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Giving Mill Pain

While we’re having a mini-Mill-fest, I thought I’d try out the following wee argument, which I’ve been thinking about lately.


John Stuart Mill [thanks, Dale M.] famously held that ‘higher pleasure’ (roughly, pleasure of the intellect) was superior to ‘lower pleasure’ (pleasure of the senses). Moreover, on what is perhaps the standard interpretation of Mill, he held that the value of higher pleasure was so much greater as to have lexical priority over lower pleasure. Of any two lives differing only in the quantities of higher and lower pleasure they contain, the life with greater higher pleasure is always better, regardless of the particular quantities involved. No gain in lower pleasure, however great, could ever by itself fully compensate for a loss in higher pleasure, however slight.

It is, I gather, somewhat controversial whether this interpretation of Mill is correct, whether he really did hold the extreme, lexical priority view. Here, however, I am not so much interested in interpretative questions as in the substantive philosophical question whether this view commonly attributed to Mill, whether correctly or not, is itself plausible. If Mill himself did not hold the view, others do. (For example, Roger Crisp, who attributes the view to Mill, also endorses it himself in his book Mill on Utilitarianism.) So it’s worthy of investigation, independently of its historical connection with Mill.

I shall argue that the view is not plausible. As any hedonist surely must agree, pleasure is not all that matters in evaluating a life. Pain matters too. Two lives that are equal in pleasure might nonetheless be unequal in overall value, because the pleasure in one might be accompanied by greater pain than the pleasure in the other. However, as I shall argue, any plausible hedonistic view of the value of life, which incorporates both pleasure and pain, will be inconsistent with the lexical priority view.

For our purposes we may represent a life as an ordered triple (l,h,p), where l, h and p are numbers measuring respectively the quantities of lower pleasure, higher pleasure, and pain contained in the life. (For example, (3,5,2) represents a life containing 3 units of lower pleasure, 5 units of higher pleasure, and 2 units of pain.)

The lexical priority view, which, for the sake of a convenient label, I shall call ‘Mill’s Principle’, may then be stated as follows:

Mill’s Principle. If h > h’ and p = p’, then (l,h,p) is better than (l’,h’,p’).

This states simply that, holding the quantity of pain fixed, a life with more higher pleasure is always better than a life with less.

My argument against Mill’s principle has two premises:

Weak Pain Aversion. If l = l’, h = h’, and p =< p', then (l,h,p) is at least as good as (l',h',p').

The Triangle Principle. There exist numbers l, l’, h, h’, p, p’, p” such that:

  • 0 =< l < l'
  • 0 =< h < h'
  • 0 =< p < p' =< p''
  • (l,h,p) is at least as good as (l,h’,p’)
  • (l’,h,p”) is at least as good as (l,h,p)

(Note, =< means less than or equal to.)

Weak Pain Aversion seems entirely uncontentious. It claims only that, holding the quantities of higher and lower pleasure fixed, a life with less pain cannot be worse than a life with more.

The Triangle Principle, which is less straightforward, is illustrated by the following diagram:

Diagram1a

Depicted here is a three-dimensional space, where the dimensions represent lower pleasure, higher pleasure, and pain, as labelled. Each point in the space represents a possible life (or more accurately, a possible combination of quantities of higher pleasure, lower pleasure, and pain). The three points labelled A, B, C represent the three lives described in the Triangle Principle. (For simplicity, in the diagram I’ve set l = h = p = 0, but this is not essential.) For example, A = (l,h’,p’). An arrow between two points indicates that the point to which the arrow points is at least as good as the point from which it points. Moving in the direction of the arrows preserves overall value.

Now suppose you begin with A, which you then exchange for B. In so exchanging, you receive decreases in two quantities, higher pleasure (decreased by h’ – h) and pain (decreased by p’ – p), while the other quantity, lower pleasure, remains constant. The former decrease is a change for the worse: all else equal, the less higher pleasure a life contains, the less value it has. The latter, in contrast, is a change for the better: all else equal, the less pain a life contains, the more value it has. However, the latter decrease is so great, and the former so small, that the latter at least compensates for the former, and their net effect on the value of the life you possess is therefore non-negative. This value might not have gone up, but it cannot have gone down. In other words, B is at least as good as A.

