The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have received adequate justification: the (...) assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories. (shrink)

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the (...) key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4). (shrink)

Exact philosophy consists of various disciplines scattered and separated. Formal semantics and philosophy of science are good examples of two such disciplines. The aim of this paper is to show that there is possible to find some integrating bridge topics between the two fields, and to show how insights from the one are illuminating and suggestive in the other.