Abstract: Stalnaker (1974, 1979) made
two seminal claims about presuppositions. The most influential one was
that presupposition projection is computed by a pragmatic mechanism
based on a notion of ‘local context’. Due to conceptual and technical
difficulties, however, the latter notion was reinterpreted in purely
semantic terms within ‘dynamic semantics’ (Heim 1983). The second claim
was that some instances of presupposition generation should also be
explained in pragmatic terms. But despite various attempts, the
definition of a precise ‘triggering algorithm’ has remained somewhat
elusive. We discuss possible extensions of both claims. First, we
offer a reconstruction of ‘local contexts’ which circumvents some of
the difficulties faced by Stalnaker’s original analysis. We preserve
the idea that local contexts are computed by a pragmatic mechanism that
aggregates the information that follows from an incomplete sentence
given the global context; but we crucially rely on a modified notion of
entailment (‘R-entailment’), whose plausibility should be assessed on
independent grounds. Second, we speculate that local contexts might
prove necessary (though by no means sufficient) to understand how some
presuppositions are triggered. In a nutshell, we suggest that a
presupposition is triggered when the semantic contribution of an
expression to its local context is in some sense ‘heterogeneous’.
Without giving an analysis of the latter notion, we note that
this architecture implies that presuppositions should be triggered on
the basis of the meaning that an expression has relative to its local
context (what we call its ‘local meaning’); we sketch some possible
consequences of this analysis.