Mathematical formalisms in scientific practice: From denotation to model-based representation

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.
Keywords Representation  Denotation  Mathematical formalism  Inferential utility  Scientific models
Categories (categorize this paper)
DOI 10.1016/j.shpsa.2010.11.035
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,667
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
David Lewis (2004). Void and Object. In John Collins, Ned Hall & L. A. Paul (eds.), Causation and Counterfactuals. MIT Press 277-290.
Mauricio Suarez (2003). Scientific Representation: Against Similarity and Isomorphism. International Studies in the Philosophy of Science 17 (3):225-244.

View all 26 references / Add more references

Citations of this work BETA
Gabriele Gramelsberger (2011). What Do Numerical (Climate) Models Really Represent? Studies in History and Philosophy of Science 42 (2):296-302.

Add more citations

Similar books and articles
Adam Toon (2010). Models as Make-Believe. In Roman Frigg & Matthew Hunter (eds.), Beyond Mimesis and Convention: Representation in Art and Science. Boston Studies in Philosophy of Science
R. I. G. Hughes (1997). Models and Representation. Philosophy of Science 64 (4):336.
Otávio Bueno (2006). Representation at the Nanoscale. Philosophy of Science 73 (5):617-628.
Axel Gelfert (2011). Model-Based Representation in Scientific Practice: New Perspectives. Studies in History and Philosophy of Science 42 (2):251-252.

Monthly downloads

Added to index


Total downloads

63 ( #54,147 of 1,726,249 )

Recent downloads (6 months)

5 ( #147,227 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.