The thesis of the empirical underdetermination of theories (U-thesis) maintains that there are incompatible theories which are empirically equivalent. Whether this is an interesting thesis depends on how the term incompatible is understood. In this paper a structural explication is proposed. More precisely, the U-thesis is studied in the framework of the model theoretic or emantic approach according to which theories are not to be taken as linguistic entities, but rather as families of mathematical structures. Theories of similarity structures are (...) studied as a paradigmatic case. The structural approach further reveals that the U-thesis is related to problems of uniqueness in the representational theory of measurement, questions of geometric conventionalism, and problems of structural underdetermination in mathematics. (shrink)

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920s-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is _algebraic_ in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive (...) scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity: matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities---indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity. The Putnam-Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th-21st century space-time philosophy in the light of particle physics. An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction of conventionality and constructs the 'universal force' influencing the causal structure. Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space-time theory that would have blocked Moritz Schlick's supposed refutation of synthetic _a priori_ knowledge, and how Einstein's false analogy between the Neumann-Seeliger-Einstein modification of Newtonian gravity and the cosmological constant \Lambda generated lasting confusion that obscured massive gravity as a conceptual possibility. (shrink)

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 Grunbaum's view (Grunbaum 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. (shrink)

Most relational theories assert both that spatial discourse is reducible to talk about physical objects and their spatial relations, and that the relation of congruence derives from a non-metrical relation which intervals bear or possibly bear to measuring instruments. We have shown that there are serious logical difficulties involved in maintaining both these positions and the thesis of the continuity of space. We have also shown that Grünbaum's motivating argument for the reduction of congruence is unsound, and, moreover, that the (...) prospects of formulating the kind of definition which this reduction requires seem to rest upon a wholly vague notion of physical possibility. Alternatively, if congruence is taken as primitive, it seems plausible that spatial discourse can be reconstructed so that there is no ontological commitment to spatial objects other than physical objects. Whether or not this relational thesis is ultimately defensible requires more elaboration of the relational theory, and investigation of its role in the formalizations of current physical theories. It is odd, considering the wide currency of relational theories, that this work has never been done. (shrink)

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)