Invariance and Logicality in Perspective

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the invariance criterion is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force

Material consequences and counter-factuals

A conclusion is a “material consequence” of reasons if it follows necessarily from them in accordance with a valid form of argument with content. The corresponding universal generalization of the argument’s associated conditional must be true, must be a covering generalization, and must be true of counter-factual instances. But it need not be law-like. Pearl’s structural model semantics is easier to apply to such counter-factual instances than Lewis’s closest-worlds semantics, and gives intuitively correct results

Le concept de conséquence logique chez Tarski et sa critique

Il est commun, dans les manuels de logique, de présenter une définition sémantique du concept de conséquence logique. Cette approche est le fruit d'une tradition qu'on peut faire remonter au moins jusqu'aux travaux d'Alfred Tarski dans les années 1920 et 1930, lequel propose une définition du concept de conséquence en termes de modèles et de satisfaction : une conclusion est une conséquence logique d'un ensemble de prémisses si et seulement si tous les modèles des prémisses sont aussi un modèle de la conclusion. Autrement dit, une conclusion est une conséquence logique d'un ensemble de prémisses si la vérité est nécessairement préservée des prémisses à la conclusion. Cette définition a le mérite, selon Tarski, de rapporter le concept de conséquence aux critères de formalité et de nécessité. John Etchemendy a remis à l'ordre du jour l'analyse du concept de conséquence logique, dans les années 1980 et 1990, par sa critique de la définition de Tarski. Ses arguments visent à identifier des problèmes de nature conceptuelle et de nature extensionnelle dans la définition tarskienne. Selon lui, la définition repose d'abord sur une confusion entre les approches représentationnelle et interprétationnelle de la sémantique. Elle échoue ensuite à caractériser adéquatement la nécessité du concept de conséquence logique. Enfin, la définition tarskienne déclare ou bien trop, ou bien trop peu d'arguments comme étant valides. Ce mémoire porte sur la définition tarskienne du concept de conséquence logique et sur la littérature critique qu'elle a suscitée, particulièrement depuis les années 1990 et les travaux de John Etchemendy. Après des présentations philosophiques détaillées de la définition de Tarski et de sa critique par Etchemendy, je tente de réhabiliter la définition tarskienne en montrant des limites de cette critique sur chacun des trois axes.\ud ______________________________________________________________________________ \ud MOTS-CLÉS DE L’AUTEUR : Conséquence logique, Alfred Tarski, John Etchemendy, définition, sémantique, théorie des modèles

Did Tarski commit "Tarski's fallacy"?

In his 1936 paper, On the Concept of Logical Consequence, Tarski introduced the celebrated definition of logical consequence: “The sentenceσ follows logically from the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentence σ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentence σ is false. Moreover, … we are concerned here with the concept of logical, i.e., formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since

Invariance and intensionality : new perspectives on logicality

What are logical notions? According to a very popular proposal, a logical notion is something invariant under some “transformation” of objects, usually permutations or isomorphisms. The first chapter is about extending “invariance” accounts of logicality to intensional notions, by asking for invariance under arbitrary permutations of both possible worlds and objects. I discuss the results one gets in this extended theory of invariance, and how to fix many technical issues. The second chapter is about setting out a better theory of logicality. I discuss the limits of invariance frameworks, and the need for a theory of logicality with a more solid philosophical ground. I believe that the concept of information can play a major role in defining what logic is and what logical notions are. I spell out this intuition, by designing a new test for logicality. A notion is logical iff it behaves in a certain way, by checking only “structural aspects of information”, and it does so under arbitrary transformations of its “informational inputs”. In the last chapter I explore some interesting features of my theory. I show how, contrary to standard invariance, in mine logical notions tend to stay persistent across different models of information. I also spell out an intermediate notion of quasi-logicality to make sense of the formality of “world-sensitive” notions: notions whose behaviour changes across worlds. I finally propose a case study: deontic modals. I discuss how one can argue for their quasi-logicality, in my framework. The dissertation is concluded with a technical appendix, in which I prove that my theory is a restriction of standard permutation invariance (at least for a class of items) when we model the space of information in a certain way: as a set of complete powersets of some sets

Did Tarski commit "Tarski's fallacy"?

In his 1936 paper, On the Concept of Logical Consequence, Tarski introduced the celebrated definition of logical consequence: “The sentenceσ follows logically from the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentence σ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentence σ is false. Moreover, … we are concerned here with the concept of logical, i.e., formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since