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. (shrink)

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 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. (shrink)

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.

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. (shrink)