By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

The simplest quantified modal logic combines classical quantification theory with the propositional modal logic K. The models of simple QML relativize predication to possible worlds and treat the quantifier as ranging over a single fixed domain of objects. But this simple QML has features that are objectionable to actualists. By contrast, Kripke-models, with their varying domains and restricted quantifiers, seem to eliminate these features. But in fact, Kripke-models also have features to which actualists object. Though these philosophers have introduced variations (...) on Kripke-models to eliminate their objectionable features, the most well-known variations all have difficulties of their own. The present authors reexamine simple QML and discover that, in addition to having a possibilist interpretation, it has an actualist interpretation as well. By introducing a new sort of existing abstract entity, the contingently nonconcrete, they show that the seeming drawbacks of the simplest QML are not drawbacks at all. Thus, simple QML is independent of certain metaphysical questions. (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

Four questions are raised about the semantics of Quantified Modal Logic. Does QML admit possible objects, i.e. possibilia? Is it plausible to admit them? Can sense be made of such objects? Is QML committed to the existence of possibilia?The conclusions are that QML, generalized as in Kripke, would seem to accommodate possibilia, but they are rejected on philosophical and semantical grounds. Things must be encounterable, directly nameable and a part of the actual order before they may plausibly enter into the (...) identity relation. QML is not committed to possibiha in that the range of variables may be restricted to actual objects.Support of the conclusions requires some discussion of substitution puzzles; also, the semantical distinction between proper names which are directly referring, and descriptions even where the latter are "rigid designators".Views of W.V. Quine, B. Russell, K. Donnellan, D. Kaplan as well as S. Kripke are invoked or evaluated in conjunction with these issues. (shrink)

Four questions are raised about the semantics of Quantified Modal Logic. Does QML admit possible objects, i.e. possibilia? Is it plausible to admit them? Can sense be made of such objects? Is QML committed to the existence of possibilia? The conclusions are that QML, generalized as in Kripke, would seem to accommodate possibilia, but they are rejected on philosophical and semantical grounds. Things must be encounterable, directly nameable and a part of the actual order before they may plausibly enter into (...) the identity relation. QML is not committed to possibilia in that the range of variables may be restricted to actual objects. Support of the conclusions requires some discussion of substitution puzzles; also, the semantical distinction between proper names which are directly referring, and descriptions even where the latter are "rigid designators". Views of W.V. Quine, B. Russell, K. Donnellan, D. Kaplan as well as S. Kripke are invoked or evaluated in conjunction with these issues. (shrink)

The theorems of the simplest and strongest sensible quantified modal logic include the Barcan Formula and its converse. Both formulas face strong intuitive objections. This paper develops a theory of possibilia to meet those objections.

It has been suggested that a substitutional semantics for quantification theory lends itself to nominalistic aims. I should like in this paper to explore that claim.