In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

Necessitism is the view that necessarily everything is necessarily something; contingentism is the negation of necessitism. The dispute between them is reminiscent of, but clearer than, the more familiar one between possibilism and actualism. A mapping often used to ‘translate’ actualist discourse into possibilist discourse is adapted to map every sentence of a first-order modal language to a sentence the contingentist (but not the necessitist) may regard as equivalent to it but which is neutral in the dispute. This mapping enables (...) the necessitist to extract a ‘cash value’ from what the contingentist says. Similarly, a mapping often used to ‘translate’ possibilist discourse into actualist discourse is adapted to map every sentence of the language to a sentence the necessitist (but not the contingentist) may regard as equivalent to it but which is neutral in the dispute. This mapping enables the contingentist to extract a ‘cash value’ from what the necessitist says. Neither mapping is a translation in the usual sense, since necessitists and contingentists use the same language with the same meanings. The former mapping is extended to a second-order modal language under a plural interpretation of the second-order variables. It is proved that the latter mapping cannot be. Thus although the necessitist can extract a ‘cash value’ from what the contingentist says in the second-order language, the contingentist cannot extract a ‘cash value’ from some of what the necessitist says, even when it raises significant questions. This poses contingentism a serious challenge. (shrink)

The problem with model-theoretic modal semantics is that it provides only the formal beginnings of an account of the semantics of modal languages. In the case of non-modal language, we bridge the gap between semantics and mere model theory, by claiming that a sentence is true just in case it is true in an intended model. Truth in a model is given by the model theory, and an intended model is a model which has as domain the actual objects of (...) discourse, and which relates these objects in an appropriate manner. However, the same strategy applied to the modal case seems to require an intended modal model whose domain includes mere possibilia. Building on recent work by Christopher Menzel (Synthese 85 (1990)), I give an account of model-theoretic semantics for modal languages which does not require mere possibilia or intensional entities of any kind. Menzel has offered a representational account of model-theoretic modal semantics that accords with actualist scruples, since it does not require possibilia. However, Menzel's view is in the company of other actualists who seek to eliminate possible worlds, but whose accounts tolerate other sorts of abstract, intensional entities, such as possible states of affairs. Menzel's account crucially depends on the existence of properties and relations in intension. I offer a purely extensional, representational account and prove that it does all the work that Menzel's account does. The result of this endeavor is an account of model theoretic semantics for modal languages requiring nothing but pure sets and the actual objects of discourse. Since ontologically beyond what is prima facie presupposed by the model theory itself. Thus, the result is truly an ontology-free model-theoretic semantics for modal languages. That is to say, getting genuine modal semantics out of the model theory is ontologically cost-free. Since my extensional account is demonstrably no less adequate, and yet is at the same time more ontologically frugal, it is certainly to be preferred. (shrink)

Hilary Putnam's famous arguments criticizing Tarski's theory of truth are evaluated. It is argued that they do not succeed to undermine Tarski's approach. One of the arguments is based on the problematic idea of a false instance of T-schema. The other ignores various issues essential for Tarski's setting such as language-relativity of truth definition.

It seems to be an obvious truth that There could be something that doesn't actually exist.That is, it seems to be obiously true that ◊∃×).It is sufficient for the truth of that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of that there could be some pepole, or trees, or cars that are distinct from all those that actually exist. Do and suchlike statements involve a commitment to possibilia, (...) to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which and its ilk commit us? These simple little questions are at the tip of an iceberg. (shrink)

Depuis 1967, Donald Davidson defend l'idée qu'une théorie de la signification pour une langue naturelle doit prendre la forme d'une théorie tarskienne de la vérité. Je me propose ici d'exposer les grandes lignes de l a conception davidsonienne de la sémantique des langues naturelles et de chercher à préciser en quel sens une theorie tarskienne de la vérité pour une langue L constitue, selon Davidson, une théorié de la signification pour L. Je ferai pour cela abstraction des obstacles qu'il pourrait (...) y avoir à la réalisation du programme de Davidson. (shrink)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject (...) many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (shrink)