In Mill's view, of what kind of proof is the principle of utility susceptible?
Is it really capable of any kind of proof?

At the start of Chapter 4 of Utilitarianism, Mill makes the point that "questions of ultimate ends do not admit of proof, in the ordinary acceptation of the term" [U-4:1(1)]  This statement has traditionally been interpreted as Mill claiming that no valid deductive argument can be offered for the truth of Utilitarianism.  But this interpretation overlooks the position that Mill takes in his A System of Logic.  In that work, Mill maintains that a "proof", properly so called, necessarily involves inference.  For an argument to involve inference, there must be more to the conclusion than just the premises.  Mill's project in his A System of Logic was to show that there is no such thing as deductive inference.  According to Mill, all inference (and consequently all "proof") is inductive.[CW-VII:186-193(2)]  Hence Mill's claim that no proof can be offered must be seen as a claim that no non-deductive (i.e. inductive or abductive) argument can be offered.

An examination of Mill's reasoning in Utilitarianism, in the context of his other positions available from his Collected Works, makes it clear that he does actually construct a deductively valid argument in support of the Principle of Utility -- given certain then plausible but now debatable premises.

In this essay, I will show how Mill constructs this deductive argument.  Along the way, I will insert some comments where Mill's key premises are at least highly debatable, if not actually false.  From these, I will conclude that no "proof" (deductive, inductive or abductive) can be offered.  We must start with three key background premises that constitute the context within which Mill constructs his argument. 


(I)  Mill accepts the "is/ought distinction" described by Hume(3) (and later made famous by Moore as the "naturalistic fallacy"). 

"Propositions of science assert a matter of fact: an existence, a co-existence, a succession, or a resemblance. The propositions now spoken of do not assert that anything is, but enjoin or recommend that something should be. They are a class by themselves. A proposition of which the predicate is expressed by the words ought or should be, is generically different from one which is expressed by is or will be." [SL-6:12:6(4)]

For Mill, ought-type propositions are forms of imperatives -- they enjoin actions but do not state facts.  Because the Principle of Utility is an ought-type sentence, it is not possible to provide a fact-based "proof" of its truth.  Being an ought-type principle, it does not make sense to talk of it in terms of true or false.  The argument that Mill proceeds to construct must therefore be considered rather as a reasonable justification for belief and not as a proof of the truth of a statement of fact.

(II)  In A System of Logic, Mill makes it clear that he maintains a foundationalist theory of belief justification.  When beliefs are justified by other beliefs, there are only two methods available: (i) an infinite regress of justifications; or (ii) a self-supporting network of justifications (labelled as "circular" or "coherence" according to whether you approve or not).  Relying on belief justification chains that terminate beliefs that are not themselves justified is called foundationalism.  In a survey of fallacies in A System of Logic, Mill rejects the first two options.  He says that "there cannot be an infinite series of proof, a chain suspended from nothing"[CW-VIII:746] and "Reasoning in a Circle" is simply a "more complex and not uncommon variety of Petitio Principii, or begging the question"[CW-VIII:820].  Foundationalism, on the other hand, involves "propositions which may reasonably be received without proof"[CW-VIII:746].  Being an empiricist, Mill relies on the senses to provide the foundational basis of beliefs that may reasonably be received without further justification.  This empiricist foundationalism is the key to understanding the contentious "visible-desirable" analogy that Mill employs in his proof. 

(III)  Mill's Utilitarianism is, of course, a consequentialist view of morality. 

"That the morality of actions depends on the consequences which they tend to produce, is the doctrine of rational persons of all schools; that the good or evil of those consequences is measured solely by pleasure or pain, is all of the doctrine of the school of utility, which is peculiar to it." [CW-X:111]

Moral reasoning is reasoning about what ends one ought to be trying to achieve.  Moral reasoning, like practical reasoning, is also reasoning about how to best bring about those ends.  Mill's concept of morality is teleological in an Aristotelian vein.  This is in sharp contrast with, for example, religious morality, where the morality of actions is dictated by the nature of the action, rather than the consequences of the action.  Depending on how narrowly one interprets the teleological nature of consequentialism, it may also be contrasted with a deontological morality (such as Kant's) where the morality of actions is determined by whether or not they fulfill one's duties.

Mill's "Proof"

Step 1 of Mill's argument was to demonstrate that for a thing to be desired (as an end rather than as a means to an end) is sufficient proof that the end in question is worthy of being desired. 

Step 1.1 of this demonstration was to establish that the terms "utility", "pleasure", and "happiness" are to be considered synonymous.

