Many philosophers doubt the possibility of unknowable moral truths. E.g. Thomas Nagel said (in The View from Nowhere, p. 139):
I do not believe that the truth about how we should live could extend radically beyond any capacity that we might have to discover it (apart from its dependence on nonevaluative facts that we might be unable to discover).
But in fact, there is a simple argument -- unsurprisingly, broadly Williamsonian in inspiration -- that shows that there must be unknowable moral truths.
Note (added on 10 August 2010): Jussi Suikkanen has correctly pointed out that he made what is in all essentials the very same argument on this blog over two years ago. The record also reveals that I read his post at that time (although I somehow now have no recollection of having done so). So it is Jussi, and not I, who should be regarded as the first to have presented this argument in public!
The argument rests on the following assumptions:
- Classical logic applies to moral propositions.
- Our powers to discriminate very similar cases from each other are limited; as a result, knowledge is subject to a "margin for error" principle.
- There is a continuous spectrum of possible cases, which leads smoothly from cases where acting in a certain way (e.g. killing an innocent person) is not permissible, all the way to cases where acting in that way is permissible.
Here is one example of the kind of spectrum of cases that we need to consider. All the cases in this spectrum involve a choice between two options: (i) killing an innocent person, and (ii) refraining from killing the innocent person. For every case Ci, the following case Ci+1 does not differ from case Ci at all -- except that in Ci+1, killing the innocent person does very slightly more good than in Ci (and killing the innocent person is also the only available means of achieving this good). At one end of the spectrum, we have case C0, in which killing the innocent person does no good at all. At the other end of the spectrum we have case Cn (where n is some huge number), in which killing the innocent person is the only way to save the whole world from imminent destruction.
Almost all moral philosophers, whether they are consequentialists or not, will say that it is not permissible to kill the innocent person in case C0, but it is permissible (indeed perhaps even obligatory) to kill the innocent person in case Cn. (The only dissenters are extreme absolutists, who say that killing is always impermissible, no matter how terrible the consequences of refraining from killing might be.)
Classical logic includes the law of excluded middle (LEM). LEM tells us that every case Ci is such that either it is permissible to kill the innocent person in Ci, or it is not permissible to kill the innocent person in Ci.
So there must be a lowest number j such that it is not permissible to kill the innocent person in case Cj, but it is permissible to kill the innocent person in case Cj+1. In effect, the difference between case Cj and case Cj+1 marks the threshold between the cases in which the killing is not permissible and the cases in which it is permissible.
But we could obviously never know for certain where this threshold lies. Only godlike powers of discrimination could enable a moral thinker to know such things.
Moreover, even though it is permissible to kill the innocent in case Cj+1, Williamson's "margin for error" principle guarantees that it is impossible for us to know that killing is permissible in this case. This is because case Cj+1 is so close to case Cj (where killing is not permissible) that Cj+1 falls into the "margin for error". If you believed the true proposition that killing is permissible in Cj+1, your belief would not be "safe": there is a very nearby case in which you believe almost the same proposition on almost the same basis, but believe something false.
So even though it is permissible to kill the innocent in Cj+1, it is impossible for you to know that it is. (Indeed, if it is reasonable for you to think that either (a) killing is not permissible in Cj+1, or (b) both killing and refraining from killing are permissible in Cj+1, it will probably be safer for you to act as if killing is not permissible in Cj+1 -- even though in fact it is permissible.)
At all events, it seems quite clear that if the assumptions of this argument are correct, there must be unknowable moral truths.