 Even though Montague tended to play down the difference, the switch from senses to intensions is known to have dramatic consequences on the fine-grainedness of semantic analysis. In particular, as mentioned in section 2.4, any two logically equivalent sentences come out as having the same intension; yet their senses will diverge if their truth value is not determined in the same way. Montague indicated how this unwelcome consequence may be avoided in terms of mismatches between worlds and contexts, creating what he called ‘“unactualizable” points of reference’ (ibid., 382), but he did not provide a detailed analysis to substantiate his sketchy remarks.