~a
AT” ~a
AT”’ (AWP & AU & APDM)
~AD
with falsum a contradiction or falsehood and ~ the negation sign. If something leads to a contradiction, then we conclude to the falsehood of the assumptions themselves.
There is a Kantian distinction between technical, pragmatic and moral (categorical) imperatives. Utility, as commonly regarded by economists, likely is of the pragmatic kind. Interestingly, theorists on morality have developed something called ‘deontic logic’, which appears to give many similar results as economic theory. Deontic logic however applies to propositions and not to commodity domains. It is possible, though, to integrate all these kinds of preferences into an integral utility index, when we replace a point x in the commodity domain by a statement “The state of the world is x”. This integral utility index likely would be lexicographic, in that some moral and constitutional issues might dominate pragmatic results in the commodity domain. Thus, while we would use the same symbols R, P and I, we would need to look into the structure of the index to find the Kantian distinction as made by the particular agent. We conclude that we can usefully introduce and apply some terms from deontic logic. Define:
Ap
