Ludwig Boltzmann’s Bildtheorie has been portrayed as a pre-cursor of the semantic view of theories and as such, the word “Bild” is translated as model. But this anachronistic understanding of Boltzmann’s use of Bilder fails to account for the wide range of roles they play in his understanding of scientific methodology. When the concept of Bild is understood historically in Viennese thought, a much broader sense emerges that leads to the investigation of its use in multiple ways in various contexts (...) in the process of proposing, pursuing, and justifying scientific beliefs. (shrink)

The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful (...) representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources. (shrink)