Page 375 - Encyclopedia of Philosophy of Language

this way of analyzing and accounting for the 'de dicto' reading is satisfactory in all respects is a question still widely debated (see e.g., Gamut 1991).
The two readings of John seeks a unicorn are obtained in the following way. For the 'de re' reading, a quantification rule introduces the expression a unicorn. And if the expression a unicorn is introduced directly, that is, without the intervention of a quanti- fication rule, the result is the 'de dicto' reading. In principle, this method is analogous to the method used to express scope differences. One may, in fact, regard the distinction between 'de dicto' and 'de re' readings as a distinction due to scope differences of the inten- sional operator seek.
8. Developments
PTQ (Montague 1973) signaled the start of a large amount of formal semantic research. This section reviews some of the developments that emanated from PTQ.
PTQis restricted in at least two ways. First, it restric- ted itself to a 'fragment' of English, which in itself consituted a severe limitation as regards its coverage. In the majority of publications that were inspired by PTQ, attempts are made to extrapolate from Mon- tague's fragment to larger areas of English and other languages. Second, the formal tools of PTQare restric- ted. For instance, it uses a primitive kind of syntax, has semantic models of a certain type, and deals only with isolated declarative sentences. Several attempts have been made at improving the situation without losing any of the benefits already achieved. This sec- tion concentrates on this second class of publications because they give a perspective on the present-day possibilities in Montague grammar. Thereafter, the first class of publications will be considered briefly.
The relative lack of syntactic sophistication in PTQ appears, for example, from the absence of syntactic features, well-motivated constituent structures, and grammatical functions, and from the occurrence of several clearly ad hoc rules. As far back as the earliest years of Montague grammar, proposals were made to incorporate syntactic know-how as developed in linguistics into Montague grammar. The theory of transformational grammar was, of course, a promi- nent source of inspiration in this respect. It was this theory that led some reasearchers (Partee 1975; Dowty 1982) to devise systems where the rules of syntax oper- ate on tree structures (constituent structures) rather than on strings, as is done in PTQ. Partee's ideas on how to combine Montague grammar with trans- formational grammar are worked out in the very large grammar used in the machine translation project ROSETTA(Rosetta 1994).
The syntactic rules used in PTQ are not subject to any formal restriction. They may carry out any for- mally well-defined operation on syntactic material. For logicians, this is a comfortable situation, as they
can now focus on the semantic problems and are not hampered by syntactic qualms. In linguistics, on the other hand, this is felt as a severe loss in empirical force, as unrestricted rule systems may generate any formally defined language, and not just the restricted class of natural languages. Several proposals have been offered by linguists to restrict the format of syn- tactic rules in a Montague grammar context. Partee (1979) aims at allowing only a few basic operations in the syntax, and at restricting the relations between syntactic and semantic rules. Hausser (1984) claims what he calls 'surface compositionality' for syn- tactico-semantic analyses. Generalized phrase struc- ture grammar, or GPSG (Gazdar, et al. 1985), is a special form of Montague grammar in which the rules are context-free. Categorial grammar can be seen as a further restriction on the syntax.
The smallest units in PTQare the words of a sentence. Their meanings are regarded as basic and remain unanalyzed except for a few logically inter- esting words such as the quantifiers and the verb be. Often, however, it is linguistically interesting to carry the internal analysis of word meanings further. In Sect. 2, examples (5) and (6) featured the word cool, which can be an adjective, an intransitive verb, and a causative verb (Dowty 1979). Tense phenomena require an analysis of verb forms and temporal adverbials (Dowty 1979). Compound words allow sometimes for an analysis in terms of their parts (Moortgat 1987).
Certain meaning assignments in PTQseem coun- terintuitive. The noun phrase John, for example, is not interpreted as denoting an individual, but as denoting a set of properties, only because other noun phrases in the same syntactic position require this semantic type (see Sect. 6). This strategy is frequently followed and is called 'generalization to the most difficult case.' Yet other strategies are easily imaginable. One could, for example, stick to the intuitive notion that the expression John denotes an individual and introduce rules that raise interpretations to a higher type when- ever required. Type-shifting rules make for greater flexibilityin the relation between a word and its sem- antic type, a property which has earned this approach the name of 'flexible Montague grammar' (see, for example, Partee and Rooth (1983), Keenan and Faltz (1985), Hendriks (1987), Groenendijk and Stokhof (1989)).
The largest linguistic units in PTQ are the sentences. The task of extending Montague's method to dis- courses looked unrewarding at first, in particular in view of cross-sentential anaphora phenomena. The first Montague-inspired attempt to widen the coverage of the theory to discourses (Kamp 1981) was not entirely compositional. Groenendijk and Stokhof (1991) later provided a fully compositional way of doing this. This makes it possible to incorporate on the text level results obtained earlier in Montague
Montague Grammar
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