The relationship between formal logic and general philosophy is discussed under headings such as A Re-examination of Our Tense-Logical Postulates, Modal Logic in the Style of Frege, and Intentional Logic and Indeterminism.

It seems obvious that I could have failed to exist. My parents could easily never have met, in which case I should never have been conceived and born. The like applies to everyone. More generally, it seems plausible that whatever exists in space and time could have failed to exist. Events could have taken an utterly different course. Our existence, like most other aspects of our lives, appears frighteningly contingent. It is therefore surprising that there is a proof of my (...) necessary existence, a proof that generalizes to everything whatsoever. I will explain the proof and discuss what to make of it. A first reaction is that a ‘proof’ of such an outrageous conclusion must contain some dreadful fallacy. Yet the proof does not collapse under scrutiny. Further reflection suggests that, suitably interpreted, it may be sound. So interpreted, the conclusion is not outrageous, although it may not be the view you first thought of. (shrink)

The author describes an interpreted modal language and produces some clear examples of logical and analytic truths that are not necessary. These examples: (a) are far simpler than the ones cited in the literature, (b) show that a popular conception of logical truth in modal languages is incorrect, and (c) show that there are contingent truths knowable ``a priori'' that do not depend on fixing the reference of a term.

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)

One of the logical problems with which Arthur Prior struggled is the problem of finding, in Prior’s own phrase, a “logic for contingent beings.” The difficulty is that from minimal modal principles and classical quantification theory, it appears to follow immediately that every possible object is a necessary existent. The historical development of quantified modal logic (QML) can be viewed as a series of attempts---due variously to Kripke, Prior, Montague, and the fee-logicians---to solve this problem. In this paper, I review (...) the extant solutions, finding them all wanting. Then I suggest a new solution inspired by Kripke’s theory of rigid designation and Kaplan’s logic of demonstratives, the latter in particular. It turns out that the basic mechanism of Kaplan’s logic can be exploited to yield a version of QML that will serve as a viable logic for contingent beings. This result, as I show, sheds new light on the problems of singular negative existential propositions, the question of actualism, the question of the existence of the contingent a priori, the relation between logical truth and necessity, and various modal problems and paradoxes going back to Chrysippus, Ramsey, and Moore. (shrink)

Designed for use by philosophy students, this 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion of philosophical issues (...) concerning the development of modal logic is woven into the text. The book uses natural deduction systems and also includes a diagram technique that extends the method of truth trees to modal logic. This feature provides a foundation for a novel method for showing completeness, one that is easy to extend to systems that include quantifiers. (shrink)

The book also sheds new light on the nature of metaphysical theorizing by exploring the interaction of semantic and metaphysical issues, the connections between different metaphysical issues, and the nature of ontological commitment.

This paper traces the course of Prior’s struggles with the concepts and phenomena of modality, and the reasoning that led him to his own rather peculiar modal logic Q. I find myself in almost complete agreement with Prior’s intuitions and the arguments that rest upon them. However, I argue that those intuitions do not of themselves lead to Q, but that one must also accept a certain picture of what it is for a proposition to be possible. That picture. though, (...) is not inevitable. Rather, implicit in Prior’s own account is an alternative picture that has already appeared in various guises, most prominently in the work of Adams, Fine, Deutsch, and Almog. I, too, will opt for this alternative, though I will spell it out rather differently than these philosophers. I will then show that, starting with the alternative picture, Prior’s intuitions can lead instead to a much happier and more standard quantified modal logic than Q. The last section of the paper is devoted to the formal development of the logic and its metatheory. (shrink)