  G. E. Moore argued that ethical egoism is self-contradictory.  If I am an egoist, I hold that I ought to maximize my good.  I deny that others ought to maximize my good (they should maximize their own goods).  But to say that x is “my good” is just to say that my possessing x is good.  (I cannot possess the goodness.)  If my possession of x is good, then I must hold that others ought to maximize my possession of it.  I both deny and am committed to affirming that others ought to maximize my good. (Sometimes Moore suggests instead that “my good” be glossed as “x is good and x is mine.” This does not yield the contradiction above, since it does not claim that my possession of x is good.  But it yields a different contradiction: if x is good, everyone ought to maximize it wherever it appears; egoists hold that I ought to maximize x only when it appears in me.)