We generalize an observation made by Goldblatt in "Diodorean modality in Minkowski spacetime" by proving that each -dimensional integral spacetime frame equipped with Robb's irreflexive `after' relation determines a unique temporal logic. Our main result is that, unlike -dimensional spacetime where, as Goldblatt has shown, the Diodorean modal logic is the same for each frame , in the case of -dimensional integral spacetime, the frame determines a unique Diodorean modal logic.

We consider the problem of axiomatizing various natural "successor" logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the "standard" modal language (i.e. the language containing □ and ◊) is not finitely axiomatizable.

Neoplatonic Exegeses of Plato's Cosmogony JOHN F. PHILLIPS AMONG THE MANY CONTROVERSIES to which the long history of interpretation of Plato's Timaeus has given rise, that concerning the eternity of the cosmos is one of the most enduring and complex, and the source of almost continuous debate from the time of Xenocrates to the present. The importance to all Platonists of a doctrinally consistent answer to the question of whether or not the universe had a beginning in time is made (...) amply clear in the statement attributed to Iamblichus by Proclus that proper understand- ing of the creation of the world is crucial for the entire theory of Nature. Iamblichus here refers obliquely to the orthodox Platonist position that the universe is not a temporal being subject to decay and destruction. The princi- pal problem for all of them, of course, was that, taken literally, Plato's account of the creation in the Timaeus, particularly the passage 27C-a8C, appears to be an unequivocal affirmation of a temporal beginning to the cosmos. Espe- cially troublesome was Plato's use of the verb y~yovev in Timaeus 28b 7, which seems to be an explicit claim for an &QX1] in time. That this passage did indeed refer to a temporal beginning was a point that was made repeatedly and forcefully by the chief opponents of the Platonists on this issue, the Peripa- tetics, who, following Aristotle, read the Timaeus creation account literally.' To.. (shrink)

The main project of this dissertation is to analyze various temporal conceptions of modality for discrete n-dimensional spacetime. The first chapter contains an introduction to the problem and known results. Chapter 2 consists of a study of logics which are analogues of the so-called 'logic of today and tomorrow' and 'logic of tomorrow' investigated by Segerberg and others. We consider the analogues of these successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages and prove completeness (...) theorems. We also establish that the irreflexive successor logic in the "standard" modal language is not finitely axiomatizable. ;Chapter 3 investigates the axiomatization problem for 2-dimensional integral spacetime frames with Robb's irreflexive 'after' relation. We provide an axiomatization in a multimodal language and prove that this axiomatization is complete. We use this result to prove the system in the "standard" modal language is decidable. ;In Chapter 4 we take up the problem of what the correct Diodorean modal logic is for 2-dimensional integral spacetime. We show that the corresponding Diodorean modal logic is not S4.2, nor indeed any known modal system. We then present several candidate axioms and prove their independence in the context of S4.2. We also study some of the sublogics of the Diodorean modal logic for 2-dimensional discrete spacetime . ;The final chapter contains some general results. First we prove that for every n ≥ 2 the n-dimensional frame determines a unique Diodorean modal logic. We also consider temporal logics in the language with F and P for two kinds of irreflexive spacetime frames. We prove that for every n ≥ 2 the n-dimensional frame with Robb's 'after' relation determines a unique temporal logic. We also prove a generalized completeness theorem for n-dimensional irreflexive successor logics. Finally, in an appendix, we provide a list of selected open problems and indicate directions for future research in this area. (shrink)

This anthology contains twelve papers on various aspects of Platonism, ranging from Plato's Republic to the Neoplatonism of Plotinus, Iamblichus, Proclus and Hermias, to the use of Platonic philosophy by Cudworth and Schleiermacher. The papers cover topics in ethics, psychology, religion, poetics, art, epistemology, and metaphysics.

Objective probability, or objective chance, is the probability of some event occurring in the future independent of what anyone thinks. This paper presents and defends a theory of objective chance. I develop an informal analysis of objective chance, taking the common sense picture underlying our talk about the likelihood of future events as our starting point. A formal semantics is introduced, and I argue that the theory presented satisfies certain criteria of adequacy for a theory of probability.