We shall understand, then, that by Greatest Happiness is meant the greatest possible surplus of pleasure over pain, the pain being conceived as balanced against an equal amount of pleasure, so that the two contrasted amounts annihilate each other for purposes of ethical calculation. And of course, there as before, the assumption is involved that all pleasures included in our calculation are capable of being compared quantitatively with one another and with all pains; that every such feeling has a certain intensive quantity, positive or negative (or, perhaps, zero), in respect of its desirableness, and that this quantity may be to some extent known: so that each may be at least roughly weighed in ideal scales against any other. This assumption is involved in the very notion of Maximum Happiness; as the attempt to make 'as great as possible' a sum of elements not quantitatively commensurable would be a mathematical absurdity. [Hackett edition, pg. 413, my italics]So...pain and pleasure are positives and negatives on the same scale. You can therefore "sum" them:
-92 [pain] + 3 [pleasure] = -89 [balance]
That's me getting my teeth cleaned. -92 is the misery, and 3 is the dental hygienist telling a joke. The 3 annihilates just a little bit of the pain, making the balance -89.
As often as I've read and taught this story, it's never really struck me full force that this cannot be. Here goes--a quick argument why not.
Suppose it's a hot afternoon in Texas (not a difficult supposition, because we're in the middle of a heat wave). It's 102 degrees. I am a good utilitarian mother with a 5 year old child (neither is the truth). I'm trying to decide how to keep him happy for the next couple of hours. The right course of action is the one with the best consequences. I'm fully committed to that--I'm not going to change my mind about it.
So I think about two options and I think about them as Sidgwick proposes--pain and pleasure annihilate each other. Here's what I wind up with--
Option #1: we sit at home and enjoy the dull pleasure of playing board games while listening to Burl Ives. This will be pleasant for little Charlie, and not at all unpleasant. The calculation is something like this:
0 [pain] + 15 [pleasure] = 15 [balance]
Option #2: we walk 10 blocks to the local McDonald's in 102 deg. heat where Charlie will have riotous fun for many hours on the play structure while I read Henry Sidgwick. I know that at the very least, the balance is going to be 15.
-100 [pain] + 115 [pleasure] = 15 [balance]
(Effects on others? The same in both cases. Other things are equal.)
Given (1) my consequentialist assumption about rightness, and (2) my Sidgwickian assumption about how to calculate value, there is no moral difference between choosing option #1 and choosing option #2. But (wait for it...) there is a difference.
Obviously, obviously, a morally acute mother will see a difference between giving her child a bland afternoon of games and music, and imposing a miserable walk on him, so that he can have a wildly good time. I'm not saying one is clearly the right option, but the choice is difficult, not easy. This isn't a toss-up.
If consequentialism is not to be questioned (and please, let's assume it's not), then there's got to be a problem with this way of calculating value. And the problem has got to be that pain and pleasure do not "annihilate" each other. There is no balance in each case, there's just a lump of pain and a lump of pleasure.
"But .... but ... but there has to be some way to integrate the information about pain and pleasure, combining it into one value assessment." One hopes so, but this way is the wrong way--pain and pleasure just don't annihilate each other.