Suppose next you exchange B for C. Again there are changes both for the worse (pain increased by p” – p) and for the better (lower pleasure increased by l’ – l), and again the latter at least compensates for the former. So C is at least as good as B. Notice that the increase in pain moving from B to C must be at least as great as the decrease in pain moving from A to B, i.e. it must be that p’ =< p''. But for now let us assume that it is strictly greater (as shown in the diagram), since this makes the case against Mill's Principle slightly more difficult.

You have now moved from A to C (via B) without losing any value on the way. Since C is at least as good as B, and B at least as good as A, it follows (by transitivity) that C is at least as good as A. Although C has more lower pleasure and A more higher pleasure, this does not yet contradict Mill’s Principle. The latter applies only in cases where pain is held fixed, but in this case, by our assumption, C has greater pain. Although the Triangle Principle allows that A and C are equal in pain, it doesn’t require this, and so it is logically consistent with Mill’s Principle.

In order to complete my argument against Mill’s principle, I need only the other premise stated earlier, Weak Pain Aversion. Consider now a fourth life, D = (l’,h,p’), as shown in the following diagram:

Diagram2a

D differs from C only in pain. Since D has less pain, it follows from Weak Pain Aversion that D is at least as good as C, as shown by the arrow in the diagram. Therefore D is at least as good as A. This plainly contradicts Mill’s Principle, which implies that A is better than D, because A has more higher pleasure than D and there is no difference in pain.

Perhaps Mill would object to the Triangle Principle. (Weak Pain Aversion seems hard to deny.) There are two obvious objections he might try. First, he might object that B could not be as good as A, i.e. that A must be better than B, because higher pleasure has lexical priority over pain (or the absence of pain). No decrease in the pain, however great, could compensate for a decrease in higher pleasure, however slight. But this is implausible. A life containing, say, five minutes of mild higher pleasure followed by a hundred years of excruciating pain would surely be worse than a life containing neither higher pleasure nor pain.

Second, he might object that C could not be as good as B, because pain has lexical priority over lower pleasure. No increase in the lower pleasure, however great, could compensate for a increase in pain, however slight. But again this is implausible. A life containing, say, five minutes of mild pain followed by a hundred years of intense lower pleasure is surely better than a life containing neither pain nor lower pleasure.

Suppose, then, Mill concedes both (a) that some decreases in higher pleasure may be compensated for by decreases in pain, and (b) that some increases in pain may be compensated for by increases in lower pleasure. This is not yet to concede the Triangle Principle. For it might be that the decreases in pain described in (a) are all of them greater than the increases in pain described in (b); this remains a logical possibility, at least. Still, if Mill (or another defender of Mill’s Principle) were to claim that this were in fact the case, he would then owe us some explanation as to why. It doesn’t seem obvious. I cannot think of a good explanation, and so I’m inclined instead to reject Mill’s principle.

22 Responses to Giving Mill Pain

  1. Dale Dorsey says:

    Hi Campbell:
    This is an interesting argument. It’s similar to one that’s run by Gustaf Arrhenius in “Superiorities in Value” in Phil Studies in, I think, 2005. (I’m thinking of Arrhenius’ “g1, g2, g3” argument.) Anyway, it seems to me obvious that the principle Mill would deny is the principle that B is better than A. (Cf. “Socrates dissatisfied,” etc.) You claim that this is implausible: “A life containing, say, five minutes of mild higher pleasure followed by a hundred years of excruciating pain would surely be worse than a life containing neither higher pleasure nor pain”. Quite right! But Mill need not deny this. Higher pleasures are, as we were discussing in the last post, “modes of existence” (that could be read in a hedonist or non-hedonist way). Seems to me five minutes of Socraticity is not a “mode of existence”. You’re right to say that the “five minutes” claim is crazy, but I don’t think any reasonable fan of lexical priorities (including Mill) need accept it. (I try to defend something like this view, in Headaches, Lives, and Value, where I also discuss Arrhenius’ argument.) You might restate the claim that a Socratic mode of existence is not worth overwhelmingly excrutiating pain during its duration. (Or, at least, the maximum pain that would be possible while living a Socratic life.) But this would just be to assert what Mill denies, I think.