"Those who know anything about the matter are aware that every writer, from Epicurus to Bentham, who maintained the theory of utility, meant by it, not something to be contradistinguished from pleasure, but pleasure itself, together with exemption from pain;" [U-2:1]

"By happiness is intended pleasure, and the absence of pain; by unhappiness, pain, and the privation of pleasure." [U-2:2]

"I have dwelt on this point, as being a necessary part of a perfectly just conception of Utility or Happiness, considered as the directive rule of human conduct." [U-2:3]

Step 1.2 was to equate the desiring of a thing with the finding of that thing pleasant.  For one to desire something (as an end, rather than as simply a means to some end) is to believe that the thing will deliver (or be a part of) utility / pleasure/ happiness. 

"I believe that these sources of evidence, impartially consulted, will declare that desiring a thing and finding it pleasant, aversion to it and thinking of it as painful, are phenomena entirely inseparable, or rather two parts of the same phenomenon; in strictness of language, two different modes of naming the same psychological fact: that to think of an object as desirable (unless for the sake of its consequences), and to think of it as pleasant, are one and the same thing; and that to desire anything, except in proportion as the idea of it is pleasant, is a physical and metaphysical impossibility." [U-4.10]

"Whatever is desired otherwise than as a means to some end beyond itself, and ultimately to happiness, is desired as itself a part of happiness, and is not desired for itself until it has become so." [U-4:8]

From there we get to the famous (and much critiqued) analogy between "visible" and "desirable".

"The only proof capable of being given that an object is visible, is that people actually see it. The only proof that a sound is audible, is that people hear it: and so of the other sources of our experience. In like manner, I apprehend, the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it." [U-4:3]

For a thing to be desired (as an end) is for that thing to be regarded by the person doing the desiring as worthy of desire.  For an empiricist like Mill, the only proof capable of being given that something is visible is that someone is actually seeing it.  In an analogous fashion, the only evidence it is possible to produce that a foundational belief that something is desirable, is that someone does actually regard that thing as desirable.  As a foundational belief, the chain of justification ends there.  Nothing further can be said.  Mill is neither assuming nor arguing that something is worthy because we desire it (the usually critique of this passage).  Rather, given his foundationalism, he is relying on our desiring it as establishing that we see it as worthy.  Of course, this leaves open the possibility that what we see as worthy, may not actually be worthy, and that brings us to the second step of the argument.

Step 2 of Mill's argument was to demonstrate that, as a matter of empirical fact, the only thing that people see as worthy of desire (as an end) is happiness.  Mill's support for psychological hedonism is relatively brief, and deals with few objections.  But having already set things up so that whatever is desired as an end, constitutes part of happiness [U-4:8], this "empirical demonstration" proceeds rather easily.

"It results from the preceding considerations, that there is in reality nothing desired except happiness." [U4:8]

Step 3 of Mill's argument, therefore, proceeds quite naturally.  If to desire some thing (as an end, foundationally) is sufficient to establish that we see that thing as worthy of desire, and if there is but one thing that we do so see as worthy of desire (as an end, foundationally), then it logically follows that there is but one thing that is worthy of desire (as an end, foundationally).  And that thing is happiness / utility / pleasure.

"If the opinion which I have now stated is psychologically true- if human nature is so constituted as to desire nothing which is not either a part of happiness or a means of happiness, we can have no other proof, and we require no other, that these are the only things desirable. If so, happiness is the sole end of human action, and the promotion of it the test by which to judge of all human conduct;" [U-4:9]

Step 4 of Mill's argument invokes three hidden, but for Mill relatively simplistic, premises. 

Step (4.1)  If something is of value to someone, it is because it is of value simpliciter.  The impact of this premise comes out most clearly in a private letter from Mill to Henry Jones (13/6/1868):

"[W]hen I said that the general happiness is a good to the aggregate of all persons I did not mean that every human being's happiness is a good to every other human being; though I think, in a good state of society & education it would be so. I merely meant in this particular sentence to argue that since A's happiness is a good, B's a good, C's a good, &c., the sum of all these goods must be a good." [CW-XVI:1414]

Mill is here clearly talking about happiness as a good simpliciter rather than possessively.  Happiness is of value independently of whose happiness it is.  In Mill's day, this was a common belief about the nature of value.  Mill's Utilitarianism was first published (in Fraser's Magazine) in 1861(5).  Adam Smith's The Wealth of Nations was published in 1776(6).  David Ricardo's Principles of Political Economy and Taxation was published in 1817(7). And Karl Marx's Das Kapital was published in 1867(8).  These three classical political economists shared a common approach to developing their theories of value. They all searched for value in the conditions of production.  In other words, they believed that a thing had value simpliciter rather than possessively.  This was still the common view of value as late as Moore's Principia Ethica, published in 1903(9). 

