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

Ray Jackendoff and I seem to concur in most essential points. At the level of overall architecture, his parallel grammar model (Jackendoff 2002:199) and my model of SEMANTIC SYNTAX (SeSyn; Seuren 1996) bear a nontrivial resemblance.Apart from technical details such as the properties of the rule systems concerned, these models seem to differmainly in two respects.

Abstract

It was with great pleasure that I read Ray Jackendoff’s discussion note ‘What is the human language faculty? Two views’, published in Language 87.3.586–624 (September 2011). Since it was not presented as an ordinary article but as a ‘discussion note’, it seemed appropriate to ask the editors of Language to print a short reaction, meant to make a positive contribution to the discussion.

Abstract

It has been known at least since Abelard (12th century) that the classic Square of Opposition suffers from so-called undue existential import (UEI) in that this system of predicate logic collapses when the class denoted by the restrictor predicate is empty. It is usually thought that this mistake was made by Aristotle himself, but it has now become clear that this is not so: Aristotle did not have the Conversions but only one-way entailments, which ‘saves’ the Square. The error of UEI was introduced by his later commentators, especially Apuleius and Boethius. Abelard restored Aristotle’s original logic. After Abelard, some 14th- and 15th-century philosophers (mainly Buridan and Ockham) meant to save the Square by declaring the O-corner true when the restrictor class is empty. This ‘leaking O-corner analysis’, or LOCA, was taken up again around 1950 by some American philosopher-logicians, who now have a fairly large following. LOCA does indeed save the Square from logical disaster, but modern analysis shows that this makes it impossible to give a uniform semantic definition of the quantifiers, which thus become ambiguous—an intolerable state of affairs in logic. Klima (Ars Artium, Essays in Philosophical Semantics, Medieval and Modern, Institute of Philosophy, Hungarian Academy of Sciences, Budapest, 1988) and Parsons (in Zalta (ed.), The Stanford Encyclopedia of Philosophy, http://plato.standford.edu/entries/square/, 2006; Logica Univers. 2:3–11, 2008) have tried to circumvent this problem by introducing a ‘zero’ element into the ontology, standing for non-existing entities and yielding falsity when used for variable substitution. LOCA, both without and with the zero element, is critically discussed and rejected on internal logical and external ontological grounds.