Brian Ellis has argued that the assigning of forces is, in the final analysis, a matter of convention. This conclusion is backed by the premises (1) that forces and force-effects are necessary and sufficient for each other, and (2) that the classification of some state of affairs as a force-effect is at least partly conventional. We argue that the first premise is false, that the second premise is ambiguous as between several senses of “conventional,” and finally that he has not established that force-effects are conventional in the sense required for the conclusion he wishes to draw.

Much of Grünbaum's work may be regarded as a careful development and systematic elaboration of the Riemann–Poincaré thesis of the conventionality of congruence, the thesis that the continuous manifolds of space, time, and space-time are intrinsically metrically amorphous, i.e. are devoid of intrinsic metrics. Therefore, to appreciate Grünbaum's philosophical contributions, one must have a clear understanding of what he means by an intrinsic metric. The second and fourth sections of this paper are exegetical; in them we try to piece together, from his sundry remarks about intrinsic metrics, what Grünbaum means by the term ‘intrinsic metric.’ We shall argue that, the customary carefulness and precision of Grünbaum's writings notwithstanding, there are residual unclarities and difficulties which beset his conception of an intrinsic metric. In the fifth section we shall propose an explication of Grünbaum's notion of an intrinsic metric which seems on the whole faithful to Grünbaum's intuitions and insights and which also seems capable of performing the philosophical services which his work demands of that notion. The third section is a digression on Zeno's metrical paradox of extension.

This paper is a critique of Kenneth Arrow's thesis concerning the logical impossibility of a constitution. I argue that one of the premises of Arrow's proof, that of the transitivity of indifference, is untenable. Several concepts of preference are introduced and counter-instances are offered to the transitivity of indifference defined along the standard lines in terms of these concepts. Alternate analyses of indifference in terms of preference are considered, and it is shown that these do not serve Arrow's purposes either. Finally, it is argued that in the single special case in which indifference could plausibly be held to be transitive, Arrow's thesis is innocuous.

Professor Massey's exposition and analysis [5] of Professor Grünbaum's writings on metric aspects of space seem to me both very helpful in understanding those writings and to contain a considerable original contribution to the subject. Nevertheless I would like to argue that there is an alternative to Massey's explication which seems to me more faithful to Grünbaum's remarks; it seems at least to have the virtue of not forcing Grünbaum to reject the usual mathematical definitions of the notions used.

Ellis and Bowman's account of nonstandard signal synchronizations is examined as a prolegomenon to this paper. Attention is called to some consequences of an important ambiguity in their account of the transitivity of nonstandard synchrony. Then an analysis is given of the principle of relativity (first postulate of the STR) to assess E & B's claim that this principle either restricts nonstandard signal synchronisms or rules them out altogether. It is argued that the latitude for choices of nonstandard synchronisms is not circumscribed by the factual content of the principle of relativity; instead, the exclusion of such synchronisms by this principle depends on a tacit appeal to the particular conventions implicit in certain formulations of the principle. Hence E & B's claim is rejected as an argument against the factual tenability of nonstandard synchronisms.

After describing a new method of synchronizing spatially separated clocks by means of clock transport, this paper discusses the philosophical import of the existence of such methods, including those of Ellis and Bowman and of Bridgman, with special reference to the Ellis-Bowman claim that “the thesis of the coventionality of distant simultaneity ... is thus either trivialized or refuted.” I argue that the physical facts do not support this philosophical conclusion, and that a substantial part of their argument against Reichenbach, in particular, is misdirected. Finally, I suggest that Ellis and Bowman employ seriously unclear notions of triviality and “good physical reasons” that tend to obscure rather than clarify the basic philosophical issues. An objective criterion of nontriviality of conventions is advanced.

The Fitzgerald–Lorentz contraction hypothesis, proposed as an explanation of the Michelson–Morley result, fails to account for the Kennedy–Thorndike result. Hence, Grünbaum argues, the hypothesis has been falsified.

However, the contraction hypothesis as formulated by Lorentz is false for the very fundamental reason that it entails a contradiction, namely, the consequence that light waves must have a variable velocity along what by definition is taken to be a rest length. Furthermore, the attempt to resolve this contradiction by coupling the Fitzgerald–Lorentz contraction with the hypothesis that clock rates are a function of velocity, is open to a sound, methodological objection. The Michelson–Morley result is fully satisfied, provided only that the lengths of the interferometer arms, in the longitudinal and transverse positions, are thought to be related to one another in a certain ratio, and this ratio may be interpreted as a contraction in both arms. Since this twofold contraction hypothesis suffices to explain both the Michelson–Morley and the Kennedy–Thorndike results, and since it entails no contradiction, there is no need to correct both the length of rods and the rate of clocks. Therefore, the combined clock-rod hypothesis, and with it the Fitzgerald–Lorentz contraction hypothesis, must be rejected.

