I just heard that, in the case of Hilary Putnam's "Twin Earth" experiment, Tyler
Suppose we individuate concepts by "reference," so two mental states/thoughts are identical if they are about the same things, otherwise different. If (arguably) one twin's thoughts 'refer to' H2O and the other's 'refer to' XYZ, then they would count as different thoughts or concepts. What you are merely presuming is that the notion of 'concept' should be narrowly individuated (ie defined only in terms of what's 'in the head', so the two twins shoudl have the same concept). But that is the very thing that is explicitly being debated in the classic papers by Putnam, Burge, and all the rest ....!