  2. Dale Miller says:

    John WHAT Mill? 🙂
    I can’t fault the argument. However, even though nothing Campbell says hinges on this, I think that it is worth being clear about the fact that Mill does not in fact commit himself to the lexical view.
    Mill writes:
    “Of two pleasures, if there be one to which all or almost all who have experience of both give a decided preference, irrespective of any feeling of moral obligation to prefer it, that is the more desirable pleasure. If one of the two is, by those who are competently acquainted with both, placed so far above the other that they prefer it, even though knowing it to be attended with a greater amount of discontent, and would not resign it for any quantity of the other pleasure which their nature is capable of, we are justified in ascribing to the preferred enjoyment a superiority in quality, so far outweighing quantity as to render it, in comparison, of small account.” (UII5)
    The second sentence might refer to something even stronger than “Mill’s Principle”; Mill seems to be describing a case in which a person is better off with more of a higher quality pleasure and MORE pain (“a greater amount of discontent”) than with less of the higher quality pleasure, less pain, and as much lower quality pleasure as you like. Notice, by the way, that Mill still isn’t saying what some interpreters take him to say, namely that an experience of higher quality pleasure is infinitely more valuable than lower quality pleasure. He limits himself to talking (as does Campbell) to amounts of lower quality pleasure that could be experienced in a single human life.
    More importantly, though, notice that the second of the sentences that I quoted is not just a restatement of the first. The scenario that Mill describes in the second sentence involves considerably more than competent judges having a decided preference for one pleasure over another. The implication of the first sentence is that equal quantities of the two pleasures are being compared; one pleasure is found to be better than another if a given quantity of one is decidedly preferred to the same amount of another. Only in the second sentence is the possibility raised of comparing less of the higher quality pleasure to more of the lower. The first sentence describes the test that must be met for us to know that one pleasure is of higher quality than the other. The second sets out a much more stringent test, and Mill does not commit himself to its being satisfied by any pair of pleasures. At most, he acknowledges the possibility.

  3. Dale,
    I take the first sentence to define just what it is for one pleasure (higher or lower) to be better than another. Then, as I read him, the second sentence tells us how to tell higher from lower quality pleasures. It doesn’t itself tell us how to weight higher against lower, but given that the people who have experience give higher lexical priority over lower, it seems reasonable to attribute to Mill the thought that that is what we should do as well.
    On Campbell’s issue, I’m somewhat moved by the lots of pain cases he constructs, though I’d like to resist them. What seems worst about severe pain in real life is that it keeps you from doing anything much of value. So for most real lives increases in pain also cause decreases in higher pleasure. That might explain why a life with lots of severe pain is so bad for most real life cases. Campbell’s nice trick is to put the pain at the end of a life and let it go on for a long time. Thus he can keep adding more pain by increasing the time span without decreasing the higher pleasures in the life and ask whether there isn’t some point at which it might be worth reducing the higher pleasure in that life just a little to get rid of that much pain. And I admit I feel the pull.
    If time spent not having any higher pleasure (for humans) counted as lexically worse than pain and it were so bad that it could cancel the value of higher pleasure in other parts of a life there might be a way out. But I’m not sure it is true. Is a short brilliant life followed by an early death really better than a similar early life with just a hair more higher pleasure in it than the first followed by a long life of only lower pleasure? I guess I can get in a state of mind where I’d consider choosing the former over the latter. At least while listening to Rust Never Sleeps . . .

  4. Dale Miller says:

    Mark,
    Well, at least we agree that the meaning of the sentences is distinct, which I puts us in the minority—the elite!, the vanguard!—of Mill’s readers. I think that my reading is slightly better supported by the text, though. The first sentence of the paragraph, which precedes the two I quoted, raises the question of how we know that one pleasure is of higher quality than another, and does so in a way that suggests (to me) that the next sentence contains the answer. Also, I think that my reading is preferable on grounds of charity, since it avoids attributing an implausible view about the value of pleasure to Mill, one vulnerable to objections like Campbell’s.

