Abstract
Scientific models are often said to be more or less general depending on how many cases they cover. In this paper we argue that the cardinality of cases is insufficient as a metric of generality, and we present a novel account based on measure theory. This account overcomes several problems with the cardinality approach, and additionally provides some insight into the nature of assessments of generality. Specifically, measure theory affords a natural and quantitative way of describing local spaces of possibility. The generality of models can be understood as the measure of possibilities to which the models apply. In order to illustrate our view, we consider the example of structural genomics, the ongoing project of building three-dimensional models of biological macromolecules like proteins. Using measure theory, we interpret the practice of homology modeling, where such models are understood to apply widely but imperfectly to the space of possible proteins.
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Notes
Measure theory is identified by Michael Strevens as the appropriate formalism for capturing ‘abstractness,’ a property related to generality (Strevens 2004, p. 170). Our proposal is largely inspired by this suggestion.
For a more precise treatment of precision, and a discussion of the potential tradeoff between precision and generality, see Weisberg (2004).
In some contexts 50 % sequence similarity is much more than is necessary for proteins to exhibit structural similarities. Under the influence of natural selection, evolved proteins often differ by 75 % or more of their sequence and retain structural similarities (Rost 1999).
For more details on how novel leverage is calculated, see the Supplementary Information to Liu et al. (2007), available online: http://www.nature.com/nbt/journal/v25/n8/extref/nbt0807-849-S1.
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Acknowledgments
We would like to thank audiences at Duke University, the Canadian Society for the History and Philosophy of Science 2014 annual meeting, and at the IHPST Toronto, for their invaluable feedback on earlier versions of this paper. We would also like to thank Denis Walsh, Philippe Huneman, Burkhard Rost, and our reviewers, for helpful comments.
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Lewis, C.T., Belanger, C. The generality of scientific models: a measure theoretic approach. Synthese 192, 269–285 (2015). https://doi.org/10.1007/s11229-014-0567-2
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DOI: https://doi.org/10.1007/s11229-014-0567-2