Mill’s Proof of the Principle of Utility

Author: Dale E. Miller
Category: Ethics, Historical Philosophy
Wordcount: 999

It may seem obvious that happiness is valuable, but is it the only thing valuable for its own sake, as opposed to being useful as a way to get something else?

The 19th-century utilitarian philosopher John Stuart Mill (1806-1873) argues that it is.[1] His argument is notorious because some critics charge that it contains obvious errors. This essay considers whether Mill really makes elementary blunders.

Cartoon drawing of John Stuart Mill
Cartoon drawing of John Stuart Mill

1. Mill’s Principle of Utility

Mill’s name for the claim that only happiness is valuable for its own sake is the “principle of utility.” This is ripe for confusion.

Mill offers this claim in the course of discussing the moral theory called utilitarianism. In its simplest form, utilitarianism says that actions are right if they would maximize the total amount of happiness in the world in the long run; otherwise they’re wrong.[2]

Yet Mill’s principle of utility doesn’t directly concern the morality of actions.[3] Instead it concerns what’s “desirable as an end.” It’s the foundation of Mill’s utilitarianism, not the theory itself.[4] This subtlety often goes unnoticed.

2. The Proof

Mill’s argument appears in Chapter 4 of his essay Utilitarianism. Today it’s called Mill’s “proof,” although the name is misleading since he admits that the “considerations” he offers aren’t a tidy deduction.[5]

Mill’s argument consists of three steps, each meant to establish a different claim:

1. Happiness is desirable as an end.
2. The “general happiness” is desirable as an end.
3. Nothing except happiness is desirable as an end.

Mill takes these three claims together to compose the principle of utility.

2.1. First Step

In the first step, Mill writes that:

“The only proof … that an object is visible, is that people actually see it. … In like manner, … the sole evidence … that anything is desirable, is that people do actually desire it.”

One criticism of this step is that Mill overlooks the fact that while ‘visible’ means “capable of being seen,” to call something desirable means not that we can desire it but that we ought to. While our actually doing something is proof positive that we can do it, it doesn’t mean that we should.[6]

But notice the shift in Mill’s wording from “only proof” to “sole evidence.” Even if the fact that everyone actually desires happiness doesn’t logically entail that they should, it might still be evidence for this. If happiness isn’t desirable then all of humanity has made the same huge mistake, which may seem implausible.[7]

2.2. Second Step

In the same paragraph, Mill turns to the second step:

“No reason can be given why the general happiness is desirable, except that each person … desires his own happiness.”

Elsewhere, Mill restates this step:

“since A’s happiness is a good, B’s a good, C’s a good, &c., the sum of these goods must be a good.”[8]

Some critics have charged Mill with committing the “fallacy of composition,” which is the fallacy of reasoning that because the members of a collection all have some property, the collection must have it, too.[9] An apple is spherical, but a bushel of apples isn’t. But while collections don’t always have the properties that their members share, sometimes they do. If I know that one gold bar is heavy, I’m not reasoning badly if I conclude that a pallet of these bars will be heavy, too.

Sometimes combining good things might produce something bad, like topping a pizza with hot fudge sauce. Often, though, a collection of valuable items will also be valuable. It depends on the natures of the items, their value, and the collection.

Mill reasons that if every person’s happiness is valuable then a world that contains more happiness is better than one that contains less, other things equal. That’s not obviously fallacious. 

2.3. Third Step

In the third step, Mill argues that happiness is the only thing we desire for itself. This means that it’s the only thing for whose desirability in itself we have evidence.

Someone might challenge Mill by saying that other things are valuable in themselves. On the surface, Mill’s strategy is to agree that people “do desire things which, in common language, are … distinguished from happiness”[10] for their own sakes.  His chief example is being virtuous. However, he asserts, people only desire virtue for its own sake if they have incorporated it into their happiness. If virtue partially constitutes someone’s happiness, then they desire it “as a part of their happiness.” Hence “there is in reality nothing desired except happiness.”[11]

But now Mill may appear inconsistent. He defines ‘happiness’ as “pleasure, and the absence of pain.”[12] How then, some of his critics have challenged, can virtue be part of our happiness? Virtue ≠ pleasure.[13]

The key may be in Mill’s account of how something like virtue can become part of our happiness. He explains how the experience of being treated better by others when we behave virtuously can cause us to form a mental association between virtue and pleasure. When people associate virtue with pleasure then the awareness or “consciousness” that they’re virtuous becomes pleasurable for them.

It might then be this pleasure—not virtue itself, strictly speaking—that they desire as an end. If this is his intention, then contrary to surface appearances Mill’s really denying that some people desire to be virtuous for its own sake. But he’s explaining why they seem to: for them, the connection between virtue and pleasure has become much closer than it is for people who only want to be virtuous so they’ll be treated better.[14]

Reading Mill this way still lets us say that he takes happiness to be the only thing we desire for itself, albeit at the cost of not taking his talk about virtue’s becoming part of our happiness or our desiring it as an end entirely literally.

3. Conclusion

Perhaps, then, Mill’s “proof” doesn’t contain clumsy mistakes. At least Mill has some responses available to the critics who allege that it does. More work would be needed to judge whether the argument ultimately succeeds, and more work still to get from this principle to utilitarian morality, but Mill’s contribution shouldn’t be hastily dismissed.[15]


[1] Mill 1969 [1861], 234–9.

[2] More specifically, this is true of the simplest form of the theory, which is sometimes called classical act utilitarianism.

