Peter Simons

Occurrents are entities that exist in time and, with few or no exceptions, extend over time as well, that is, they have parts corresponding to the different times at which they exist. This makes it very easy to say what makes it true that they exist at the times at which they do. Singular existential propositions, being contingent, positive and arguably atomic, stand in need of truth-makers, entities in virtue of whose existence they are true. The obvious candidate for what makes it true that Tony Blair exists is the Right Honourable Member for Sedgefield himself: by virtue of his existing, it is true that he exists. Nothing could be more straightforward. However, things that exist in time, with few exceptions, exist at some times and not at others. So a proposition to the effect that a certain object exists at a certain time likewise stands in need of a truth-maker, one matching the requirements of the existential proposition in question in its temporal specificity. Take an occurrent such as a boxing match and suppose it is going on twenty minutes after starting: by virtue of what is this true? The obvious answer here is that it is by virtue of the existence of that temporal part or phase which extends just over the time in question. Other temporal parts of the same occurrent which do not extend over this time do not act as truth-maker for the temporally specific existential proposition, this one does. There is no problem because occurrents do have temporal parts which can do this job.

Despite its lack of influence in analytical philosophy, and independently of its content as a process philosophy, Whitehead's system in Process and Reality affords a valuable lesson on how to pursue revisionary systematic metaphysics. This paper argues the case generally for metaphysical revision and system, describes the structure of Whitehead's categorial scheme, endorses his idea of an ultimate which is not an entity, and outlines an alternative, “digital” ultimate or basis composed of several analytical factors. [I]n the absence of a well-defined categoreal scheme of entities, issuing in a satisfactory metaphysical system, every premise in a philosophical argument is under suspicion.

I consider the idea of a propositional logic of location based on the following semantic framework, derived from ideas of Prior. We have a collection L of locations and a collection S of statements such that a statement may be evaluated for truth at each location. Typically one and the same statement may be true at one location and false at another. Given this semantic framework we may proceed in two ways: introducing names for locations, predicates for the relations among them and an “at” preposition to express the value of statements at locations; or introduce statement operators which do not name locations but whose truth-conditional effect depends on the truth or falsity of embedded statements at various locations. The latter is akin to Prior’s approach to tense logic. In any logic of location there will be some basic operators which we can define. By ringing the changes on the topology of locations, different logical systems may be generated, and the challenge for the logician is then in each case to find operators, axioms and rules yielding a proof theory adequate to the semantics. The generality of the approach is illustrated with familiar and not so familiar examples from modal, tense and place logic, mathematics, and even the logic of games. To the memory of Ted Dawson, who introduced me to philosophy and the writings of Arthur Prior.

I argue, along lines first explored by Wittgenstein in the Tractatus and elaborated by Peter Geach, (1) that the logical notion of negation may be illuminated by exploiting the notion of a toggle; (2) that the toggle nature of negation may best be appreciated by studying the logical notion of duality; (3) that apparent obstacles to the application of duality due to semantic opacity in intentional contexts may be overcome, and (4) that the result illuminates the connection between duality and the semantics for relevant logics. © 2011 Elsevier B.V., All rights reserved.

Modal logic like many others sustains a hexagon of opposition, with the two “additional” vertices expressing contingency and non-contingency. We first illustrate hexagons of opposition generally by treating them as cut-down entailment lattices with order distinctions among multiple arguments suppressed. We then approach the modal case by treating it heuristically as a particular case of the hexagon for quantified propositions. Historically, possibility and contingency were sometimes confused: we show using the notion of duality that contingency, as negation-symmetric, is logically less interesting than possibility