Presuppositions, negation, and existence

Abstract
Last year (2005) marked the 100th anniversary of the publication of Russell’s classic ‘On denoting’. It should not cast any shadow on that great work to note that the problems it provided solutions to are still the subject of controversy. Two of those problems involved noun phrases (NPs) which fail to denote. Russell’s examples (1a) and (1b) (1) a. The king of France is bald. b. The king of France is not bald. are puzzling because they have the form of simple contradictories, and yet we are not inclined to say either one is true. Example (2) (2) Pegasus does not exist. is even more problematic; the lack of denotation for Pegasus, which makes the sentence true, also seems to rob it of a meaningful constituent. Once the king of France is unpacked according to Russell’s analysis, (1b) is revealed to be ambiguous. It’s logical forms are given in (3). (3) a. ∃x[Kx ∧ ∀y[Ky ↔ y=x] ∧ ¬Bx] b. ¬∃x[Kx ∧ ∀y[Ky ↔ y=x] ∧ Bx] (3a) says that there is a unique (French) king who is not bald (obviously false), but (3b), the logical contradictory of (1a) says that it is not the case that there is a unique king who is bald (which is true). We can apply the analysis to sentence (2) once we recognize Pegasus as a concealed definite description, e.g. the winged horse of Greek mythology. (2) can then be unpacked as (4) (4) ¬∃x[Wx ∧ ∀y[Wy ↔ y=x]] which seems both meaningful and true, as required. Problems solved. Well, not quite. Strawson (1950) challenged the first solution above, arguing that neither (1a) nor (1b) could be used to assert the existence of a king of France. Rather, use of such sentences presupposes the existence of a king of France, and failing that existence, neither of (1a) or (1b) could be used to make either a true or a false statement – in Strawson’s words, “the question of whether it’s true or false simply doesn’t arise” (Strawson 1950, 330).1 In an extended series of essays, and one book, Jay Atlas (1977, 1978, 1979, 1989, 2004) has taken issue with the work of both Russell and Strawson..
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