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)

Models such as the simple pendulum, isolated populations, and perfectly rational agents, play a central role in theorising. It is now widely acknowledged that a study of scientific representation should focus on the role of such imaginary entities in scientists’ reasoning. However, the question is most of the time cast as follows: How can fictional or abstract entities represent the phenomena? In this paper, I show that this question is not well posed. First, I clarify the notion of representation, and (...) I emphasise the importance of what I call the “format” of a representation for the inferences agents can draw from it. Then, I show that the very same model can be presented under different formats, which do not enable scientists to perform the same inferences. Assuming that the main function of a representation is to allow one to draw predictions and explanations of the phenomena by reasoning with it, I conclude that imaginary models in abstracto are not used as representations: scientists always reason with formatted representations. Therefore, the problem of scientific representation does not lie in the relationship of imaginary entities with real systems. One should rather focus on the variety of the formats that are used in scientific practice. (shrink)

The ArgumentThis paper sets out a framework for understanding how the scientific community constructs computer simulation as an epistemically and pragmatically useful methodology. The framework is based on comparisons between simulation and the loosely-defined categories of “theoretical work” and “experimental work.” Within that framework, the epistemological adequacy of simulation arises from its role as a mathematical manipulation of a complex, abstract theoretical model. To establish that adequacy demands a detailed “theoretical” grasp of the internal structure of the computer program. Simultaneously, (...) the pragmatic usefulness of simulation arises from its role as a “virtual laboratory.” That role is made possible by black-boxing the internal structure of the program, such that the scientist can interact with the computer in an intuitive, “experimental” manner. Thus simulation is rendered authoritative, opening up encoded theories to a novel, “experimental” type of manipulation. (shrink)