This paper presents a representational theory of derived physical measurements. The theory proceeds from a formal definition of a class of similar systems. It is shown that such a class of systems possesses a natural proportionality structure. A derived measure of a class of systems is defined to be a proportionality-preserving representation whose values are n-tuples of positive real numbers. Therefore, the derived measures are measures of entire physical systems. The theory provides an interpretation of the dimensional parameters in a large class of physical laws, and it accounts for the monomial dimensions of these parameters. It is also shown that a class of similar systems obeys a dimensionally invariant law, which one may safely subject to a dimensional analysis.

The purpose of this paper is to resolve two paradoxes, which occur in quantum theory, by using the discussion of the theory of measurement presented in two earlier papers by the author [3], [4], [5]. The two paradoxes discussed will be the Schrödinger cat paradox and the Einstein, Podolski, Rosen paradox [2]. An introductory section will be included which summarizes the relevant results from the author's previous papers. Also a discussion will be made regarding the author's interpretation of the density operator.

This paper draws its title from the recent symposium of which it was part; it attempts to respond to the question raised by that title, taking current work in set theory into account. To this end the paper contrasts set theory with number theory, examines a severe brand of set-theoretic realism that is suggested by a passage from Gödel, and sketches a first-order way of looking at the results about competing extensions of Zermelo-Fraenkel set theory. A formalistic sentiment may be detectable in some portions of the paper.

This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logical truth and logical consequence. Adequacy criteria for systems of the first two types include: effectiveness, soundness, completeness, Post completeness, “strong soundness” and strong completeness. Consideration of a logical system as a theory of deduction leads us to attempt to formulate two adequacy criteria for systems of proofs. The first deals with the concept of rigor or “gaplessness” in proofs. The second is a completeness condition for a system of proofs. An historical note at the end of the paper suggests a remarkable parallel between the above hierarchy of systems and the actual historical development of this area of logic.

Adolf Grünbaum has introduced into the literature [4], and several times revised and restated [5] [6], a description of a putative crucial experiment. The outcome of this experiment is supposed to be the conclusive falsification of an hypothesis to the effect that the geometry of a certain region of space, or of a certain surface, is Euclidean. Hereafter, in this paper, I shall refer to this example experiment, in any and all of the different versions of it that Grünbaum has articulated, along with the argumentation with which he has supplemented it, as “Grünbaum's Falsification Example.” I will be concerned with all versions of the experiment itself, but only with the most recent supplementary argumentation that Grünbaum has offered, since the ways in which this differs from earlier arguments reflect a taking into account, on Grünbaum's part, of points critics have raised and flaws that they have purported to find in some of those earlier arguments [7–11].

There are three separate important theses against which one or another version of Grünbaum's Falsification Example may be taken to have been directed. Each of these Grünbaum has either explicitly claimed to refute or at least left himself open to the interpretation that he has sought to refute, by means of the example. I propose to try to make clear that none of these three theses is refuted, or even threatened with counterevidence, by Grünbaum's Falsification Example.

In this paper we examine Ellis and Bowman's argument, that simultaneity in inertial frames of reference is not conventional, from the axiomatic point of view. In Part I we examine the role of conventions in an axiomatic physical theory, and in Part II the relation of simultaneity in Reichenbach's axiomatization of the space-time theory of special relativity.

In Chapter 4 of [2] Grünbaum sets out to refute Einstein's philosophy of physical geometry. The latter's theory is seen as lying within the tradition of “anti-empiricist conventionalism” of Duhem and Quine as opposed to the “qualified empiricism” of Poincaré, Carnap and Reichenbach. Consequently Grünbaum sets the stage for his critique of Einstein by discussing certain of the views of these other thinkers. But in these preliminary discussions the various theses are confused and misrepresented in such a way as to make it almost impossible to evaluate Grünbaum's final treatment of Einstein's thesis. For this reason I will deal only with those parts of this chapter in which the roots of Grünbaum's confusion are to be found. This will involve analyses of two theories which are not clearly distinguished by Grünbaum. The first is Duhem's denial of the “crucial experiment” in physics; the second is Quine's version of “pragmatism.”

Entropy is proposed as a concept which in its broader scope can contribute to the study of the General Information System. This paper attempts to identify a few fundamental subconcepts and lemmas which will serve to facilitate further study of system order. The paper discusses: partitioning order into logical and arbitrary kinds; the relationship of order to pattern; and suggested approaches to evaluating and improving the General Information System.

The traditional role which correspondence rules, coordinating definitions, or semantical rules, have in a logical analysis of a scientific theory is questioned by providing an alternative analysis. The alternative account suggests that scientific theories are “meaningful” prior to the establishment of correspondence rules, and that correspondence rules are introduced to permit explanation and testing in the “observational” sector. The role of models is briefly assessed in connection with this prior or “antecedent theoretical meaning,” and a causal sequence analysis of a class of correspondence rules is presented which makes explicit the interdependence of scientific theories.

The demonstration that slow transport of clocks can be used to define simultaneity in inertial frames of reference leads to the question of whether clock transport can similarly be used in noninertial frames. It is shown that there are certain types of reference frames in which the clock-transport method cannot be used in a self-consistent manner. It is also shown that there are other types of noninertial frames in which the clock-transport method will succeed. The discussion includes noninertial frames in flat space-time as well as the case of curved space-times.