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)

This paper investigates the relationship between reality and model, information and truth. It will argue that meaningful data need not be true in order to constitute information. Information to which truth-value cannot be ascribed, partially true information or even false information can lead to an interesting outcome such as technological innovation or scientific breakthrough. In the research process, during the transition between two theoretical frameworks, there is a dynamic mixture of old and new concepts in which truth is not well (...) defined. Instead of veridicity, correctness of a model and its appropriateness within a context are commonly required. Despite empirical models being in general only truthlike, they are nevertheless capable of producing results from which conclusions can be drawn and adequate decisions made. (shrink)