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Frank Jackson and David Chalmers have suggested that the diagonal intensions defined by their two-dimensional framework can play the two key roles of Fregean senses: they provide a priori accessible extension conditions for a representation and they provide the identity conditions for meanings and thought contents. In this paper, I clarify the nature of the psychological abilities that are needed to underwrite the first role. I then argue that these psychological abilities are not sufficiently stable or cognitively salient to individuate meanings or thought contents.