the reader must decide for himself if this account is plausible. However, even if this account is correct, Mill does not show that people should be concerned with general happiness instead of their own. Mill simply assumed this idea because he believes that morality must be impartial between all people. His failure to “prove” this would seem to weaken his argument, however.
