Some years ago, Howard Wettstein provided an original defense of the New Theory of Reference (NTR), the doctrine that singular terms such as names and indexicals are directly referential terms (DRTs), contributing only their reference to the truth-conditions of the tokened sentence they occur in. Wettstein maintained that in order to be semantically adequate, NTR does not have to account for what he calls Frege’s data on cognitive significance, those puzzling facts about language that prompt one to think that meaning (...) entails more than reference to (real) objects. He later put forward another, apparently paradoxical, thesis, namely that whatever this cognitive significance that explains Frege’s data is, it cannot be reduced to the representations one has in one’s mind. In what follows, however, I will first apply the notion of referential anaphorical transfer to mixed contexts in order to show that a New Theorist has to reject Wettstein’s initial thesis as it stands, although she may endorse a weaker version of it, one that especially tallies with his second thesis. I will further argue that, insofar as rejecting Wettstein’s initial thesis does not force the New Theorist to revert to a representional conception of cognitive significance, in particular one based on the notion of a mental file, the latter thesis is absolutely correct. It is thus fitted to become a cornerstone of the New Theory, whatever form of non-mentalistic interpretation the New Theorist might wish to give to the notion of cognitive significance. (shrink)