In ordinary life we may say, " All men are mortal," " All centaurs are figments," " All square circles are impossibilities," " All candidates arriving five minutes late are fined " (the last proposition being an example of the identification of categorical with hypothetical in Keynes's Formal Logic).
That to fit the actions and distances covered by Alexander into such a scheme, assuming that he went by Seistan and Kandahar, would involve physical impossibilities has been pointed out by Count Yorck v.
Given perfect information, frictionless markets, and other theoretical impossibilities, a finite amount of utility can be achieved in that way.
How would you define impossibilities? Add your definition here.