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)

The issue of the conventionality of geometry is considered in the light of the special theory of relativity. The consequences of Minkowski's insights into the ontology of special relativity are elaborated. Several logically distinct senses of "conventionalism" and "realism" are distinguished, and it is argued that the special theory vindicates some of these possible positions but not others. The significance of the usual distinction between relativity and conventionality is discussed. Finally, it is argued that even though the spatial metric within (...) an inertial reference frame is euclidean, it is impossible to define unique objects which can serve as the relativistic surrogates of the spatial points of classical geometry. (shrink)

Incommensurability constitutes the focal point of Kuhn’s departure from the prevailing traditions in Philosophy of Science. The paper traces the mathematical origin of the concept of “incommensurability” and philosophical environment that constrained the introduction of the idea in the literature. It then discusses the stages through which the concept of “incommensurability” evolved in Kuhn’s thought. The final account of “incommensurability,” viz., Kinds Theory of Incommensurability or Taxonomic Incommensurability, is also expounded, and some associated philosophical problems are discussed. We analyze two (...) case studies, provide textual and historical evidence, and cite the work of scholars supporting the conceptual continuity across the revolutionary divide in both the case studies. Kuhn acknowledges the rigidity of his earlier position and softens his stand on incommensurability in his last formulation of the thesis, justifying the title of the paper that Kuhn’s thesis lost its bite. At the end of the paper, we discuss some of the philosophical problems arising out of it and make certain critical remarks on the final account. (shrink)