Abstract
In the semantic revolution that has led many philosophers of language away from Fregeanism and towards the acceptance of direct reference, the notion of rigidity introduced by Saul Kripke in Naming and Necessity (Kripke 1972) has played a crucial role. The notions of rigidity and direct reference are indeed different, but proponents of new theories of reference agree that there is a one way connection between them: although not all rigid terms are directly referential (witness rigid definite descriptions), all directly referential terms are rigid. My purpose in this paper is to contest this widely held view. I will argue that, on a certain conception of what direct reference is (a conception present in the works of the main proponents of the theory),
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