  5. David Sobel says:

    I agree with Mark’s first point. Also, Liz Anderson interprets, not implausibly, this line:
    If one of the two is, by those who are competently acquainted with both, placed so far above the other that they prefer it, even though knowing it to be attended with a greater amount of discontent, and would not resign it for any quantity of the other pleasure which their nature is capable of, we are justified in ascribing to the preferred enjoyment a superiority in quality, so far outweighing quantity as to render it, in comparison, of small account.”
    to be saying that a pleasure is higher if you would not resign it–that is prefer to have none of it–for any amount of the other pleasure.
    She points out, again plausibly by my lights, that this would be a poor test as one might not be willing to resign chocolate for any amount of novels but also not willing to resign novels for any amount of chocolate.

  6. David Sobel says:

    I agree with Mark’s first point. Also, Liz Anderson interprets, not implausibly, this line:
    If one of the two is, by those who are competently acquainted with both, placed so far above the other that they prefer it, even though knowing it to be attended with a greater amount of discontent, and would not resign it for any quantity of the other pleasure which their nature is capable of, we are justified in ascribing to the preferred enjoyment a superiority in quality, so far outweighing quantity as to render it, in comparison, of small account.”
    to be saying that a pleasure is higher if you would not resign it–that is prefer to have none of it–for any amount of the other pleasure.
    She points out, again plausibly by my lights, that this would be a poor test as one might not be willing to resign chocolate for any amount of novels but also not willing to resign novels for any amount of chocolate.

  7. David Sobel says:

    I agree with Mark’s first point. Also, Liz Anderson interprets, not implausibly, this line:
    If one of the two is, by those who are competently acquainted with both, placed so far above the other that they prefer it, even though knowing it to be attended with a greater amount of discontent, and would not resign it for any quantity of the other pleasure which their nature is capable of, we are justified in ascribing to the preferred enjoyment a superiority in quality, so far outweighing quantity as to render it, in comparison, of small account.”
    to be saying that a pleasure is higher if you would not resign it–that is prefer to have none of it–for any amount of the other pleasure.
    She points out, again plausibly by my lights, that this would be a poor test as one might not be willing to resign chocolate for any amount of novels but also not willing to resign novels for any amount of chocolate.

  8. Jussi Suikkanen says:

    I worry that there is something too simplified in the presentation of the issue. I don’t think that Mill would have thought that there were just two separate categories of things ‘lower pleasures’ and ‘higher pleasures’ to which we could classify each pleasure and then say how much of that thing there were in each instance of pleasure. So, I think the graphs and the ordered triplets do not capture his view really.
    I thought that he was arguing that quality is a property that pleasures can have to different degrees on a scale in the same way that they can have quantatity (duration, intensity and so on) to different degrees on a scale. If this is right, then it could be that there are *some* pleasures that score so highly on the quality measure that no quantatity of a pleasure that scores very low on the quality scale can outweigh the goodness of that pleasure. But, surely he wouldn’t say that this is always the case as the quality difference between some pleasure can only be slight.
    Furthermore, I do think that for the sake of consistency he would say the same thing about pains or suffering. They do come in different qualities – higher and lower. Some pains, say physical pain, we share with animals. But, we are also being able to experience higher pains, for instance loss of different freedoms and abilities to pursue worthwhile personal projects. So, it could be that pains higher up in the quality ranking require also higher quality pleasures to compensate.

  9. Campbell Brown says:

    Dale D,
    Thanks for the references. I look forward to reading Arrhenius’s paper and yours when I get a chance.
    Let me reply to a couple of your comments.

    You claim that this is implausible: “A life containing, say, five minutes of mild higher pleasure followed by a hundred years of excruciating pain would surely be worse than a life containing neither higher pleasure nor pain”. Quite right! But Mill need not deny this.

    The claim of mine in the quoted passage is consistent with Mill’s Principle. But in the context where I made the claim, I was supposing that Mill held, not only that higher pleasure has lexical priority over lower pleasure (i.e. Mill’s Principle), but also that higher pleasure has lexical priority over pain. The latter view is, as I understand it, straightforwardly inconsistent with the quoted claim. You don’t mean to deny this, do you?

    Higher pleasures are, as we were discussing in the last post, “modes of existence” (that could be read in a hedonist or non-hedonist way). Seems to me five minutes of Socraticity is not a “mode of existence”.