"When…I talk of anything I get as 'my own good,' I must mean either that the thing I get is good, or that my possessing it is good. In both cases it is only the thing or the possession of it which is mine, and not the goodness of that thing or that possession… The good of it can in no possible sense be 'private' or belong to me; any more than a thing can exist privately or for one person only. The only reason I can have for aiming at 'my own good,' is that it is good absolutely that what I so call should belong to me -- good absolutely that I should have something, which, if I have it, others cannot have. But if it is good absolutely that I should have it, then everyone else has as much reason for aiming at my having it, as I have myself. If, therefore, it is true of any single man's 'interest' or 'happiness' that it ought to be his sole ultimate end, this can only mean that that man's 'interest' or 'happiness' is the sole good … What Egoism holds, therefore, is that each man's happiness is the sole good -- that a number of different things are each of them the only good thing there is -- an absolute contradiction."
                                {G. E. Moore, Principia Ethica, 98-99.}

Given a modern understanding of "value", this is the single most contentious premise of Mill's.  Our modern conception of "value" is thoroughly possessive.  Without this premise, the second half of Mill's argument completely collapses.  It might be possible to provide a proof that one ought to maximize one's own happiness.  But it would be impossible to then demonstrate that one ought to maximize happiness in general, regardless of the possessor of that happiness.

Step (4.2)  Mill makes the assumption that the value (simpliciter) of happiness, inherent in various things, is both comparable and additive.  By treating happiness / pleasure / utility as "a good", Mill makes it clear that he considers this good as a singular kind of good -- regardless of what might be the source of one's happiness / pleasure / utility, it is always the same kind of good.  Different sources of utility are thus comparable.  And, of course, if one is going to attempt to maximize the net utility -- either for oneself or for the "aggregate of all people", then this utility must necessarily be additive.  That this was then a common assumption about value is evidenced by the attitude of economics towards economic value.  Classical economists (like Smith, Ricardo, and Marx) clearly considered the value of goods to be comparable and additive.  So Mill is just reflecting the then common attitude towards the notion of value.

But when it comes to the value of happiness / pleasure / utility, this assumption is highly debatable.  It is the second most contentious premise underlying Mill's argument.  It is not at all obvious that the happiness I experience from consuming an ice cream sundae on a hot summer's afternoon is in any way comparable (much less additive) with the happiness I experience from earning a good mark in a Philosophy course exam, or from helping out a friend in need.  That various sources of utility are comparable or additive (by me) is highly contentious when the person involved is me.  It is an insupportable hypothesis when there are two people involved.

Step (4.3)  Mill adopts the obvious fundamental ethical premise that whatever is of value, whatever is "a good", ought to be maximized.  Hardly a controversial premise.  It forms the basis of corporate finance, economics, and all forms of non-religious ethics from Aristotle's eudaimonia to Mill's utilitarianism.  With these three hidden premises in hand, Mill is in a position to reach his first ethical conclusion:  One ought to maximize one's values of happiness / pleasure / utility.

Step 5  To extend his argument from the maximization of one's own happiness to the maximization of happiness generally and in the aggregate, Mill requires two additional steps in his chain of reasoning.  The first of these is the establishment of an objective criterion by which to rank different sources of happiness. 

"Of two pleasures, if there be one to which all or almost all who have experience of both give a decided preference . . . that is the more desirable pleasure." [U-2:5]

From this verdict of the only competent judges, I apprehend there can be no appeal. On a question which is the best worth having of two pleasures, or which of two modes of existence is the most grateful to the feelings . . . the judgment of those who are qualified by knowledge of both, or, if they differ, that of the majority among them, must be admitted as final. And there needs be the less hesitation to accept this judgment respecting the quality of pleasures, since there is no other tribunal to be referred to even on the question of quantity. What means are there of determining which is the acutest of two pains, or the intensest of two pleasurable sensations, except the general suffrage of those who are familiar with both? What is there to decide whether a particular pleasure is worth purchasing at the cost of a particular pain, except the feelings and judgment of the experienced? [U-2:8]

The test of quality, and the rule for measuring it against quantity, [is] 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. [U-2:10]

Mill here provides a decisive criterion of desirability.  From this "verdict of the only competent judges . . . there can be no appeal"[U-2:9].  The competent judges (those with experience of both forms of happiness) are not being called upon to report some independent matter of fact.  Mill's competent judges are infallible.  The judicial metaphor is key: a judicial verdict constitutes the legal fact.  Mill is not suggesting that objective rankings of utilities are reflected (possibly inaccurately) by the preferences of the judges.  Rather he is arguing that the comparative rankings are actually constructed from the preferences.

