Publications

Abstract

This study is a prolegomenon to a formal theory of the natural growth of conceptual and lexical fields. Negation, in the various forms in which it occurs in language, is found to be a powerful indicator. Other than in standard logic, natural language negation selects its complement within universes of discourse that are, for practical and functional reasons, restricted in various ways and to different degrees. It is hypothesized that a system of cognitive principles drives recursive processes of universe restriction, which in turn affects logical relations within the restricted universes. This approach provides a new perspective in which to view the well-known clashes between standard logic and natural logical intuitions. Lexicalization in language, especially the morphological incorporation of negation, is limited to highly restricted universes, which explains, for example, why a dog can be said not to be a Catholic, but also not to be a non-Catholic. Cognition is taken to restrict the universe of discourse to contrary pairs, splitting up one or both of the contraries into further subuniverses as a result of further cognitive activity. It is shown how a logically sound square of opposition , expanded to a hexagon (Jacoby 1950, 1960, Sesmat 1951, Blanché 1952, 1953, 1966), is generated by a hierarchy of universe restrictions, defining the notion ‘natural’ for logical systems. The logical hexagon contains two additional vertices, one for ‘some but not all’ (the Y-type) and one for ‘either all or none’ (the U-type), and incorporates both the classic square and the Hamiltonian triangle of contraries . Some is thus considered semantically ambiguous, representing two distinct quantifiers. The pragmaticist claim that the language system contains only the standard logical ‘some perhaps all’ and that the ‘some but not all’ meaning is pragmatically derived from the use of the system is rejected. Four principles are proposed according to which negation selects a complement from the subuniverses at hand. On the basis of these principles and of the logico-cognitive system proposed, the well-known nonlexicalization not only of *nall and *nand but also of many other nonlogical cases found throughout the lexicons of languages is analyzed and explained

Abstract

Since Aristotle and the Stoa, there has been a clash, worsened by modern predicate logic, between logically defined operator meanings and natural intuitions. Pragmatics has tried to neutralize the clash by an appeal to the Gricean conversational maxims. The present study argues that the pragmatic attempt has been unsuccessful. The “softness” of the Gricean explanation fails to do justice to the robustness of the intuitions concerned, leaving the relation between the principles evoked and the observed facts opaque. Moreover, there are cases where the Gricean maxims fail to apply. A more adequate solution consists in the devising of a sound natural logic, part of the innate cognitive equipment of mankind. This account has proved successful in conjunction with a postulated cognitive mechanism in virtue of which the universe of discourse (Un) is stepwise and recursively restricted, so that the negation selects different complements according to the degree of restrictedness of Un. This mechanism explains not only the discrepancies between natural logical intuitions and known logical systems; it also accounts for certain systematic lexicalization gaps in the languages of the world. Finally, it is shown how stepwise restriction of Un produces the ontogenesis of natural predicate logic, while at the same time resolving the intuitive clashes with established logical systems that the Gricean maxims sought to explain

Abstract

In this study it is argued that scope, as a property of scope‐creating operators, is a real and important element in the semantico‐grammatical description of languages. The notion of scope is illustrated and, as far as possible, defined. A first idea is given of the ‘grammar of scope’, which defines the relation between scope in the logically structured semantic analysis (SA) of sentences on the one hand and surface structure on the other. Evidence is adduced showing that peripheral preposition phrases (PPPs) in the surface structure of sentences represent scope‐creating operators in SA, and that external datives fall into this category: they are scope‐creating PPPs. It follows that, in English and Dutch, the internal dative (I gave John a book) and the external dative (I gave a book to John) are not simple syntactic variants expressing the same meaning. Instead, internal datives are an integral part of the argument structure of the matrix predicate, whereas external datives represent scope‐creating operators in SA. In the Romance languages, the (non‐pronominal) external dative has been re‐analysed as an argument type dative, but this has not happened in English and Dutch, which have many verbs that only allow for an external dative (e.g. donate, reveal). When both datives are allowed, there are systematic semantic differences, including scope differences.