The thesis under consideration is this:
Coarse and fine belief are related as determinable and determinate respectively, because the latter metaphysically makes for the former.
The worry was something like this.
(1) The mere fact that ~p means that mental state MS1 is mistaken if MS1 is the belief that p.
(2) On any Lockean view worth its salt, it is possible that a mental state MS2 is a level of confidence in p's truth less than certainty while also being the belief that p.
(3) If MS1 is related to MS2 as determinable and determinate respectively, if MS1 is mistaken, MS2 is mistaken.
(4) However, the mere fact that ~p does not make MS2 mistaken if MS2 is a level of confidence in p that is less than certainty.
(C) Thus, the Lockean view is wrong because it has the implication that it is possible for MS2 to be both mistaken and not mistaken under the same condition.
Mike raised the following concern. Doesn't the argument equivocate on 'mistaken'?
There's nothing with with MS2 being mistaken in one sense while not being mistsaken in some different sense. So, there's no problem here.
It seemed at first that there's a way of fixing the argument. Consider:
Necessarily, the mere fact that ~p means that there is a sense in which mental state MS1 is mistaken if MS1 is the belief that p. The mere fact that ~p does not mean that there is _any_ sense in which that mental state MS2 is mistaken if MS2 is a level of confidence in the truth that p less than certainty. On any Lockean view worth its salt, a belief that p can consist of a level of confidence less than certainty. But, it seems to follow that MS1 is not MS2. But, it seems that we'd want to say that MS1 could be MS2 in just the same sense that the red of this cup could be an instance of scarlet.
We might agree that there are two ways of thinking of a belief as being mistaken. It might be false or it might be justified. However, in the relevant sense of 'mistaken', I'm assuming only that it is mistaken in the first sense. If there's no sense in which the mere fact that ~p can show that a level of confidence in the hypothesis that p can be a mistake, I don't see that the possible equivocation could really cause trouble for this argument.
To this, I suppose someone might say the following. It might sound odd to say that a level of confidence in p less than certainty is mistaken just because ~p, but that's because the norms we use in contexts where we're focused on coarse grained belief are different from those we use in contexts where we're interested in fine grained belief. The infelicity of saying that a level of confidence less than certainty is mistaken stems from this fact and not the falsity of saying that MS2 is mistaken. The situation might be something like this. I'm holding a red coffee mug. The redness of this cup is an instance of scarlet. It might be that this instance of scarlet is bad (aesthetically) even if the redness of this cup is good because I've been asked to paint it some shade of red. In contexts where the redness is at issue we are interested in my complying with the order to paint the cup red, so it would be odd to say that the redness of the cup is bad in such contexts. In contexts where the fact that the cup is scarlet is at issue, we are interested in the cups aesthetic qualities in ways that whoever asked me to paint the cup red might not have been.
If we think of things this way, we seem to have a problem. We have a problem if we want there to be one and only one set of norms governing beliefs coarse and fine.