    Not sure I see your point here. Are you denying that it’s possible for a life to contain only five minutes of higher pleasure? Or are you rejecting the idea of quantifying higher pleasure by its duration? Do you think it’s meaningless to talk about ‘five minutes of higher pleasure’, or ‘three years of higher pleasure’, and so on?

  10. Campbell Brown says:

    Mark,
    Be careful listening to Neil Young. You know what happened to Kurt Cobain.

  11. Campbell Brown says:

    Jussi,
    I think my argument against the simple view could be generalised to provide an argument against your more sophisticated proposal.

  12. Jussi Suikkanen says:

    Why?

  13. Jussi Suikkanen says:

    I guess the point is that the assumption that there is always a value-preserving move from A to B seems to already assume that Mill’s principle is false. It assumes that there are no such pleasures that score so highly on the quality scale that they are so valuable that no move towards lesser amount of pain compensates this. But, this could be questioned.
    So, I might think that if my life contains the five minutes of pleasure during which all the secrets of the universe are revealed to me it wouldn’t matter how much physical suffering I would need to also endure. If that’s right then the move from A to B is not available. But, surely this is something we would not want to say even if I intensively was allowed enjoy the higher pleasure of listening to an opera. That is something that would be outweighed and compensated by the decreases in the amount of pain. So, whether there is always a intuitive move from A to B seems to depend on the quality in a way that isn’t immediately captured by the argument.

  14. Campbell Brown says:

    Jussi,
    I can quickly sketch how the argument would go in the case where there are three qualitative levels of pleasure. I hope that will indicate how to generalise to greater numbers of levels.
    Call the three levels lower pleasure, medium pleasure, and higher pleasure. We could then represent a life by an ordered quadruple in the obvious way. Then Mill’s Principle would be something like this: for any life x and numbers l and h, if h > 0 then x + (l,0,h,0) is better than x (i.e. increasing higher pleasure while holding medium pleasure and pain fixed always makes a life better). Weak Pain Aversion would be: for any life x and number p, if p < 0 then x + (0,0,0,p) is at least as good as x (i.e. reducing pain while holding all else fixed can't make a life worse). And the Triangle Principle would be: there exist lives x, y, and z and positive numbers l,h,p,p' with p =< p' such that y = x + (0,0,-h,-p), z = y + (l,0,0,p'), y is at least as good as x, and z is at least as good as y. Mill's Principle could then be shown to be inconsistent with the conjunction of Weak Pain Aversion and the Triangle Principle.

  15. Jussi Suikkanen says:

    Campbell,
    thanks that helps. I can see how to that would go. I guess someone symphatetic to the Millian principle would then deny the existence of y that would be as good as x once we get to high enough quality-levels of pleasure (unless we also get to high-enough quality pains). You might also think that some of the higher-pleasures come in quantums. You need to have the whole hog or none. Certain pleasures of important achievements might be like this. In this case, the move to less pain would move you also to lower levels of pleasure and thus no compensation would be forthcoming from the lesser pain according to the Millian.

  16. Jussi,
    Yes, I see your point now. The more fine-grained the division of pleasures into qualitative levels, the more plausible it is that some sufficiently high level of pleasure has lexical priority over pain. I think that’s right. Still, I doubt there could a level high enough, no matter how fine-grained the division.

  17. Dale Dorsey says:

    Campbell –
    All good questions. I’m not quite sure I have anything satisfactory to say. I have no idea what Mill might say, so maybe I’ll throw a thought or two out there to see if that helps the cause. So it’s right to say, I think, that Mill (or, if you like Mill-as-I-am-taking-liberties-with-him) believes that higher pleasures have lexical priority over pain. But Mill needn’t commit himself to the “five minutes” claim–a higher pleasure, you might think, has a minimum temporal duration, whatever is enough to constitute a “mode of existence”. Five minutes of listening to good music is not a higher pleasure.
    Alternatively, you might make a distinction in types of lexical priority views: trumping and discontinuity. Trumping says that some amount of x no matter how small is always better than any amount of y no matter how large. Discontinuity says that there is some amount of x such that the achievment of that amount of x outweighs any amount of y. So Mill could believe discontinuity: there has to be a long enough temporal duration in order for a higher pleasure to be lexically superior; but it’s not the case that five minutes meets that threshold. This is, perhaps, nothing like what Mill would actually say, but for what it’s worth, it seems to me a more plausible view.

