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.

Abstract

In his paper ‘On Horn's dilemma: presupposition and negation’ Burton-Roberts (1989a) presents an ambitious programme, formulated right at the outset. He seeks to establish three points: (i) Under the ‘standard logical definition of presupposition’ a pre-suppositional semantics is INCOMPATIBLE with a SEMANTICALLY AMBIGUOUS NEGATION operator (SAN), on pain of the theory being rendered ‘empirically empty and theoretically trivial’,. (ii) From this it follows that the one unambiguous negation is presupposition preserving. Cases that have been identified as presupposition-cancelling negation should be re-analysed as ‘instances of a pragmatic phenomenon’, not unlike what has been proposed in Horn (1985), that is as METALINGUISTIC NEGATION (MN). (iii) This pragmatic analysis of MN ‘itself implies a presuppositional semantics’, that is to say ‘a presuppositional theory of truth-value gaps’.

Abstract

This paper is an attempt to show that given the available observations on the behaviour of negation and presuppositions there is no simpler explanation than to assume that natural language has two distinct negation operators, the minimal negation which preserves presuppositions and the radical negation which does not. The three-valued logic emerging from this distinction, and especially its model-theory, are discussed in detail. It is, however, stressed that the logic itself is only epiphenomenal on the structures and processes involved in the interpretation of sentences. Horn (1985) brings new observations to bear, related with metalinguistic uses of negation, and proposes a “pragmatic” ambiguity in negation to the effect that in descriptive (or “straight”) use negation is the classical bivalent operator, whereas in metalinguistic use it is non-truthfunctional but only pragmatic. Van der Sandt (to appear) accepts Horn's observations but proposes a different solution: he proposes an ambiguity in the argument clause of the negation operator (which, for him, too, is classical and bivalent), according to whether the negation takes only the strictly asserted proposition or covers also the presuppositions, the (scalar) implicatures and other implications (in particular of style and register) of the sentence expressing that proposition. These theories are discussed at some length. The three-valued analysis is defended on the basis of partly new observations, which do not seem to fit either Horn's or Van der Sandt's solution. It is then placed in the context of incremental discourse semantics, where both negations are seen to do the job of keeping increments out of the discourse domain, though each does so in its own specific way. The metalinguistic character of the radical negation is accounted for in terms of the incremental apparatus. The metalinguistic use of negation in denials of implicatures or implications of style and register is regarded as a particular form of minimal negation, where the negation denies not the proposition itself but the appropriateness of the use of an expression in it. This appropriateness negation is truth-functional and not pragmatic, but it applies to a particular, independently motivated, analysis of the argument clause. The ambiguity of negation in natural language is different from the ordinary type of ambiguity found in the lexicon. Normally, lexical ambiguities are idiosyncratic, highly contingent, and unpredictable from language to language. In the case of negation, however, the two meanings are closely related, both truth-conditionally and incrementally. Moreover, the mechanism of discourse incrementation automatically selects the right meaning. These properties are taken to provide a sufficient basis for discarding the, otherwise valid, objection that negation is unlikely to be ambiguous because no known language makes a lexical distinction between the two readings.