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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.
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.
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
Intention-based Semantics
By Emma Borg
If we want to develop an intention-based semantics for natural language, it seems that we should follow the weaker, A-style approach (here attributed to Grice) rather than assign any more substantive role to speaker intentions. Yet, if this is the case, a question might now emerge concerning the relation of IBS to other varieties of semantic theory. Specifically, it is no longer clear to what degree IBS constitutes a genuine alternative to the approach of formal semantics (e.g. a truth-conditional approach, such as that instigated by Davidson). According to formal semantic theories the route to semantic content follows an exclusively syntactic path. That is to say, all propositional or truth-conditional semantic content can be traced back to the syntactic level and it is delivered by formal operations over the syntactic representations of sentences. Just as with an A-style IBS approach, the formal theorist will maintain that (formally described) sentences, rather than utterances, are the primary bearers of semantic content.
Source: Online Papers in Philosophy
From Semantic Restrictions to Reciprocal Meanings
By Yoad Winter & Sivan Sabato
This paper proposes a new approach to the interpretation of reciprocal expressions using the Strongest Meaning Hypothesis of Dalrymple et al (1998). We propose a system in which reciprocal meanings are derived directly from semantic restrictions using the SMH, and characterize this derivation process. We present methods to construct a linguistic test for the availability of a reciprocal meaning, or otherwise to prove that a specific meaning is not available for reciprocals. These methods are then used to analyze two controversial reciprocal meanings.
Source: Online Papers in Philosophy
A Metasemantic Account of Vagueness
By Agustin Rayo
I argue for an account of vagueness according to which the root of vagueness lies not in the type of semantic-value that is best associated with an expression, but in the type of linguistic practice that renders the expression meaningful. I suggest, in particular, that conventions about how to use sentences involving attributions of vague predicates to borderline cases prevail to a lesser degree than conventions about how to use sentences involving attributions of vague predicates to clear cases.
Source: PhOnline
See also.
An Inconsistency in Direct Reference Theory
By George Bealer
My goal [here] is to expose a series of internal difficulties in direct reference theory, ultimately revealing an inconsistency which concerns neither meaning nor the propositional attitudes but rather our standard logic of identity itself. I will not focus on specific formulations, such as those put forward at one time or another by David Kaplan, John Perry, Jon Barwise, Nathan Salmon, Scott Soames, Mark Richard, Mark Crimmins, and many others. By the end it should nonetheless be evident that direct reference theory’s basic tenets make this inconsistency inevitable.
Source: Online Papers in Philosophy
Machine Learning and the Cognitive Basis of Natural Language
By Shalom Lappin
Machine learning and statistical methods have yielded impressive results in a wide variety of natural language processing tasks. These advances have generally been regarded as engineering achievements. In fact it is possible to argue that the success of machine learning methods is significant for our understanding of the cognitive basis of language acquisition and processing. Recent work in unsupervised grammar induction is particularly relevant to this issue. It suggests that knowledge of language can be achieved through general learning procedures, and that a richly articulated language faculty is not required to explain its acquisition.
Source: Online Papers in Philosophy
Uncertainty and the suppression of inferences
By Guy Politzer
The explanation of the suppression of Modus Ponens inferences within the framework of linguistic pragmatics and of plausible reasoning (i.e., deduction from uncertain premises) is defended.
First, this approach is expounded, and then it is shown that the results of the first experiment of Byrne, Espino and Santamaría (1999) support the uncertainty explanation but fail to support their counterexample explanation.
Second, two experiments are presented. In the first one, aimed to refute one objection regarding the conclusions observed, the additional conditional premise (if N, C) was replaced with a statement of uncertainty (it is not certain that N); the answers produced by the participants remained qualitatively and quantitatively similar in both conditions. In the second experiment, a fine-grained analysis of the responses and justifications to an evaluation task was performed. The results of both experiments strongly supported the uncertainty explanation.
Source: Jean Nicod, Online Papers in Philosophy
happy
Where do presuppositions come from
By Richard Zuber
Source: Semantics Archive
Free Choice in Romanian
By Donka F. Farkas
This paper explores the determiner corner of the ‘any’ land in Romanian, taking Lee and Horn 1994 and Horn 2000a as tour guides. The immediate interest of the task lies in the fact that the work done in English by the over-employed determiner any is carried out in Romanian by a host of more specialized (and, one fears, lower paid) morphemes, which I review in the rest of this section. My aim is to introduce the details of the Romanian facts onto the scene and to show that an ‘indefinitist’ view that generalizes the scalar approach advocated in Horn’s work is useful in helping us understand the much more crowded Romanian field. The theory of any that serves as my starting point is summarized in Section 2. Section 3 proposes a generalization of the scalar view advocated by Horn in terms of an alternative-based approach in the spirit of Krifka 1995, Giannakidou 2001 and Kratzer and Shimoyama 2002, based on a novel way of defining alternatives. Section 4 looks at the consequences of the proposal, Section 5 considers ways of extending it, and Section 6 is a brief conclusion. The approach suggested here falls under what Horn calls quodlibetic theories. Its claim is that the unifying characteristic of both existentially and universally flavored free choice-like items is that they denote a maximal set of alternatives that verify the expression in which the item occurs. The scalar view is the important special case in which these alternatives form an implicational scale with respect to verifying the relevant expression.
To appear in a Festschrift for Larry Horn edited by Gregory Ward and Betty Birner
Source: Semantics etc.
(1) Socrates wrote no book.
(2) The Pope is a very good Protestant.
(3) The Pope is not a very good Protestant.
(4) The man who discovered the Americas was an Iberian.
(4’) There is an x such as x the Americas and X was an Iberian.
On Strawsonian contexts
By Varol Akman
P.F. Strawson proposed in the early seventies a threefold distinction regarding how context bears on the meaning of ‘what is said’ when a sentence is uttered. The proposal was somewhat tentative and, being aware of this aspect, Strawson himself raised various questions to make it more adequate. In this paper, we review Strawson’s scheme, note his concerns, and add some of our own. We also defend its essence and recommend it as an insightful entry point re the interplay of intended meaning and context.Being endless, the burden of context is too difficult to bear. It is the sort of burden with which one should learn to live intelligently rather than expect to think away.
Ben-Ami Scharfstein (1989:185)
Keywords: context, disambiguation, illocutionary force, indexical, literary theory, meaning, reference, translation, ‘what is said’
Appeared in Pragmatics & Cognition 13:2 (2005), 363?382.
