Time, Truth, Actuality, and Causation: On the Impossibility of Divine Foreknowledge

In this essay, my goal is, first, to describe the most important contemporary philosophical approaches to the nature of time, and then, secondly, to discuss the ways in which those different accounts bear upon the question of the possibility of divine foreknowledge. I shall argue that different accounts of the nature of time give rise to different objections to the idea of divine foreknowledge, but that, in addition, there is a general argument for the impossibility of divine foreknowledge that is independent of one’s account of the nature of tim

A new problem of descriptive power

No abstract available

On Conceiving the Inconsistent

This work has been developed within the 2013–15 ahrc project The Metaphysical Basis of Logic: The Law of Non-Contradiction as Basic Knowledge (grant ref. ah/k001698/1). A version of the paper was presented in September 2013 at the Modal Metaphysics Workshop in Bratislava. I am grateful to the audiences there and at the Aristotelian Society meeting for many helpful comments and remarks.Peer reviewedPostprin

The Broadest Necessity

In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given

The Modal Dimension

Space and time are two obvious candidates as dimensions of reality. Yet, are they the only two dimensions of reality? Famously, David Lewis maintained the doctrine o

Two-Dimensional Tableaux

We present two-dimensional tableau systems for the actuality, fixedly, and up-arrow operators. All systems are proved sound and complete with respect to a two-dimensional semantics. In addition, a decision procedure for the actuality logics is discussed

The Logic of Sequence Frames

This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction

The inheritance of dynamic and deontic integrity constraints or: Does the boss have more rights?

In [18,23], we presented a language for the specification of static, dynamic and deontic integrity constraints (IC's) for conceptual models (CM's). An important problem not discussed in that paper is how IC's are inherited in a taxonomic network of types. For example, if students are permitted to perform certain actions under certain preconditions, must we repeat these preconditions when specializing this action for the subtype of graduate students, or are they inherited, and if so, how? For static constraints, this problem is relatively trivial, but for dynamic and deontic constraints, it will turn out that it contains numerous pitfalls, caused by the fact that common sense supplies presuppositions about the structure of IC inheritance that are not warranted by logic. In this paper, we unravel some of these presuppositions and show how to avoid the pitfalls. We first formulate a number of general theorems about the inheritance of necessary and/or sufficient conditions and show that for upward inheritance, a closure assumption is needed. We apply this to dynamic and deontic IC's, where conditions arepreconditions of actions, and show that our common sense is sometimes mistaken about the logical implications of what we have specified. We also show the connection of necessary and sufficient preconditions of actions with the specification of weakest preconditions in programming logic. Finally, we argue that information analysts usually assume constraint completion in the specification of (pre)conditions analogous to predicate completion in Prolog and circumscription in non-monotonic logic. The results are illustrated with numerous examples and compared with other approaches in the literature