The 'Utilitarianism' (1861/63), ch. 4 quote reads in full :
'No reason can be given why the general happiness is desirable,
except that each person, so far as he believes it to be attainable,
desires his own happiness. This, however, being a fact, we have
not only all the proof which the case admits of, but all which it is
possible to require, that happiness is a good: that each person's
happiness is a good to that person, and the general happiness
therefore a good to the aggregate of all persons.'
One point is that Mill does not claim to offer a strict proof here, i.e. one that demonstrates the truth of his thesis - only 'all the proof which the case admits of'. He advances only 'considerations ... capable of determining the
intellect'. That aside, and the central point, does Mill commit the fallacy of composition here ? Does he infer from each desiring their own happiness (a form of psychological hedonism he endorses) to each desiring the happiness of all ?
If Mill were to be making a purely psychological - psychological hedonist -
claim that if each person desires their own happiness, then the aggregate of persons desires the happiness of the aggregate of persons, the broken-backed nature of the argument would be indisputable. It would be a straight fallacy of composition. But this isn't his claim. His claim is that it is by desiring the aggregate happiness we make the maximisation of our own happiness most likely. This is why 'the general happiness [is] a good to the aggregate of all persons'.
It must be admitted that Mill expresses himself clumsily. But put the point like this. Mill says that each person desires their own happiness. We can add, each person desires to maximise their own happiness. What is the most rational policy for achieving the maximisation of our own happiness ? It is to maximise the aggregate happiness. The assumption is that maximising the aggregate happiness will as a matter of fact maximise our own happiness or make its maximisation most likely. There is no fallacy in the argument with this assumption inserted.
But you might challenge : is this what Mill said or might have said or might have thought ? There is good evidence that Mill did make this assumption. In his 'Autobiography' he writes about the period after his nervous breakdown (1826):
'I never, indeed, wavered in the conviction that happiness
is the test of all rules of conduct, and the end of life. But I now
thought that this end was only to be attained by not making it the
direct end. Those only are happy (I thought) who have their
minds fixed on some object other than their own happiness; on
the happiness of others, on the improvement of mankind, even
on some art or pursuit, followed not as a means, but as itself an
ideal end. Aiming thus at something else, they find happiness by
'Those only are happy (I thought) who have their minds fixed on some object other than their own happiness; on the happiness of others' : this is, I suggest, the assumption at work in the 'Utilitarianism', ch. 4 quote.
[Whether maximising the aggregate happiness will maximise our own happiness or make its maximisation most likely, I am none too sure. And I do not endorse psychological hedonism. But I set these matters aside in an examination of the logic of Mill's aergument.]
- Tim Mawson, 'Mill's Proof', Philosophy, Vol. 77, No. 301 (Jul., 2002), pp. 375-405.
- Mary Warnock, 'Utilitarianism : John Stuart Mill', London : HarperCollins, 1972, Introduction.