Unfortunately for Mill, this step of his argument runs afoul of the consequence that he is basing the "proof" of his principle of utility on the beliefs of people who have already been brought up to believe that the best things in life are to be had from a social environment.  If he was basing his argument on the facts that empirically the best things in life are to be had from a social environment, it would be one thing.  But he is not.  He is basing his argument on the learned preferences of competent judges, and not on the facts of the matter.  So his argument is essentially circular.

But granting Mill his position, he can now employ this "objective" standard of comparative utilities to "correct" the desires of individuals.  Something that someone views as desirable can now be objectively verified as desirable or not.  Something that someone does not in fact desire can be objectively determined to be desirable for him nonetheless.  Thus, if a preference for the general happiness can be shown to be the preference of the majority of the competent judges, then it is necessarily also desirable for any particular individual.  Even if that particular individual does not in fact actually desire it.  And this leads into the next step.

Step 6 of Mill's argument is that, for various reasons, a policy of acting with the explicit aim of maximizing the general happiness is more likely than not to have the consequence of maximizing one's own happiness than any other policy - including a policy of acting with the explicit aim of maximizing one's own happiness.

"whatever amount of this feeling [for the good of others] a person has, he is urged by the strongest motives . . . of interest . . . to the utmost of his power to encourage it in others; and even if he has none of it himself, he is as greatly interested as any one else that others should have it. Consequently, the smallest germs of the feeling are laid hold of and nourished by . . . the influences of education; and a complete web of corroborative association is woven round it, by the powerful agency of external sanctions.
. . . the influences are constantly on the increase, which tend to generate in each individual a feeling of unity with all the rest; which feeling, if perfect, would make him never think of, or desire, any beneficial condition for himself, in the benefits of which they are not included. If we now suppose this feeling of unity to be taught as a religion, and the whole force of education, of institutions, and of opinion, directed, as it once was in the case of religion, to make every person grow up from infancy surrounded on all sides both by the profession and by the practice of it, I think that no one, who can realize this conception, will feel any misgiving about the sufficiency of the ultimate sanction for the Happiness morality." [U-3:9].

It is Mill's argument that in a civilized society, social institutions and cultural pressures will together act in to reinforce the impulses of sympathy.  Man is not commonly motivated to anti-social behaviour.  Instead, we are motivated to promote the general happiness.  Mill argues that there are two classes of motivations that drive us in this direction.  First, there are external motivations arising from our hope of pleasing, and fear of displeasing, other members of our society -- social and peer group pressures; laws and judicial punishments.  More importantly, there is internal motivation.  For Mill, this consists of an amalgam of sympathy, learned (habitual) reactions, and feelings of self-worth.  The binding force is the experience or anticipation of pleasure or pride when one acts according to these feelings, and of pain or remorse when one acts against them.  Mill argues that the motivations we have towards the general happiness is subjective and develops only with experience in a civilized society.

"Of the external sanctions it is not necessary to speak at any length. They are, the hope of favour and the fear of displeasure, from our fellow creatures or from the Ruler of the Universe, along with whatever we may have of sympathy or affection for them, or of love and awe of Him, inclining us to do his will independently of selfish consequences.  . . .  The whole force therefore of external reward and punishment, whether physical or moral, and whether proceeding from God or from our fellow men, together with all that the capacities of human nature admit of disinterested devotion to either, become available to enforce the utilitarian morality, in proportion as that morality is recognised; and the more powerfully, the more the appliances of education and general cultivation are bent to the purpose." [U-3:4]

"The internal sanction of  . . .  is one and the same- a feeling in our own mind; a pain, more or less intense, attendant on violation of duty, which in properly cultivated moral natures rises, in the more serious cases, into shrinking from it as an impossibility. This feeling,  . . .  is the essence of Conscience; though in that complex phenomenon as it actually exists, the simple fact is in general all encrusted over with collateral associations, derived from sympathy, from love, and still more from fear; from all the forms of religious feeling; from the recollections of childhood and of all our past life; from self-esteem, desire of the esteem of others, and occasionally even self-abasement." [U-3:5]

