Volume III is the most interesting philosophically, since it is really only here that we get Bentham's full argument against what he keeps calling ascetic self-denial. Bentham's hatred of this idea is very, very strong: the greatest pleasure for the greatest number of people requires that there only be self-denial for the specific purpose of getting even greater pleasures, and Bentham does not hesitate to make clear that he regards advocates of ascetic self-denial as morally detestable. It has often been noted that to this end he strongly advocates the importance of abortion and homosexual sex for population control; it's somewhat less often recognized that he also advocates infanticide and pedophilia. I found the discussion of infanticide particularly interesting, since he argues that the pain caused by punishment of infanticide far exceeds any pain caused by infanticide, because infanticide causes no pain of the first order -- infant psychology is too undeveloped to be seriously harmed -- and no pain of the second order -- since the death of one infant cannot make other infants anxious -- whereas punishing infanticide, particularly as a form of murder, causes great pain of the first order -- since the punishment induces pain -- and also of the second order -- since it prevents others from using the remedy to eliminate misery. Plus, infanticide is a remedy for overpopulation -- "this gentlest of all remedies", which seems a bit of an exaggeration even on his own terms.
In any case, I found his response to the claim that this should not be a matter of calculation to sum Bentham up to a T:
No calculation! no calculation! exclaims the shallow and empty-headed sentimentalist, who, by ostentation of passion, trusting to congenial weakness on the part of his reader, trusts, and in point of experience on but too good grounds, to drive reason out of the field.
No calculation! as if the distinction of right and wrong—as if the determination of an act in respect of conduciveness or destructiveness to human happiness—depended on any thing else than calculation.
In morals or politics, no calculation! in trade, as well might a man cry, no taking of stock! no keeping of accounts: thus thinking to serve economy―economy in trade.
The trade analogy is curiously not to the point. The objection to which he is responding is not committed to saying that reasoning is never appropriate but
only to saying that there are at least some topics on which utilitarian calculation is not appropriate. No serious businessman thinks that every business decision is determined by taking of stock and keeping of accounts; even in the most blatant caricatures one can find of greedy businessmen one rarely finds any suggestion that there are no areas of business that should be governed by just bare ordinary human decency and respectability rather than calculation for profit. Economy in trade does not reduce to taking stock and keeping accounts; these things simply trace the line between what is feasible and what is not.
It is interesting, too, to contrast this attitude on the question with Mill's utilitarianism, in which "the determination of an act in respect of conduciveness or destructiveness to human happiness" does depend on something else besides calculation (namely, cultivated taste).