Spatio-temporal logic is a variant of branching temporal logic where one of the so-called causal relations on spacetime plays the role of a time flow. Allowing only rational numbers as space and time co-ordinates, we prove that a first-order spatio-temporal theory over this flow is recursively enumerable if and only if the dimension of spacetime does not exceed 2. The situation is somewhat different compared to the case of real co-ordinates, because we establish that even dimension 2 does not permit (...) recursive enumerability in this case. The proof of the result on rational spacetime involves a more deeper portion of spacetime geometry than the corresponding, more evident result for the real co-ordinates. (shrink)

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is (...) also studied. (shrink)

It continues to be alleged that superluminal in uences of any sort would be inconsistent with special relativity for the following three reasons: they would imply the existence of a ‘distinguished’ frame; they would allow the detection of absolute motion; and they would violate the relativity of simultaneity. This paper shows that the first two objections rest upon very elementary misunderstandings of Minkowski geometry and on lingering Newtonian intuitions about instantaneity. The third objection has a basis, but rather than invalidating (...) the notion of faster-than-light influences it points the way to more general conceptions of simultaneity that could allow for quantum nonlocality in a natural way. (shrink)

I present a thought experiment in quantum mechanics and tease out some of its implications for the doctrine of “peaceful coexistence”, which, following Shimony, I take to be the proposition that quantum mechanics does not force us to revise or abandon the relativistic picture of causality. I criticize the standard arguments in favour of peaceful coexistence on the grounds that they are question-begging, and suggest that the breakdown of Lorentz-invariant relativity as a principle theory would be a natural development, given (...) the general trend of physics in this century. (shrink)

Minkowski geometry is axiomatized in terms of the asymmetric binary relation of optical connectibility, using ten first-order axioms and the second-order continuity axiom. An axiom system in terms of the symmetric binary optical connection relation is also presented. The present development is much simpler than the corresponding work of Robb, upon which it is modeled.

The standard mathematical apparatus of classical electromagnetic theory in Minkowski space-time allows an interpretation in terms of retarded distant action, as well as the standard field interpretation. This interpretation is here presented and defended as a scientifically significant alternative to the field theory, casting doubt upon the common view that classical electromagnetic theory provides scientific support for the physical existence of fields as fundamental entities. The various types of consideration normally thought to provide evidence for the existence of the electromagnetic (...) field are surveyed and analyzed in retarded distant action terms, from both a contemporary viewpoint and with regard to the late 19th century context within which the field theory was first generally accepted. It is concluded that acceptance of the field as real is not evidentially justified in either context, and that the customary historical explanation of the triumph of field theory as due to its empirical superiority is inadequate. An alternative explanation is suggested but not developed, appealing to non-empirical factors associated with the research program based on the conservation of energy. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)