We examine critically the interdependence between science and philosophy which Sklar asserts in Space, Time, and Spacetime. We find that such a view makes it difficult to criticize the ideas of science, like that of absolute space, on their own merits, without importing extraneous philosophical associations. It also impedes appreciation of the importance, and subtlety, of explanation in scientific theory. As a result, particular explanations, such as the one Newton offered of his bucket experiment, are dismissed facilely—indeed, all geometric explanation appears illegitimate—, and such general attitudes as conventionalism appear to lack rationale.

The issue of the conventionality of geometry is considered in the light of the special theory of relativity. The consequences of Minkowski's insights into the ontology of special relativity are elaborated. Several logically distinct senses of “conventionalism” and “realism” are distinguished, and it is argued that the special theory vindicates some of these possible positions but not others. The significance of the usual distinction between relativity and conventionality is discussed. Finally, it is argued that even though the spatial metric within an inertial reference frame is euclidean, it is impossible to define unique objects which can serve as the relativistic surrogates of the spatial points of classical geometry.

A detailed analysis is made of Grünbaum's claim that the Abraham-Lorentz (AL) and Dirac-Lorentz (DL) equations have no bearing on causality. It is pointed out that (a) both equations are derived from F = ma, and thus should obey the same causality conditions as Newton's law, (b) independently of what boundary conditions are imposed, non-causal behavior is always along the same straight line as the force, (c) the distinction in status between laws and boundary conditions which Grünbaum imposes is one which is not always useful, especially since what is a law in one formulation of the theory can become a boundary condition in another, and thus it is argued that a complete theory must be such that laws and boundary conditions form a coherent whole, (d) the asymptotic boundary conditions that are applied are in agreement with experiment, (e) the AL equation is such that if the “effect,” the acceleration as function of time, is known, then the “cause,” the force, can be determined. In addition, it is noted that in the DL equation the acceleration at times later than t influences the acceleration at t. Finally, it is pointed out that electrodynamics is indeed a causal field theory, and that retrocausality is due to the transition from a field description to a particle description.

In a previous paper (Simon and Groen 1973) it was proposed that theories of empirical phenomena should satisfy conditions of finite and irrevocable testability (FITness conditions). Roughly speaking, a theory is finitely testable if, for every set of observations that falsifies the theory, there exists a finite subset of observations that falsifies it. A theory is irrevocably testable if, for any finite set of observations that falsifies the theory, any superset of observations that includes that set also falsifies it—a theory falsified by observations cannot be resuscitated by adding new observations to the original set.

Wesley C. Salmon (1977) has written a characteristically elegant and ingenious paper The Curvature of Physical Space'. He argues in it that the curvature of a space cannot be intrinsic to it. Salmon relates his view that space is affinely amorphous to Grünbaum's view (Grünbaum 1973, esp. Ch. 16 & 22) that it is metrically amorphous and acknowledges parallels between the arguments which have been offered for each opinion. I wish to dispute these conclusions on philosophical grounds quite as much as on geometrical ones. Although I concentrate most on arguing for a well defined, intrinsic affinity for physical space the arguments extend easily to support a well defined, intrinsic metric.

Dirac's classical electrodynamics countenances “preaccelerations” of charged particles at a time t as mathematical functions of external forces applied after the time t. These preaccelerations have been interpreted as evidence for physical retrocausation upon assuming that, in electrodynamics no less than in Newton's second law, external forces sustain an asymmetric causal relation to accelerations. And this retrocausal interpretation has just been defended against the critiques in (Grünbaum 1976), (Grünbaum and Janis, 1977 and 1978) by appeal to the formal assimilation of the electrodynamic laws of motion to Newton's second law. It is argued below that this latest defense of the retrocausal interpretation is even more ill-founded than the prior ones in the literature.

Frank Jackson and Robert Pargetter (1977) propose a method for synchronizing clocks at rest at distant points of an inertial system in Euclidean space, which, they claim, (i) does not depend on Einstein's signalling method (Einstein 1923, pp. 27–29) and (ii) provides a basis for denying the conventionality of distant simultaneity. I am afraid, however, that the new method presupposes that the simultaneity of distant events relatively to the chosen inertial system has been already determined by Einstein's or some other method. Jackson and Pargetter describe their method as follows:

It is usually supposed that the ‘fundamental’ laws of nature must be general, i.e. must essentially begin with a universal quantifier (Hempel and Oppenheim 1965, p. 272). Other ‘derivative’ laws may not satisfy this requirement but only because they are the logical or mathematical consequences of a set of fundamental laws. As it stands, this requirement is either too strong or trivial. Consider the Newtonian gravitational law: where FG(x, y, t) is the impressed gravitational force on x due to y at t, ms(x) is the mass of x, d(x, y, t) is the displacement of the center of mass of x from the center of mass of y at t, and G is the universal gravitational constant. (For simplicity, we ignore the vector nature of FG). What is the role of the constant “G”? Reflection shows that it is actually a disguised existential quantifier, or, more precisely, a Skolem function replacement for one. Rendering Newtonian mechanics in a parsimonious language, we could drop the “G” and rewrite (1) as

The constant “G” could then be defined, if desired, as the unique r satisfying (2) (the propriety of this definition is guaranteed by (2)). Such a theory would have exactly the same deductive consequences as (1). But (2) has an initial existential quantifier essentially.

In their recent paper, Jackson and Pargetter (1977) have attempted to prove that simultaneity is not a matter of convention. They attempt to show that it is an empirical fact whether or not a moving rod A′B′ is perpendicular to a plane XY. If it is an empirical fact, then such a perpendicular rod can be used to synchronize clocks. We shall show that it is not an empirical fact, but it is in fact synchronization dependent.

Robert Torretti's objection is verificationism writ large. We reply that verificationism is to be rejected. Carlo Giannoni's objection is that our test for tilting fails because the rod might tilt and yet no current flow through its mid-point. We reply that nevertheless we can test for tilting because there would still be differences detectable with a glavanometer.