In general, Hume takes men's propensities towards approval and disapproval as given. His aim is to explain them, not to justify or criticise them. Yet his own rejection of religion has obvious critical implications for conventional morality. If there is no God, and no life after death for him to reward or punish us in, this must have a bearing on the utility of our actions. Bentham acknowledged a great indebtedness to Hume but he put his ethical inheritance to critical uses that formed no part of the intentions of his benefactor. Where Hume sought to show that ordinary, unreflective morality has a rational foundation of which men are largely unaware, Bentham put this rational foundation to work as an instrument for the radical criticism and reformation of ordinary morality.
(Anthony Quinton, Utilitarian Ethics, New Studies in Ethics, ed. W. D. Hudson [New York: St. Martin's Press, 1973], 22)
Note from KBJ: Hume and Bentham made different uses of utilitarianism (the Greatest Happiness Principle). Hume, the conservative, used it to explain, and thereby to rationalize, conventional morality. Bentham, the progressive, used it to criticize, and thereby to change, conventional morality. Hume put utilitarianism to constructive uses; Bentham put it to destructive uses. Henry Sidgwick is the intellectual heir of Hume; Peter Singer is the intellectual heir of Bentham.
Note 2 from KBJ: Another way to put it is that, for Hume, utilitarianism was a positive theory, whereas, for Bentham, it was a normative theory. See here for the difference between positive and normative theories.