"Now, society between human beings, except in the relation of master and slave, is manifestly impossible on any other footing than that the interests of all are to be consulted. Society between equals can only exist on the understanding that the interests of all are to be regarded equally. And since in all states of civilisation, every person, except an absolute monarch, has equals, every one is obliged to live on these terms with somebody; and in every age some advance is made towards a state in which it will be impossible to live permanently on other terms with anybody. In this way people grow up unable to conceive as possible to them a state of total disregard of other people's interests." [U-3:12]

According to Mill, it follows from one's being civilized and having developed the appropriate socialized habits of thought to act from a desire to maximize aggregate happiness, that one will maximize one's expectations of individual happiness.  This is because following the Principle of Utility provides unique sources of pleasure (i.e. the pleasures of social approbation); and being a member of a civilized social group increases one's efficiency (measured as a percentage of capacity for happiness satisfied).  If mutual concern did not, as a matter of empirical fact, promote overall happiness, Mill would oppose it on exactly the same utilitarian grounds he relies on in his logic.

Conclusion  Mill is thus now in a position to reach his final ethical conclusion that one ought to maximize the general aggregate of happiness / pleasure / utility.  The argument he has constructed does not meet his own standard of "proof" for two separate reasons.  One is its subject matter: ultimate ends are a category of ought statements - beyond the reach of factual inference or proof.  The other is the argument's form: a deductively valid argument is merely "apparent, not real"[CW-VII:158].  Yet it is a deductive construction (based on several key premises) that "may be presented capable of determining the intellect either to give or withhold its assent to the doctrine; and this is equivalent to proof."[U-1:5].


Having seen how Mill constructs his argument for the Principle of Utility, we can see that according to Mill, it is not an argument based on empirical truths of facts of the matter.  So it is not a "proof" by his own standards of "proof".  It is a deductive construct that he hopes will be persuasive to the intellect.  But since ethical first principles are not appropriate subjects of true and false, it cannot be regarded as a demonstration of the truth of the principle.

Moreover, even if we reject the consequence of the "is/ought distinction" that a "proof" is inappropriate, since the Principle itself is based on a number of highly contentious premises no kind of acceptable proof can be offered.


Notes & References

(1)  Mill, John Stuart; Utilitarianism. Online access provided by eBooks@Adelaide; URL=
(references in the essay indicated by "[U-chapter:paragraph]")

(2)  Mill, John Stuart; Collected Works of John Stuart Mill, J.M. Robson (ed.), University of Toronto Press, Toronto, Canada 33 vols. 1963-1991. Online access provided by The Online Library of Liberty; URL=
(references in the essay indicated by "[CW-volume:page]"). 

(3)  Hume, David; A Treatise of Human Nature, L.Selby-Bigge & P.H.Nidditch (eds.), Oxford University Press, Oxford, England. 1978. Book III, Section 1 "Of virtue and vice in general".

(4)  Mill, John Stuart; A System of Logic, Online access provided by CUWS (Classical Utilitarianism Web Site); URL=<>.
(references in the essay indicated by "[SL-book:chapter:section]").

(5)  Wikipedia contributors. "Utilitarianism (book)" in Wikipedia, The Free Encyclopedia. URL=

(6)  Wikipedia contributors. "The Wealth of Nations" in Wikipedia, The Free Encyclopedia. URL=

(7)  Wikipedia contributors. "On the Principles of Political Economy and Taxation" in Wikipedia, The Free Encyclopedia. URL=

(8)  Wikipedia contributors. "Das Kapital" in Wikipedia, The Free Encyclopedia. URL=

(9)  Wikipedia contributors. "G. E. Moore" in Wikipedia, The Free Encyclopedia. URL=


Ashford, Elizabeth: "Utilitarianism, Integrity, and Partiality" in The Journal of Philosophy, Vol 97, No. 8 (Aug 2000), pp 421-439

Crisp, Roger; Routledge Philosophy Guidebook to Mill on Utilitarianism, Routledge, London, England. 1997. ISBN 0-415-10978-7

Brink, David, "Mill's Moral and Political Philosophy", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL=

Mill, John Stuart; The Basic Writings of John Stuart Mill, Random House, New York, New York, 2002. ISBN 0-375-75918-2

Moore, G.E.; Principia Ethica.  URL=

West, Henry R.; Mill's Utilitarianism, Continuum Books, London, England. 2007. ISBN 0-826-49302-5

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