'Only' noun phrases, pseudo-negative generalized quantifiers, negative polarity items, and monotonicity

Journal of Semantics 13 (4):265-328 (1996)
Abstract
The theory of Generalized Quantifiers has facilitated progress in the study of negation in natural language. In particular it has permitted the formulation of a DeMorgan taxonomy of logical strength of negative Noun Phrases (Zwarts 1996a,b). It has permitted the formulation of broad semantical generalizations to explain grammatical phenomena, e.g. the distribution of Negative Polarity Items (Ladusaw 1980; Linebarger 1981, 1987, 1991; Hoeksema 1986, 1995; Zwarts 1996a,b; Horn 1992, 1996b). In the midst of this theorizing Jaap Hoepelman invited me to lecture in Stuttgart about Focus, and I took the opportunity to talk about a seminal paper on ‘only Proper Name’ and ‘even Proper Name’ by Larry Horn (1969), a paper that I had admired but that had nagged at me for years. The result of Hoepelman‘s invitation was Atlas (1991, 1993), in which I believed that I had discerned difficulties for the formal semantics of Negative Polarity Item sentences, ‘only Proper Name’ sentences licensed Zwarts’s “weak” Negative Polarity Items, e.g. ‘ever’, ‘any’, but ‘only Proper Name’ was not a downwards monotonic quantifier, thus refusing the broad semantical generalization that any NPI licenser was a downward monotonic quantifier. In fact ‘only Proper Name’ was the first of a new category of generalized quantifier: the pseudo-anti-additive quantifier. Though I have explained and defended the introduction of this new category in this paper, a particular interest of my analysis is that it opens up the theory of Negative Polarity Items for further development; it permits the formulation of entirely new questions for research (see ‘Open Questions’, Appendix 1). Along the way I was also trying to present a correct account of the formal semantics and implicatures of ‘Only a is F’, a subject of theoretical investigation for the last 700 years, but without, in my view, any theory ever arriving at the truth. There had to be something wrong with our theoretical methods or theoretical bias towards the data. So I (Atlas 1991, 1993) have tried to break out of this logjam by introducing new constraints on the acceptability of logical forms (first introduced in Atlas & Levinson 1981 for the analysis of clefts, and in Atlas 1988 for the analysis of negative existence statements). The earlier theories ignored conversational implicatures entirely; it seemed of theoretical interest to examine statements containing focal particles like ‘Only’ for their implicatures, especially as the correct prediction of implicatures tells one something about the truth-conditions and logical form of the statement itself (Atlas 1991, 1993). In this paper I review and modify my earlier theory of the logical form, semantical properties, and pragmatic properties of ‘Only a is F‘. I also provide the correct generalization to the case of ‘Only G is F‘. And I respond to the criticisms in Horn (1992, 1996b)
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