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:
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:
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.