  18. Campbell Brown says:

    Dale,
    Thanks, that helps. I had the ‘trumping’ version of lexical priority in mind. I haven’t thought much about the ‘discontinuity’ version, but I don’t like the sound of it. For one thing, I worry that it will imply intransitivity (I expect this point has been made before).
    As I understand it, the following is a version of the discontinuity view.

    For any (x,y) and (x’,y’):

    1. if x – x’ ≥ 100, then (x,y) is better than (x’,y’)
    2. if x – x’ < 100, then (x,y) is at least as good as (x',y') iff 5(x - x') ≥ (y' - y).

This sets the threshold for lexical priority at 100. An increase in x of 100 or more is better than an increase in y of any amount. But an increase in x of less than 100 is better than an increase in y only if the latter is less than 5 times as great as the former.
But this implies, e.g., that (0,500) is at least as good as (50,250), and that (50,250) is at least as good as (100,0), but that (0,500) is worse than (100,0).

  • Dale Dorsey says:

    Hi Campbell –
    Good point. I agree that that version of discontinuity implies intransitivity, which I hadn’t seen before. But I don’t think that’s the version of discontinuity I was alluding to. On my version it’s not the case that the increase in x must be 100 or more. Rather, the amount of x must be 100 or more. So, for instance, if you had 100 worth of x, you’d never trade that off for any amount of y. But if you had 99 worth of x, that could be traded off against some finite amount of y. So, in your result, the version I was alluding to would deny that (50, 250) is at least as good as (100,0), because 100 of x is better than 50 of x, and 100 of x is worth any amount of y.

  • Campbell Brown says:

    Dale,
    That’s interesting. But now I wonder whether the view you have in mind is not just an ordinary lexical priority view, of the ‘trumping’ sort.
    The following is a version of the view you have in mind (as I understand it).

    First, define two functions f and g such that:

    • f(x,y) = 1 if x ≥ 100, and f(x,y) = 0 if x < 100
    • g(x,y) = 5x + y

    Then for any (x,y) and (x’,y’):

    • if f(x,y) > f(x’,y’), then (x,y) is better than (x’,y’)
    • if f(x,y) = f(x’,y’), then (x,y) is at least as good as (x’,y’) iff g(x,y) ≥ g(x’,y’)

    This seems to capture the essential features of the ‘discontinuity’ view you describe.
    Interestingly, however, this is (or is equivalent to) a trumping view, except with the dimensions being f(x,y) and g(x,y), rather than x and y. We can characterise the view as follows: first, maximise f(x,y); then, in case of ties in f(x,y), maximise g(x,y). This is just ordinary lexical priority.

  • Campbell Brown says:

    Let me add a little more.
    Here’s another way to characterise the view I defined in my previous comment. There are two goals or aims. One goal is to get the level of x up to (or over) the threshold of 100. The other goal is to make a weighted total of x and y, in which x gets more weight, as great as possible. We can think of the functions f and g as measuring the degree of success in achieving these two goals. (Notice, for the first goal, there is no partial success. Either there is complete success, i.e. f(x,y) =1, or there is complete failure, i.e. f(x,y) = 0. A miss is as good as mile.) So the two goals are equivalent to maximising f(x,y) and g(x,y) respectively.
    Now the view in question says that any success in achieving the first goal trumps any success in achieving the second; or equivalently, maximising f(x,y) trumps maximising g(x,y). This is why I say the view has the structure of a trumping view. It can be characterised as giving two goals, one of which trumps the other.

  • Dale Dorsey says:

    Hi Campbell –
    Sorry it’s taken so long to respond. I agree that it’s a trumping view, if by trumping view you just mean a view that entails a line of lexical priority somewhere. But it’s a trumping view that wouldn’t entail that any amount of higher pleasure, no matter how short, is better than any amount of lower pleasure (or pain) no matter how long. (That’s what, for instance, Griffin calls ‘trumping’.) It would entail that a sufficient amount of higher pleasure is better than any amount of lower pleasure (or pain) no matter how long. (Which is what Griffin calls ‘discontinuity’.)