Frege on Singular Senses

In this article the author discusses what seems to be a puzzle for Frege’s notion of singular senses (i.e., the senses of singular terms), in particular senses of definite descriptions. These senses are supposed to be complete (or saturated), but they are composed of the incomplete (unsaturated) senses of conceptual terms (i.e., conceptual senses). The author asks how the definite article (or what it expresses) transforms an unsaturated sense into a saturated one and reviews some attempted explanations in the literature. He argues that none of them is compatible with Frege’s views in semantics. Next, he discusses an alternative that Frege himself endorses and argues that it is also incompatible with his semantics. The author concludes that Frege has no coherent view on the senses of definite descriptions. If we assume that every name expresses a descriptive sense, then we must conclude that Frege has no coherent explanation for singular senses in general.