Chapter 5 The Case of Indefinites: Scope and Context 1: Introduction

Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb ((1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something.) In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other intensional predicates and argued for a Nominalization Theory of special quantifiers. In this paper, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for a higher-order and substitutional analyses of special quantifiers. I will outline a new version of the Nominalization Theory of special quantifiers based on the syntactic status of '-thing' as a light noun in Richard Kayne's sense.

Following a common practice in generative grammar, HPSG treats the determiners as members of a separate functional part of speech (DET), just like the complementizers, the coordinating conjunctions, and (in some frameworks) the auxiliaries. The status of such functional parts of speech is a matter of debate and controversy. The auxiliaries, for instance, are commonly treated as members of a separate category (AUX or INFL) in many variants of generative grammar, including GB, MP and LFG, but in GPSG and HPSG, it is a matter of equally common practice to treat them as members of V and to reject the postulation of a separate functional category, see and . This text makes a similar case for the determiners; more specifically, I will argue that they are categorially heterogeneous, in the sense that some determiners are members of A, whereas others are members of N. The argumentation is mainly based on inflectional morphology and on morpho-syntactic agreement data. The consequences of the categorial heterogeneity are hard to reconcile with the specifier treatment of the determiners of (Pollard and Sag 1994), and even more with the Detas-head treatment of (Netter 1994), but it can smoothly be integrated in the functor treatment of the prenominals of (Allegranza 1998) and (Van Eynde 2003b).

International Journal on Artificial Intelligence Tools, 2006

This article constitutes a contribution to an analysis of the notion of variable. Within the framework of Combinatory Logic as a formalism without bound variables, the Logic of Determination of Objects (LDO) provides an explanation for the necessary distinction between "whatever, any" and "indeterminate, indefinite" used by the introduction and elimination rules of quantifiers in Natural Deduction. The intension of a concept and typical and atypical occurrences of a concept are also introduced yielding new quantifiers which are more adequate to natural language processing (NPL) and to the study of natural inferences in common reasoning.

2020

Generalized Quantifier Theory (GQT) is discussed as an analysis of quantifying expression (QE) in natural language. According to that theory, a quantifier denotes a relation between sets, and quantifying DPs are QE which are defined as sets of sets. Such QEs require quantifier raising (QR) and an additional mechanism that provides for the binding of bound variable pronouns. Various restrictions for scope taking in sentences with two and more quantifiers seem to apply; an alternative to scope taking via QR is scope independence, which can be modelled by choice functions or Skolem functions and is informally described in terms of Game Theory. Various data seem to require scope extension in the sense that semantic scope is wider than syntactic scope via c-command. Such extensions are discourse representation theory (DRT) and dynamic logic. Further extensions of GQT deal with pluralities.

Philosophical Perspectives, 2003

Frege's (1879, 1892) treatment of quantification is rightly regarded as a major advance in the study of logic and language. But it led Frege and others to some views that we can and should reject, given developments in the study of transformational grammar and compositional semantics. Once these views are put aside, the developments suggest that the common logical form of sentences like and (1) Every bottle is red (2) Pat kicked every bottle where 'O' ranges over ordered pairs of a special sort, but not ordered pairs of sets. If this is correct, some familiar conceptions of logical form must be modified. Pace Frege, there is no important mismatch between the structure of a sentence like (2) and the structure of the proposition (Thought, potential premise/conclusion) expressed by using the sentence. This pointabout grammatical form, logical form, and the need to revise pre-Fregean conceptions of both-will be familiar to specialists. But it has not yet pervaded the wider community that learned, often via Russell (1905, 1918), about the alleged mismatch. Correlatively, many philosophers have held that logical forms are regimentations of sentences in a natural language. So given a preference for first-order regimentation, appeal to second-order logical forms can seem misguided. But as Boolos (1998) shows, quantification into monadic predicate positions is motivated and unobjectionable, when it is construed as plural quantification (over whatever first-order variables range over) as opposed to quantification over sets. We can also reject the idea that transitive verbs are associated with functions from pairs of entities to truth values. Instead, we can adopt the following view, motivated by extensions of event analyses: all verbs are semantically monadic; combining verbs with other expressions corresponds to predicate-conjunction; and grammatical relations that verbs bear to their arguments are semantically associated with participation relations, like being an Agent of, that individuals can bear to things like events. adopts this approach to plural constructions like (3).