Some other versions of utilitarianism might apply the requirement to maximize happiness differently. For instance, rule utilitarianism says that whether actions are right or wrong depends on whether they would be permitted or forbidden by the set of rules whose general adoption would maximize happiness. So it applies the criterion of maximizing happiness directly to rules and only indirectly, via rules, to individual actions.

There is some debate about what version of utilitarianism Mill accepts.

[3] Brown (1973).

[4] To add to the potential for confusion, other philosophers (both before and after Mill’s time) have used the term ‘principle of utility’ to refer to principles that are concerned with what makes actions right or wrong. Given this, and the fact that Mill never offers a formal definition of the principle, it’s no surprise that even professional philosophers are often tripped up by this. Mill refers at one point to a ‘Greatest Happiness Principle’ (Mill 1969 [1861], 210), and it’s possible that he intends this to be a principle about the morality of actions, but if so he thinks it’s distinct from and rests on the principle of utility.

While this may sound a bit sloppy on Mill’s part, one thing to bear in mind is that he was writing for a very wide audience, not only for philosophy professors or even philosophy students. The essay that contains his “proof” first appeared in a popular magazine of the day. So he sacrificed some precision for readability.

[5] Here’s how Mill makes this point in Chapter 1:

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? The art of music is good, for the reason, among others, that it produces pleasure; but what proof is it possible to give that pleasure is good? If, then, it is asserted that there is a comprehensive formula, including all things which are in themselves good, and that whatever else is good, is not so as an end, but as a mean, the formula may be accepted or rejected, but is not a subject of what is commonly understood by proof.  We are not, however, to infer that its acceptance or rejection must depend on blind impulse, or arbitrary choice.  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. (Mill 1969, 207–8).

[6] Here’s how the early 20th-century philosopher G. E. Moore (1873-1958) articulates this objection:

Well, the fallacy in this step is so obvious, that it is quite wonderful how Mill failed to see it. The fact is that “desirable” does not mean “able to be desired” as “visible” means “able to be seen”. The desirable means simply what ought to be desired or deserves to be desired. (Moore 1903, 67).

[7] Mill makes a very similar move in Chapter 2 of Utilitarianism, where he famously argues that the only way to determine which of two pleasures is of higher quality is by appeal to the judgment of people who have experience of both (Mill 1969, 210–4).

[8] Mill 1972, 1414.

[9] For example, Mackenzie 1901, 218–20.

[10] Mill 1969, 235.

[11] Mill 1969, 235–7.

[12] Mill 1969, 210.

[13] Money is another of Mill’s examples of something that can (seemingly) become part of our happiness, although in contrast with virtue he thinks that it’s unfortunate that some people do so. Moore references this example when criticizes this step of the argument:

Does Mill mean to say that money, these actual coins, which he admits to be desired in and for themselves, are a part either of pleasure or of the absence of pain? Will he maintain that those coins themselves are in my mind, and actually a part of my pleasant feelings? If this is to be said, all words are useless: nothing can possibly be distinguished from anything else; if these two things are not distinct, what on earth is? (Moore 1903, 71–2).

[14] The example of money can help to clarify what’s going on here, since Mill thinks that very much the same process can happen with it. 

Initially, we desire money simply because we can use it to buy things that we want. In some people, though, this leads to a mental association between money and pleasure such that just thinking about their money gives them pleasure. In the case of misers, this association grows so strong that they can’t bear to spend money even on things that are very important; the pleasure of having the money has become much greater than the pleasure of using it.

Mill would say that people who have formed this association have made money part of their happiness and that they desire it as such, although this is speaking rather loosely. Strictly speaking, Mill would say, even misers don’t desire money for its own sake. What they desire for its own sake is the pleasure they get from the knowledge that they have money. It’s this pleasure that is part of their happiness, not the money itself. The real point is just that money and happiness are much more closely connected for people like this than they are for people who simply regard money as a way to buy things.

Mill does think that there’s one important difference between money and virtue in this regard. We should want people to form this association between pleasure and being virtuous. This will help to motivate them to act in ways that lead to an overall happier society. In contrast, this sort of association between pleasure and money is pathological. Society will be much happier if people simply regard money as a tool.

[15] I give a more detailed discussion of Mill’s argument for the principle of utility in Miller 2010, 31–53.


Brown, D. G. (1973). “What is Mill’s Principle of Utility?,” Canadian Journal of Philosophy III: 1–12.

Mackenzie, John S. (1901). A Manual of Ethics 4th ed. New York: Hinds, Hayden & Eldredge.

Mill, John Stuart (1969). Utilitarianism. In John M. Robson (ed.), Collected Works of John Stuart Mill vol. X. Toronto: University of Toronto Press. Originally published 1861.

—– (1972). Letter to Henry Jones (13 June 1868). In John M. Robson (ed.), Collected Works of John Stuart Mill vol. XVI. Toronto: University of Toronto Press. 1413–4.

Miller, Dale E (2010). John Stuart Mill: Moral, Social and Political Thought. Cambridge: Polity.

Moore, G. E. (1903). Principia Ethica. Cambridge: Cambridge University Press. Reprinted 1992.

For Further Reading

Brink, David (2018). “Mill’s Moral and Political Philosophy.” In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.

Related Essays

Consequentialism by Shane Gronholz

John Stuart Mill on The Good Life: Higher-Quality Pleasures by Dale E. Miller

“Can They Suffer?”: Bentham on our Obligations to Animals by Daniel Weltman

Happiness by Kiki Berk



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About the Author

Dale E. Miller is a Professor of Philosophy at Old Dominion University and the editor-in-chief of Utilitas.

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