AbstractThis thesis consists of two separate but related studies on the notion of presupposition as it occurs in philosophy and linguistics. In the first study I examine the theory of logical presupposition found in the work of Gottlob Frege. In the second I examine the theories ofDeirdre Wilson and Lauri Karttunen. These theorists reject the notion of logical presupposition in favor of pragmatic and non-logical conceptions. There are important problems with all three theories. Frege's theory fails to account for the presupposition of compound sentences. Wilsons's and Karttunen's fail to demonstrate conclusively that the presupposition of simple sentences and their negations are non-logical.Frege's theory of presupposition:Frege's theory of presupposition is a consequence of his more general semantic theory. In Part 1 I show how two different notions of presupposition can be reconstructed from his semantics; one applies directly to sentences, and the other applies directly to thoughts. This distinction is used to clarify Frege's discussion of presupposition in "On Sense and Reference".In Part 2 I maintain that a speaker who utters a sentence with a false presupposition typically succeeds in making a statement. I argue against those who interpret Frege as denying this and show how a proper understanding of his semantics eliminates one of the main problems that have led theorists to erronenous interpretations.In Part 3 I examine the relationship between negation and presupposition. I show that Frege's account of internal negation is inadequate and must be supplemented with an account of external negation. However, when external negation is introduced, his theory of logical presupposition conflicts with his theory of truth. Finally, I show that Frege's theory makes incorrect predictions about the presuppositions of compound sentences. This undermines his view that sentences are special kinds of "proper names".In the essay on Frege I also consider certain issues that apply to any theory of logical presupposition. I argue that logical presupposition in natural languages should not be defined in terms of what is entailed by a sentence and its negation. I also argue that redundancy theories of truth and falsity conflict with theories of logical presupposition.Two theories of non-logical presuppositionIn the second essay I investigate Wilson's and Karttunen's theories of non-logical presupposition. These theorists hold the following two theses:A. Theories of natural languages require an account of non-logical presupposition.B. The notion of logical presupposition should be eliminated from theories of natural languages. (A) is correct, but the arguments for (B) are not conclusive.In Part 1 of this essay I present Karttunen's notion of presupposition that applies to conjunctions, disjunctions, and conditionals. In Part2 I argue that this notion is non-logical, but that this result is compatible with restricted theories of logical presupposition based on simple sentences and their negations. In Part 3 I examine the importance of negation for such theories and evaluate Wilson's argument that negative sentences do not bear logical presupposition.Parts 4 and 5 are concerned with the pragmatic accounts of Wilson andKarttunen. In Part 4 I demonstrate that Wilson's theory is incorrect and argue that it cannot be repaired. In Part 5 I indicate several difficulties with Karttunen's view and propose modifications to resolve them.