Counterparts, Essences and Quantified Modal Logic

It is commonplace to formalize propositions involving essential properties of objects in a language containing modal operators and quantifiers. Assuming David Lewis’s counterpart theory as a semantic framework for quantified modal logic, I will show that certain statements discussed in the metaphysics of modality de re, such as the sufficiency condition for essential properties, cannot be faithfully formalized. A natural modification of Lewis’s translation scheme seems to be an obvious solution but is not acceptable for various reasons. Consequently, the only safe way to express some intuitions regarding essential properties is to use directly the language of counterpart theory without modal operators.

FIRST-ORDER POSSIBILITY MODELS AND FINITARY COMPLETENESS PROOFS

This article builds on Humberstone’s idea of defining models of propositional modal logic where total possible worlds are replaced by partial possibilities. We follow a suggestion of Humberstone by introducing possibility models for quantified modal logic. We show that a simple quantified modal logic is sound and complete for our semantics. Although Holliday showed that for many propositional modal logics, it is possible to give a completeness proof using a canonical model construction where every possibility consists of finitely many formulas, we show that this is impossible to do in the first-order case. However, one can still construct a canonical model where every possibility consists of a computable set of formulas and thus still of finitely much information.

The New Aristotelian Essentialists

In recent years largely due to the seminal work of Kit Fine and that of Jonathan Lowe there has been a resurgence of interest in the concept of essence and the project of explaining de re necessity in terms of it. Of course, Quine rejected what he called Aristotelian essentialism in his battle against quantified modal logic. But what he and Kripke debated was a notion of essence defined in terms of de re necessity. The new Aristotelian essentialists regard essence as entailing but prior in the order of explanation to de re necessity. In what follows I argue that the concept of essence so understood has not been adequately explained and that any attempt to explain it, at least along the lines most familiar from the literature, must be flagrantly circular or make use of de re modal notions.

Problemi kvantificirane epistemičke logike

Within the framework of quantified modal logic (QML) the author, in the first part of his paper, on the basis of the actualist approach to the problem of founding logical moalities, attempts to found a system of quantified epistemic logic (QEL) which presupposes a characteristic manner of problem-solving if compared to the rule of existential generalisation (EG). This is Hintikka's approach. The central issue of the second part of the paper tackles the rule of existential, as well as some other problems in connection with their applications in quantified epistemic logic. The conclusion gives counter arguments to two systems QEL (Hintikka' system K and B and Carlson's system C).