Opacity and Paradoxes

The Paraconsistent Semantics of Natural Languages

By Tony Marmo

(Draft Version 06-alpha.2. Please, comments, suggestions and corrections are welcome)

The purpose of this work is to revisit opaque contexts from the perspective of natural languages. Opacity has been understood firstly as failure of the application of Leibniz’ substitution of identicals principle and later as accessibility relations holding between possible worlds. However, opacity in the semantics of natural languages ought to be simply characterised truth-functionally, in which case it results from devices that both avoid paradoxical interpretation of sentences and circumvent the principle of Pseudo-Scotus. Accordingly, what is herein proposed is a solution based on a kind of Paraconsistent Semantics for natural languages.

Keywords: Propositional Attitudes, Semantics, Philosophy of Language, Linguistics, Logic, Accessibility Relations, Belief Reports, Consistency, Human Languages Semantics, Intensional Liar, Leibniz’ Law, Moore’s Paradox, Opacity, Paraconsistency.
Update (Of related Interest): [1]; [2]

Source: LingBuzz, Semantics Archive, Online Papers in Philosophy

Posted by Tony Marmo at 02:41 BST

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Respective Answers to Coordinated Questions

By Jean Mark Gawron & Andrew Kehler

Munn’s examples are instances of respective readings and not functional readings. Our analysis captures these readings, as well as those for a range of other filler-gap constructions, since RESP operators routinely intervene between constituent-based dependencies in the syntax and predicate-argument relations in the semantics. As a result we are able to account for cases that share essential characteristics with Munn’s examples but which are not candidates for a functional analysis. These same examples conspire to demonstrate that the identity constraint on ATB extraction cannot be maintained.

Source: Semantics Archive

Posted by Tony Marmo at 05:41 BST

Updated: Friday, 12 August 2005 05:43 BST

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Modalità e Multimodalità in English

Posted by Tony Marmo at 18:45 BST

Updated: Thursday, 11 August 2005 18:47 BST

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Les Axiomes de Tarski

Jean-Yves Béziau

A la fin des années 1920, Tarski développe une théorie connue aujourd’hui sous le nom de théorie de l’opérateur des conséquence: il présente des axiomes pour un opérateur Cn qui à chaque ensemble d’objets X associe un autre ensemble d’objets Cn(X) de même nature, appelés conséquences de X. Il s’agit d’une théorie très abstraite puisque la nature des objets sur lesquels porte cet opérateur n’est pas spécifiée outre mesure.

Cette théorie en beaucoup de sens est extraordinaire et il semblerait que malgré le récent regain d’intérêt à son régard, sa valeur, sa signification et sa portée n’ont pas encore été pleinement comprises. En particulier on n’a pas encore réalisé combien cette théorie était en avance sur son temps, comment elle marque un tournant dans l’histoire de la logique moderne, en libérant la logique du carcan formaliste et en la projetant dans la sphère de la plus haute abstraction.

Le but de cet article n’est pas de présenter et de discuter de façon systématique l’origine et le développement de la théorie de l’opérateur de conséquence— il faudrait pour cela un volume suffisamment épais pour servir de banc— mais de discuter seulement d’un de ses aspects: ses axiomes. Dans d’autres articles nous avons déjà discuté ou nous discuterons d’autres aspects de cette théorie. Le présent article n’est donc qu’un parmi d’autres dont la somme pourrait finir par constituer le dit banc.

Posted by Tony Marmo at 16:57 BST

Updated: Tuesday, 9 August 2005 17:08 BST

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Semantics WITHOUT POSSIBLE WORLDS?

Many-Valued and Kripke Semantics

By Jean-Yves Beziau

Today many people identify Kripke semantics with modal logic. Typically a book called “modal logic” nowadays is a book about Kripke semantics (cf. e.g. the recent book by [Blackburn et al (2001)]). But modal logic can be developed using other kinds of semantics and Kripke semantics can be used to deal with many different logics and it is totally absurd to call all of these logics “modal logics”. Kripke semantics are also often called “possible worlds semantics”, however this is quite misleading because the crucial feature of these semantics is not the concept of possible world but the relation of accessibility. Possible worlds can easily be eliminated from the definition of Kripke semantics and then the accessibility relation is defined directly between the bivaluations. For this reason it seems better to use the terminology “relational semantics”. Of course, if we want, we can call these bivaluations "possible worlds", this metaphor can be useful, but then why using this metaphor only in the case of relational semantics? In fact in the Tractatus Wittgenstein used the expression “truth-possibilities” for the classical bivaluations. Other concepts of the semantics of classical zero-order logic were expressed by him using a modal terminology: he said that a formula is necessary if it holds for all truth possibilities, impossible if it holds for none, and possible if it holds for some. But Wittgenstein was against the introduction of modal concepts inside the language as modal operators.
Many-valued and Kripke semantics may be philosophically controversial, anyway they are very useful and powerful technical tools which can be fruitfully used to give a mathematical account of basic philosophical notions, such as modalities. It seems to me that instead of focusing on the one hand on some little philosophical problems and on the other hand on some developments limited to one technique, one should promote a better interaction between philosophy and logic developing a wide range of techniques, as for example the combination of Kripke semantics (extended as to include Jaskowski semantics) and Many-Valued semantics (extended as to include non truth-functional many-valued semantics). My aim in this paper is to give a hint of how these techniques can be developed by presenting various examples.

Posted by Tony Marmo at 00:01 BST

Updated: Monday, 8 August 2005 05:32 BST

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Conditional truth and future reference

By Stefan Kaufmann

This paper proposes a compositional model-theoretic account of the way the interpretation of indicative conditionals is determined and constrained by the temporal and modal expressions in their constituents. The main claim is that the tenses in both the antecedent and the consequent of an indicative conditional are interpreted in the same way as in isolation. This is controversial for the antecedents of predictive conditionals like ‘ If he arrives tomorrow, she will leave ’, whose Present tense is often claimed to differ semantically from that in their stand-alone counterparts, such as ‘He arrives tomorrow ’. Under the unified analysis developed in this paper, the differences observed in pairs like these are explained by interactions between the temporal and modal dimensions of interpretation. This perspective also sheds new light on the relationship between ‘non-predictive’ and ‘epistemic’ readings of indicative conditionals.

Appeared in the Journal of Semantics, August 2005

Posted by Tony Marmo at 17:25 BST

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