Publications

Abstract

Contrary to received opinion, the Aristotelian Square of Opposition (square) is logically sound, differing from standard modern predicate logic (SMPL) only in that it restricts the universe U of cognitively constructible situations by banning null predicates, making it less unnatural than SMPL. U-restriction strengthens the logic without making it unsound. It also invites a cognitive approach to logic. Humans are endowed with a cognitive predicate logic (CPL), which checks the process of cognitive modelling (world construal) for consistency. The square is considered a first approximation to CPL, with a cognitive set-theoretic semantics. Not being cognitively real, the null set Ø is eliminated from the semantics of CPL. Still rudimentary in Aristotle’s On Interpretation (Int), the square was implicitly completed in his Prior Analytics (PrAn), thereby introducing U-restriction. Abelard’s reconstruction of the logic of Int is logically and historically correct; the loca (Leaking O-Corner Analysis) interpretation of the square, defended by some modern logicians, is logically faulty and historically untenable. Generally, U-restriction, not redefining the universal quantifier, as in Abelard and loca, is the correct path to a reconstruction of CPL. Valuation Space modelling is used to compute the effects of U-restriction.

Abstract

Semantic Syntax (SeSyn), originally called Generative Semantics, is an offshoot of Chomskyan generative grammar (ChoGG), rejected by Chomsky and his school in the late 1960s. SeSyn is the theory of algorithmical grammars producing the well-formed sentences of a language L from the corresponding semantic input, the Semantic Analysis (SA), represented as a traditional tree structure diagram in a specific formal language of incremental predicate logic with quantifying and qualifying operators (including the truth functions), and with all lexical items filled in. A SeSyn-type grammar is thus by definition transformational, but not generative. The SA originates in cognition in a manner that is still largely mysterious, but its actual form can be distilled from the Surface Structure (SS) of the sentences of L following the principles set out in SeSyn. In this presentation we provide a more or less technical résumé of the SeSyn theory. A comparison is made with ChoGG-type grammars, which are rejected on account of their intrinsic unsuitability as a cognitive-realist grammar model. The ChoGG model follows the pattern of a 1930s neopositivist Carnap-type grammar for formal logical languages. Such grammars are random sentence generators, whereas, obviously, (nonpathological) humans are not. A ChoGG-type grammar is fundamentally irreconcilable with a mentalist-realist theory of grammar. The body of the paper consists in a demonstration of the production of an English and a French sentence, the latter containing a classic instance of the cyclic rule of Predicate Raising (PR), essential in the general theory of clausal complementation yet steadfastly repudiated in ChoGG for reasons that have never been clarified. The processes and categories defined in SeSyn are effortlessly recognised in languages all over the world, whether indigenous or languages of a dominant culture—taking into account language-specific values for the general theoretical parameters involved. This property makes SeSyn particularly relevant for linguistic typology, which now ranks as the most promising branch of linguistics but has so far conspicuously lacked an adequate theoretical basis.

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.

Abstract

No idea is older in the history of linguistics than the thought that there is, somehow hidden underneath the surface of sentences, a form or a structure which provides a semantic analysis and lays bare their logical structure. In Plato’s Cratylus the theory was proposed, deriving from Heraclitus’ theory of explanatory underlying structure in physical nature, that words contain within themselves bits of syntactic structure giving their meanings. The Stoics held the same view and maintained moreover that every sentence has an underlying logical structure, which for them was the Aristotelian subject- predicate form. They even proposed transformational processes to derive the surface from the deep structure. The idea of a semantically analytic logical form underlying the sentences of every language kept reappearing in various guises at various times. Quite recently it re-emerged under the name of generative semantics.