Some philosophers, for example Quine, doubt the possibility of jointly using modalities and quantification. Simple model-theoretic considerations, however, lead to a reconciliation of quantifiers with such modal concepts as logical, physical, and ethical necessity, and suggest a general class of modalities of which these are instances. A simple axiom system, analogous to the Lewis systems S1 —S5, is considered in connection with this class of modalities. The system proves to be complete, and its class of theorems decidable.

Much has happened in modal logic since 1947. In particular, in regard to the problem of interpreting such logics. In that fateful year Quine published his seminal paper “The Problem of Interpreting Modal Logic” from which this work takes inspiration. Since then a certain kind of model theory – universally referred to as “possible worlds semantics” – has come to dominate both advanced research and introductory textbooks. Many would say that the problem of interpreting modal logic has been resolved. In (...) the work below I argue that some of the 1947 problems raised by Quine have indeed been resolved by the possible worlds model theory. But I also claim – perhaps against common perception, but in line with Quine’s persisting fifty-year-old skepticism – that one problem of Quine’s original paper is still alive: the problem of interpreting modal logic. Surprisingly, Quine’s best ally on these matters turns out to be the very philosopher who engineered the possible worlds model theory: Saul Kripke. (shrink)

In this paper, I reconstruct Quine’s arguments against quantified modal logic, from the early 1940’s to the early 1960’s. Quine’s concerns were not technical. Quine was looking for a coherent interpretation of quantified-in English modal sentences. I argue that Quine’s main thesis is that the intended objectual interpretation of the quantifiers is incompatible with any semantic reading of the modal operators, for example as expressing analytic necessity, unless the entities in the domain of quantification are intensions, i.e. definitional entities. The (...) difficulty is that it makes no sense to say of an ordinary object that it bears a property necessarily or contingently when the necessity or contingency in question is analytic. However, starting in 1960, Quine claims that quantified-in modal sentences can be coherently interpreted only as essentialist predications. When we say about an object that it necessarily F ’s, we can only coherently mean that it essentially F ’s. In the paper, I argue that adequately qualified the thesis is plausible. Two important qualifications are needed. The first is the assumption that satisfaction is an irreducibly predicative notion, making any explication of satisfaction in terms of truth inadequate. The second is the ontological rejection of purely semantic, i.e. merely definitional, entities. With these qualifications in place, Quine’s rejection of the combination of objectual quantifiers and semantic modalities can be upheld. In this way, we vindicate a qualified version of Quine’s conjecture that quantified modal logic is committed to essentialism. (shrink)