We like Euclidean geometry because we are men [sic], and have eyes and hands, and need to operate a concept of space that will be independent of orientation, distance and size. Lucas, A Treatise on Time and Space.

Die Frage, ob die Gültigkeit alternativer begrifflicher Strukturen empirisch entscheidbar oder eine Sache der willkürlichen Festsetzung ist, wird, eingeschränkt auf den Fall der physikalischen Geometrie, diskutiert. Die erkenntnistheoretischen Komponenten der empirischen Bestimmung von metrischen und topologischen Eigenschaften des physikalischen Raumes werden in der neueren Wissenschaftstheorie verfolgt. In Anschluß an die Auseinandersetzung zwischen A. Grünbaum und H. Putnam wird eine Interpretation des semantischen Status des Kongruenzprädikates vorgeschlagen, die Schwierigkeiten im Verhältnis von Intension und Extension dieses Terms beseitigen soll. Bei der Konfrontation (...) von Folgerungen aus der Konventionalitätsthese mit der dynamischen Raumtheorie, wie sie im Anschluß an Clifford von J. A. Wheeler entwickelt wurde, treten Unvereinbarkeiten auf, die in der Gegensätzlichkeit von absoluter und relationaler Raumauffassung gründen. (shrink)

“It ain't nuthin' until I call it.”Bill Guthrie, UmpireNumerous criticisms of Adolf Grünbaum's account of conventions in physics have been published, and he has replied to most of them. Nonetheless, there seem to me to be good reasons for offering further criticism. In the first place Grünbaum's philosophy seems to me at least partly an extrapolation of one aspect of the views on conventions developed by Reichenbach and others. Since I think many of the issues which Reichenbach attempted to settle (...) in his various discussions of conventions in physics are genuine and important, and I also think that those aspects of his views on which Grünbaum has focused are among the least satisfactory, it seems important to suggest questions and answers about conventions in physics which may develop more satisfactory Reichenbachian themes. Secondly, Grünbaum's philosophy centers on a distinction, that between extrinsic and intrinsic properties and relations, which has never been made satisfactorily clear either by Grünbaum or by his critics. Until it is clarified we will remain unsure of just what he is claiming and why we should think it true or think it false. Finally, Grünbaum's replies to his critics, especially his most recent reply, [9], involve unusually important claims which fail to be buttressed by the arguments he gives. I have in mind such claims as that we can learn something important about the ontological status of properties and relations by examining descriptions of them, that on the most straightforward and literal interpretation, the general theory of relativity is inconsistent, and that the foremost advocates of geometrodynamics, Clifford and Wheeler, were and are enmeshed in contradiction. My own view is that all of these claims are dubious or false, but I shall be less concerned with establishing their falsity than with discrediting the arguments offered for them. (shrink)

We give a tensor formulation of synchronization transformations within special relativity in order to bridge the gap between some philosophical discussions (e.g., by Grünbaum and Winnie) and the analyses given by physicists (e.g., Møller). As an application, we discuss a physical interpretation of the duality between covariant and contravariant indices in the tensor formulation.