§2. Let us now examine the principle itself somewhat closer. I have already attempted (Book ii. chap. i.) to render the notion of Greatest Happiness as clear and definite as possible; and the results there obtained are of course as applicable to the discussion of Universalistic as to that of Egoistic Hedonism. We shall understand, then, that by Greatest Happiness is meant the greatest possible surplus of pleasure over pain, the pain being conceived as balanced against an equal amount of pleasure, so that the two contrasted amounts annihilate each other for purposes of ethical calculation. And of course, here as before, the assumption is involved that all pleasures included in our calculation are capable of being compared quantitatively with one another and with all pains; that every such feeling has a certain intensive quantity, positive or negative (or, perhaps, zero), in respect of its desirableness, and that this quantity may be to some extent known: so that each may be at least roughly weighed in ideal scales against any other. This assumption is involved in the very notion of Maximum Happiness; as the attempt to make `as great as possible' a sum of elements not quantitatively commensurable would be a mathematical absurdity. Therefore whatever weight is to be attached to the objections brought against this assumption (which was discussed in chap. iii. of Book ii.) must of course tell against the present method.
We have next to consider who the ``all'' are, whose happiness is to be taken into account. Are we to extend our concern to all the beings capable of pleasure and pain whose feelings are affected by our conduct? or are we to confine our view to human happiness? The former view is the one adopted by Bentham and Mill, and (I believe) by the Utilitarian school generally: and is obviously most in accordance with the universality that is characteristic of their principle. It is the Good Universal, interpreted and defined as `happiness' or `pleasure,' at which a Utilitarian considers it his duty to aim: and it seems arbitrary and unreasonable to exclude from the end, as so conceived, any pleasure of any sentient being.
It may be said that by giving this extension to the notion, we considerably increase the scientific difficulties of the hedonistic comparison, which have already been pointed out (Book ii. chap. iii.): for if it be difficult to compare the pleasures and pains of other men accurately with our own, a comparison of either with the pleasures and pains of brutes is obviously still more obscure. Still, the difficulty is at least not greater for Utilitarians than it is for any other moralists who recoil from the paradox of disregarding altogether the pleasures and pains of brutes. But even if we limit our attention to human beings, the extent of the subjects of happiness is not yet quite determinate. In the first place, it may be asked, How far we are to consider the interests of posterity when they seem to conflict with those of existing human beings? It seems, however, clear that the time at which a man exists cannot affect the value of his happiness from a universal point of view; and that the interests of posterity must concern a Utilitarian as much as those of his contemporaries, except in so far as the effect of his actions on posterity---and even the existence of human beings to be affected---must necessarily be more uncertain. But a further question arises when we consider that we can to some extent influence the number of future human (or sentient) beings. We have to ask how, on Utilitarian principles, this influence is to be exercised. Here I shall assume that, for human beings generally, life on the average yields a positive balance of pleasure over pain. This has been denied by thoughtful persons: but the denial seems to me clearly opposed to the common experience of mankind, as expressed in their commonly accepted principles of action. The great majority of men, in the great majority of conditions under which human life is lived, certainly act as if death were one of the worst of evils, for themselves and for those whom they love: and the administration of criminal justice proceeds on a similar assumption.
Assuming, then, that the average happiness of human beings is a positive quantity, it seems clear that, supposing the average happiness enjoyed remains undiminished, Utilitarianism directs us to make the number enjoying it as great as possible. But if we foresee as possible that an increase in numbers will be accompanied by a decrease in average happiness or vice versa, a point arises which has not only never been formally noticed, but which seems to have been substantially overlooked by many Utilitarians. For if we take Utilitarianism to prescribe, as the ultimate end of action, happiness on the whole, and not any individual's happiness, unless considered as an element of the whole, it would follow that, if the additional population enjoy on the whole positive happiness, we ought to weigh the amount of happiness gained by the extra number against the amount lost by the remainder. So that, strictly conceived, the point up to which, on Utilitarian principles, population ought to be encouraged to increase, is not that at which average happiness is the greatest possible, as appears to be often assumed by political economists of the school of Malthus---but that at which the product formed by multiplying the number of persons living into the amount of average happiness reaches its maximum.
It may be well here to make a remark which has a wide application in Utilitarian discussion. The conclusion just given wears a certain air of absurdity to the view of Common Sense; because its show of exactness is grotesquely incongruous with our consciousness of the inevitable inexactness of all such calculations in actual practice. But, that our practical Utilitarian reasonings must necessarily be rough, is no reason for not making them as accurate as the case admits; and we shall be more likely to succeed in this if we keep before our mind as distinctly as possible the strict type of the calculation that we should have to make, if all the relevant considerations could be estimated with mathematical precision.
There is one more point that remains to be noticed. It is evident that there may be many different ways of distributing the same quantum of happiness among the same number of persons; in order, therefore, that the Utilitarian criterion of right conduct may be as complete as possible, we ought to know which of these ways is to be preferred. This question is often ignored in expositions of Utilitarianism. It has perhaps seemed somewhat idle as suggesting a purely abstract and theoretical perplexity, that could have no practical exemplification; and no doubt, if all the consequences of actions were capable of being estimated and summed up with mathematical precision, we should probably never find the excess of pleasure over pain exactly equal in the case of two competing alternatives of conduct. But the very indefiniteness of all hedonistic calculations, which was sufficiently shown in Book ii., renders it by no means unlikely that there may be no cognisable difference between the quantities of happiness involved in two sets of consequences respectively; the more rough our estimates necessarily are, the less likely we shall be to come to any clear decision between two apparently balanced alternatives. In all such cases, therefore, it becomes practically important to ask whether any mode of distributing a given quantum of happiness is better than any other. Now the Utilitarian formula seems to supply no answer to this question: at least we have to supplement the principle of seeking the greatest happiness on the whole by some principle of Just or Right distribution of this happiness. The principle which most Utilitarians have either tacitly or expressly adopted is that of pure equality---as given in Bentham's formula, ``everybody to count for one, and nobody for more than one''. And this principle seems the only one which does not need a special justification; for, as we saw, it must be reasonable to treat any one man in the same way as any other, if there be no reason apparent for treating him differently.