Anti-dynamics: presupposition projection without dynamic semantics

Heim 1983 suggested that the analysis of presupposition projection requires that the classical notion of meanings as truth conditions be replaced with a dynamic notion of meanings as Context Change Potentials. But as several researchers (including Heim herself) later noted, the dynamic framework is insufficiently predictive: although it allows one to state that, say, the dynamic effect of F and G is to first update a Context Set C with F and then with G (i.e. C[F and G] = C[F][G]), it fails to explain why there couldn’t be a ‘deviant’ conjunction and* which performed these operations in the opposite order (i.e. C[F and* G] = C[G][F]). We provide a formal introduction to a competing framework, the Transparency theory, which addresses this problem. Unlike dynamic semantics, our analysis is fully classical, i.e. bivalent and static. And it derives the projective behavior of connectives from their bivalent meaning and their syntax. We concentrate on the formal properties of a simple version of the theory, and we prove that (i) full equivalence with Heim’s results is guaranteed in the propositional case (Theorem 1), and that (ii) the equivalence can be extended to the quantificational case (for any generalized quantifiers), but only when certain conditions are met (Theorem 2). 1 The Projection Problem and the Dynamic Dilemma 1.1 The Projection Problem How are the presuppositions of complex sentences computed from the meanings of their component parts? This is the so-called ‘Projection Problem’, which is illustrated in (1): (1) a. The king of Moldavia is powerful. b. Moldavia is a monarchy and the king of Moldavia is powerful. c. If Moldavia is a monarchy, the king of Moldavia is powerful. (1)a presupposes (incorrectly) that Moldavia has a king. But the examples in (1)b-c presuppose no such thing; they only presuppose that if Moldavia is a monarchy, it has a king (a condition which is satisfied if one knows that Moldavia is in Eastern Europe and that Eastern-European monarchies are of the French type, i.e. that if they have a monarch, it is a king, not a queen). How can these facts be explained? Minimally, a theory of presupposition projection should be descriptively adequate and thus provide an algorithm to compute the presuppositions of complex sentences. If possible, the theory should also be explanatory and thus derive the algorithm from independent considerations (though what counts as more or less explanatory may be a matter of debate). 1.2 Stalnaker’s Pragmatic Approach In what might be the single most influential proposal in presupposition theory, Stalnaker 1974 offered a brilliant analysis of presupposition projection in conjunctions. His theory included three main assumptions (see also Karttunen 1974, who adopts versions of (i) and (ii) as well). *I wish to thank the following for critical comments and suggestions: Richard Breheny, Emmanuel Chemla, Danny Fox, Bart Geurts, Irene Heim, Uli Sauerland, Barry Schein, Roger Schwarzschild, Ken Shan, Benjamin Spector, Dan Sperber, Anna Szabolcsi, Arnim von Stechow, Deirdre Wilson, as well as audiences in Paris (Institut Jean-Nicod), Berlin (Semantiknetzwerk), London (University College London), Gargnano (Milan Meeting 2006) and Rutgers University. Thanks also to an anonymous referee for JoLLI. The author gratefully acknowledges the financial support of the American Council of Learned Societies ('Ryskamp Fellowship') and of UCLA.