This paper is an amalgam of physics and mathematical logic. It contains an elementary axiomatization of spacetime in terms of the primitive concepts of particle, signal, and transmission and reception. In the elementary language formed with these predicates we state AxiomsE, C, andU, which are naturally interpretable as basic physical properties of particles and signals. We then determine all mathematical models of this axiom system; these represent certain generalizations of the standard model. Also, the automorphism groups of the models are (...) determined. Finally we give another physical model and discuss the philosophical implications. (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.

Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without rigorously defining them so long as they restrict the sorts of mathematical arguments in which these concepts are involved. Restrictions of this sort allow the physicist to ignore calculations involving these concepts that might lead to contradictory results. I argue that such restrictions need not be ad hoc, but can sometimes (...) be justified by considering some of the metaphysical issues surrounding the question of the applicability of mathematics to physical reality. 1 Introduction 2 Rejecting inferential permissiveness 3 The agreement problem 4 Independent objections to the liberal view. (shrink)

Alfred A. Robb. THEOREM 54 If P1 and P2 be a pair of parallel inertia planes while an inertia plane Q1 has parallel general lines a and b in common with P1 and P2 respectively and if Q2 be an inertia plane parallel to Q1 through some ...