 Kripke’s arguments provide a strong reason for Fregeans to deny Fregean descriptivism, and hold instead that the senses of proper names are not the senses of any definite description associated with those names by speakers. The main problem for this sort of non-descriptive Fregeanism is to explain what the sense of a name might be such that it can determine the reference of the name, if it is not a condition uniquely satisfied by the reference of the name. Non-descriptive Fregean views were defended in McDowell (1977) and Evans (1981). The most sophisticated and well-developed version of the view is a kind of blend of Fregean semantics and possible worlds semantics. This is the epistemic two-dimensionalist approach to semantics which has been developed by David Chalmers. See Chalmers (2004,2006).