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Title: Mathematical formalisms in scientific practice: From denotation to model-based representation
Authors: Gelfert, A. 
Keywords: Denotation
Inferential utility
Mathematical formalism
Scientific models
Issue Date: Jun-2011
Citation: Gelfert, A. (2011-06). Mathematical formalisms in scientific practice: From denotation to model-based representation. Studies in History and Philosophy of Science Part A 42 (2) : 272-286. ScholarBank@NUS Repository.
Abstract: 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. © 2010 Elsevier Ltd.
Source Title: Studies in History and Philosophy of Science Part A
ISSN: 00393681
DOI: 10.1016/j.shpsa.2010.11.035
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