which an action, in its total effects, causes some pain but absolutely no pleasure, and (2) that in which, while it causes both pleasure and pain, the total quantity of pain is greater than the total quantity of pleasure. And of both these two cases I propose to speak, for the reason just explained, as cases in which an action causes an excess of pain over pleasure.
There remain two other cases, and two only, which are still theoretically possible; namely (1) that an action should cause absolutely no pleasure and also absolutely no pain, and (2) that, while it causes both pleasure and pain, the total quantities of each should be exactly equal. And in both these two cases, we may, of course, say that the action in question causes no excess either of pleasure over pain or of pain over pleasure.
Of absolutely every action, therefore, it must be true, in the sense explained, that it either causes an excess of pleasure over pain, or an excess of pain over pleasure, or neither. This threefold division covers all the six possible cases. But, of course, of any two actions, both of which cause an excess of
