Page 334 - Encyclopedia of Philosophy of Language

Formal Semantics
introduced in Sect. 2, in order to free the scope of quantifiers from traditional surface syntax, in order to capture the well-known ambiguity of sentences like the following(39):
Every woman loves some man. (39)
On the simplest assumption that the verb is of type e -> (e -* /), and the subject and object are corresponding (polymorphic) type-raised categories, the reading where the subject has wide scope is obtained by a purely applicative reading. The reading where the object has wide scope is obtained by composing sub- ject and verb before applying the object to the result of the composition. In this their motivation for intro- ducing composition is the combinatory relative of the A-categorial grammars of Lewis, Montague, and Cres- swell (see above). Indeed, one must sharply distinguish the level of semantic representation that is assumed in these two kinds of theory, as Lewis in fact suggested (1972:48), ascribing all these authors' operations to the level of logical form. Otherwise one must predict that those sentences which under the assumptions of the combinatory approach require function com- position to yield an analysis (as opposed to merely allowing that alternative), such as right node raising, must yield only one of the two readings. (Which read- ing is obtained will depend upon the original assign- ment of categories.) However, this prediction would be incorrect: both scopings are allowed for sentences
like the following (40), adapted from Geach:
Every girl likes, and every boy detests, some (40) saxophonist.
That is not to say that the categorial analysis is without advantages. As Geach points out, one does not appear to obtain a third reading in which two instances of the existential each have wide scope over one of the universals, so that all the girls like one particular saxophonist, and all the boys detest one particular saxophonist, but the two saxophonists are not the same. This result is to be expected if the entire substring Every girl likes and every boy detests is the syntactic and semantic constituent with respect to which the scope of the existential is denned. However, it remains the case that there is a many-to-one relation between semantic categories at this level and cat- egories and/or rules at the level which has been con- sidered up to now. The semantics itself and the nature of this relationship are a subject in their own right which it is not possible to do justice to here, but the reader is referred to important work by Partee and Rooth, and Hendriks on the question. Much of this work has recently harked back to axiomatic frame- works related to the Lambek calculus.
5. Further Reading
Two indispensible collections of readings in categorial grammarbetweenthemcontainmanyimportantpap-
ers in the area, including many of those cited above. Buszkowski et al. (1988) includes a number of his- torically significant older papers, including those by Lambek (1958) and Geach (1970). The most impor- tant omissions in the otherwise excellent historical coverage afforded by the Buszkowski volume are the original paper by Ajdukiewicz (1935), which is trans- lated together with other historically relevant material in McCall (1967), and the work of Bar-Hillel (1964). Certain papers crucial to the prehistory of CG, includ- ing Schdnfinkel (1924), are collected in translation in van Heijenoort (1967). The review articles by the edi- tors contain valuable survey material in many of the areas touched on here, and the collection is par- ticularly valuable as a source of mathematical results concerning the Lambek calculus and its extensions. The collection edited by Oehrle et al. (1988) also contains important survey articles, largely non- overlapping with those in the previous collection. The overall slant is more linguistic, and the collection includes a large number of important papers which continue to influence current work in natural language syntax and semantics. To some extent, these largely
complementary collections epitomize the two ap- proaches distinguished at the start of Sect. 3.
Besides the valuable introductory essays to these two collections, the relevant section of Lyons (1968), which heralded the revival of categorial grammar as a linguistic theory, remains one of the most accessible and inspiring brief introductions to categorial gram- mar for the general linguist. The 1993 book by Wood (which has appeared since the first version of this article was written) is the most complete review of the whole area.
As far as the mathematical foundations of CGgo, the most intuitive introduction to the relation between combinators and the A-calculus remains Curry and Feys (1958: ch. 5 and ch. 6). Hindley and Seldin (1986) provide an excellent modern introduction. Smullyan (1985), in which the combinators take the form of birds, is undoubtedly the most entertaining among recent presentations of the subject, and is a goldmine of useful results. The papers of Richard Montague were collected in Thomason (1974). The related /.- categorial approach of Cresswell is presented in a series of books of which the first appeared in 1973. Important work in Lambek-style categorial grammars is to be found in Moortgat (1989) and van Benthem (1991), the former being aimed at the linguist, the latter at the mathematical logician. Morill (1994) extends this work.
A number of collections bringing together papers on recent linguistic theories include papers on CG, and relate it to other contemporary approaches. The collections by Jacobson and Pullum (1982), Huck and Ojeda (1987), Baltin and Kroch (1989) and Sag and Szabolsci (1992) are useful in this respect. These and the two collections mentioned earlier provide ref-
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