Well, then, the first step by which Mill has attempted to establish his Hedonism is simply fallacious. He has attempted to establish the identity of the good with the desired, by confusing the proper sense of desirable, in which it denotes that which it is good to desire, with the sense which it would bear if it were analogous to such words as visible. If desirable is to be identical with good, then it must bear one sense; and if it is to be identical with desired, then it must bear quite another sense. And yet to Mill’s contention that the desired is necessarily good, it is quite essential that these two senses of desirable should be the same. If he holds they are the same, then he has contradicted himself elsewhere; if he holds they are not the same, then the first step in his proof of Hedonism is absolutely worthless. (§ 41 ¶ 1)

But now we must deal with the second step. Having proved, as he thinks, that the good means the desired, Mill recognises that, if he is further to maintain that pleasure alone is good, he must prove that pleasure alone is really desired. This doctrine that pleasure alone is the object of all our desires is the doctrine which Prof. Sidgwick has called Psychological Hedonism: and it is a doctrine which most eminent psychologists are now agreed in rejecting. But it is a necessary step in the proof of any such Naturalistic Hedonism as Mill’s; and it is so commonly held, by people not expert either in psychology or in philosophy, that I wish to treat it at some length. It will be seen that Mill does not hold it in its bare form. He admits that other things than pleasure are desired; and this admission is at once a contradiction of his Hedonism. One of the shifts by which he seeks to evade this contradiction we shall afterwards consider. But some may think that no such shifts are needed: they may say of Mill, what Callicles says of Polus in the Gorgias, that he has made the fatal admission through a most unworthy fear of appearing paradoxical; that they, on the other hand, will have the courage of their convictions, and will not be ashamed to go to any lengths of paradox, in defence of what they hold to be the truth. (§ 41 ¶ 2)