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

It is the purpose of the present paper to highlight the figure of Eubulides, a relatively unknown Greek philosopher who lived ±405–330 BC and taught at Megara, not far from Athens. He is mainly known for his four paradoxes (the Liar, the Sorites, the Electra, and the Horns), and for the mutual animosity between him and his younger contemporary Aristotle. The Megarian school of philosophy was one of the main sources of the great Stoic tradition in ancient philosophy. What has never been made explicit in the literature is the importance of the four paradoxes for the study of meaning in natural language: they summarize the whole research programme of 20th century formal or formally oriented semantics, including the problems of vague predicates (Sorites), intensional contexts (Electra), and presuppositions (Horns). One might say that modern formal or formally oriented semantics is essentially an attempt at finding linguistically tenable answers to problems arising in the context of Aristotelian thought. It is a surprising and highly significant fact that a contemporary of Aristotle already spotted the main weaknesses of the Aristotelian paradigm.