Abstract
It is argued that the notion of classical entailment faces two problems, the second argument projection problem and the P-to-Q problem, which arise because classical entailment is not designed to handle partial functions. It is shown that while the second argument projection problem can be solved either by flattening the syntactic tree or with naïve multi-valued logics, the P-to-Q problem cannot. Both problems are solved by introducing a new notion of entailment that is defined in terms of Strawson entailment (in the sense of von Fintel 1999, 2001). BibTeX info
Highlights
It is argued that the notion of classical entailment faces two problems, the second argument projection problem and the P -to-Q problem, which arise because classical entailment is not designed to handle partial functions
A widely held view is that the relation between (1a) and (1b) is that of classical entailment — or ⇒-entailment — defined informally in (2)
The second argument projection problem and the P -to-Q problem are byproducts of the assumption that the only way to account for the emergence of presuppositions is by treating natural language functions as potentially partial
Summary
The goal of this paper is to scrutinize the formal notion of entailment as it is understood and used in the semantics literature, and to propose an. While for any type-relevant x, speakers reject [‘x likes his mother’ but not ‘x likes someone’], likes his mother does not ⇒-entail likes someone by (2): if x is motherless and doesn’t like anyone, x likes his mother is neither true nor false and x likes someone is false. To solve these problems, we introduce two new relations: ⇒st-entailment, informally defined in (7), and ⇛-entailment, informally defined in (8).
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