's attempted proof may be re-formulated in the following way:
             (1) each person fundamentally desires only their own happiness; therefore,
             (3) as everybody desires only their own happiness, therefore
             (4) the general happiness is the sole good to the aggregate of all persons; therefore,
             (5) we should act only in such a way as to bring about general happiness.
             It is important to realise that Mill defines happiness in terms of well-being (the Aristotelian notion of eudaimonia), which is distinguished qualitatively as well as quantitatively. By according greater value to the 'higher' pleasures (such as appreciating poetry) in determining how one ought to act, Mill seeks to express the totality of human wants in his ethic – as he writes, "it is better to be a human being dissatisfied than a pig satisfied" (Ch.2). Mill's version of utilitarianism is, therefore, more sophisticated and attractive than that of his godfather, Jeremy Bentham, who defined "the good" solely in terms of quantities of pleasure; the latter's theory is open to the obvious objection that some pleasures are intrinsically more valuable than others (learning seems preferable to indolence, for example, even though the latter might afford the greater pleasure.)
             Problems with Mill's attempted proof
             Mill's proof seems to contain three major logical flaws. Firstly, as W D Hudson makes clear in his book Modern Moral Philosophy, Mill commits the "fallacy of composition" in supposing that, as A's happiness (AH) is a good to A, B's happiness (BH) a good to B, C's happiness (CH) is a good to C, and so on, the conjunction "AH and BH and CH" is good to each of A, B, and C respectively . This fallacy might be resolved through Mill's appeal to the principle of maximising utility: if the happiness of the whole set "A , B and C" is unattainable, and where the happ...