Questions of ultimate ends are not amenable to direct proof. Whatever can be proved to be good, must be so by being shown to be a means to something admitted to be good without proof. The medical art is proved to be good by its conducing to health; but how is it possible to prove that health is good? … There is a larger meaning of the word proof, in which this question is as amenable to it as any other of the disputed questions of philosophy. The subject is within the cognisance of the rational faculty; and neither does that faculty deal with it solely in the way of intuition. Considerations may be presented capable of determining the intellect either to give or withhold its assent to the doctrine; and this is equivalent to proof. [ch. I, 157-8]
Why truth is one of the first moral principles
[I]t would often be expedient, for the purpose of getting over some momentary embarrassment, or attaining some object immediately useful to ourselves or others, to tell a lie. But inasmuch as the cultivation in ourselves of a sensitive feeling on the subject of veracity, is one of the most useful, and the enfeeblement of that feeling one of the most hurtful, things to which our conduct can be instrumental; and inasmuch as any, even unintentional, deviation from truth does that much towards weakening the trustworthiness of human assertion, which is not only the principal support of all present social well-being, but the insufficiency of which does more than any one thing that can be named to keep back civilisation, virtue, everything on which human happiness on the largest scale depends; we feel that the violation, for a present advantage, of a rule of such transcendant expediency, is not expedient, and that he who, for the sake of a convenience to himself or to some other individual, does what depends on him to deprive mankind of the good, and inflict upon them the evil, involved in the greater or less reliance which they can place in each other’s word, acts the part of one of their worst enemies. Yet that even this rule, sacred as it is, admits of possible exceptions, is acknowledged by all moralists; the chief of which is when the withholding of some fact (as of information from a malefactor, or of bad news from a person dangerously ill) would save an individual (especially an individual other than oneself) from great and unmerited evil, and when the withholding can only be effected by denial. But in order that the exception may not extend itself beyond the need, and may have the least possible effect in weakening reliance on veracity, it ought to be recognised, and, if possible, its limits defined; and if the principle of utility is good for anything, it must be good for weighing these conflicting utilities against one another, and marking out the region within which one or the other preponderates. [ch. II, 181]
What is utilitarianism?
According to the Greatest Happiness Principle, as above explained, the ultimate end, with reference to and for the sake of which all other things are desirable (whether we are considering our own good or that of other people), is an existence exempt as far as possible from pain, and as rich as possible in enjoyments, both in point of quantity and quality; the test of quality, and the rule for measuring it against quantity, being the preference felt by those who in their opportunities of experience, to which must be added their habits of self-consciousness and self-observation, are best furnished with the means of comparison. This, being, according to the utilitarian opinion, the end of human action, is necessarily also the standard of morality; which may accordingly be defined, the rules and precepts for human conduct, by the observance of which an existence such as has been described might be, to the greatest extent possible, secured to all mankind; and not to them only, but, so far as the nature of things admits, to the whole sentient creation. [ch. II, 167]