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.

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 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.

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 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.”

Some of the controversy surrounding the Duhemian claim that in science falsification is as inconclusive as verification is reconsidered. The D-Thesis, a particular version of this claim first discussed by Adolf Grünbaum, is formulated in a more precise and perspicuous fashion as a conjunction of two subtheses. Grünbaum's attempt to refute one of the subtheses by means of a geometrical counterexample and some subsequent discussions of this example are examined critically. An argument designed to prove the other subthesis is analyzed and shown to be unsuccessful. It is concluded that the D-Thesis is as yet neither proven nor refuted.

The claim that scientific explanation is deductive has been attacked on both systematic and historical grounds. This paper briefly defends the claim against the systematic attack. Essential to this defence is a distinction between perfect and imperfect explanation. This distinction is then used to illuminate the differences and similarities between Aristotelian (anthropomorphic) explanations of certain facts and those of classical mechanics. In particular, it is argued that when one attempts to fit classical mechanics into the Aristotelian framework the latter becomes structurally incoherent. It is suggested that this, together with the fact that classical mechanics embodied the first piece of perfect knowledge, accounts, in part at least, for the historical fact of the rapid demise of the Aristotelian patterns as the new science developed. On the basis of this discussion, the inadequacies of the attack on the deductive model on historical grounds by Toulmin come to be seen.