A Counterexample to Social Externalism?

Suppose there are two linguistic communities of (roughly) equal size, dispersed throughout a large area. Both speak dialects of the same language. One community uses the term 'arthritis' to refer exclusively to a painful condition of the joints, the other uses it to refer to any painful condition in one's limbs. There is a certain smaller region in which members of both communities are to be found, and in (roughly) equal numbers. There is, however, no “overlap”: Each speaker fully adopts the convention of his or her community, they do not sometimes adopt one usage and sometimes another. The dialects are alike in every other respect. Along comes Wyman, who does not speak the language. Wyman, however, comes to learn it, and eventually speaks it, to all appearances, just as the two communities do. But he is nevertheless unaware of the difference in usage with respect to the term 'arthritis'. One day he tells his doctor, “I have a horrible case of arthritis in my thigh.” One community would judge that what Wyman said was false; and the other, that it was true. Both could not be right.

The question is: What did the term 'arthritis' mean on that occasion? Which of the two communities' incompatible usages could it have been that determined what 'arthritis' meant in Wyman's mouth? He was unaware of any difference between the two communities, both are equal in size and equally prevalent in his area, and he interacted just as much with both. To say that Wyman “really” counts as a member of one community rather than the other, and thus that the term “really” had one meaning rather than the other, seems arbitrary. And externalists cannot say that 'arthritis' had both meanings, for then what he said would have been both true and false. If externalists were to say that it was indeterminate which meaning it had, they must admit that some matters are indeterminate—which, though many may be happy to do, might not be coherent. That the statement had no meaning is something I can understand, though I find it implausible for this case; but could it really be that it's determinate that it had one or other of those meanings, but not determinate which? But however that may be, I'm interested to see what my readers think.