<p>It is common to find in the literature on natural language semantics reference to the “Frege-Strawson” theory of presuppositions and the “Frege-Strawson” theory of definite descriptions. While these labels might be useful in certain contexts, I argue that the differences between the Fregean and the Strawsonian theories of presupposition are sufficiently important to warrant separate treatment. In the first part of the paper, I consider Frege’s and Strawson’s views on presuppositions, focusing on those triggered by definite descriptions. Next, I propose a formulation of the two theories within a framework for natural language semantics inspired in Kaplan (<CitationRef CitationID="CR38">1989</CitationRef>), to which a Montague-style apparatus for semantic composition is added. I argue that Frege’s and Strawson’s respective views of presuppositions should be formally implemented as partial functions situated at different levels within this semantic framework. This offers good reasons for a negative answer to the question in the title. In the second part of the paper, I compare the predictions the two theories make for the case of definite descriptions. I argue that embeddings of definite descriptions in intensional contexts show that the Fregean theory is the more promising alternative for the presuppositions that these expressions trigger.</p>