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On Internal Structure, Categorical Structure, and Representation

Published online by Cambridge University Press:  11 February 2022

Neil Dewar Open the ORCID record for Neil Dewar [Opens in a new window]
Neil Dewar*
Affiliation:
Faculty of Philosophy, University of Cambridge, Cambridge, UK
*
Email: [email protected]
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Abstract

If categorical equivalence is a good criterion of theoretical equivalence, then it would seem that if some class of mathematical structures is represented as a category, then any other class of structures categorically equivalent to it will have the same representational capacities. Hudetz (2019a) has presented an apparent counterexample to this claim; in this note, I argue that the counterexample fails.

Type
Discussion Note
Information
Philosophy of Science , Volume 90 , Issue 1 , January 2023 , pp. 188 - 195
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Philosophy of Science Association

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References

Barrett, Thomas William. 2020. “Structure and Equivalence.” Philosophy of Science 87 (5):1184–96.CrossRefGoogle Scholar
Deleuze, Gilles. 1994. Difference and Repetition. New York: Columbia University Press.Google Scholar
Frigg, Roman, and Nguyen, James. 2017. “Models and Representation.” In Springer Handbook of Model-Based Science, edited by Magnani, Lorenzo and Bertolotti, Tommaso, 49–102. New York: Springer. http://philsci-archive.pitt.edu/id/eprint/12834.Google Scholar
Frigg, Roman, and Nguyen, James. 2018. “Scientific Representation.” In The Stanford Encyclopedia of Philosophy, edited by Edward, N. Zalta. Stanford: Stanford University Press. https://plato.stanford.edu/archives/win2018/entries/scientific-representation/.Google Scholar
Geroch, Robert. 1985. Mathematical Physics. Chicago Lectures in Physics. Chicago: University of Chicago Press.Google Scholar
Hudetz, Laurenz. 2019a. “Definable Categorical Equivalence.” Philosophy of Science 86 (1):47–75. https://www.journals.uchicago.edu/doi/abs/10.1086/701047.CrossRefGoogle Scholar
Hudetz, Laurenz. 2019b. “Defining Internal Structure in Terms of Morphisms.” Presentation at the Foundations of Categorical Philosophy of Science Conference, LMU Munich.Google Scholar
Landry, Elaine. 2007. “Shared Structure Need Not Be Shared Set-Structure.” Synthese 158 (1):1–17. http://link.springer.com/article/10.1007/s11229-006-9047-7.CrossRefGoogle Scholar
Spivak, David I. 2017. “Categories as Mathematical Models.” In Categories for the Working Philosopher, edited by Landry, Elaine, 381–401. Oxford: Oxford University Press.Google Scholar
van Fraassen, Bas C. 1987. “The Semantic Approach to Scientific Theories.” In The Process of Science: Contemporary Philosophical Approaches to Understanding Scientific Practice, edited by Nersessian, Nancy, 105–24. Dordrecht: Martinus Nijhoff.CrossRefGoogle Scholar
Wallace, David. 2021. “Against Wavefunction Realism.” In Current Controversies in the Philosophy of Science, edited by Dasgupta, Shamik, Dotan, Ravit, and Weslake, Brad, 63–74. New York: Routledge.Google Scholar
Wallace, David, and Timpson, Christopher G.. 2010. “Quantum Mechanics on Spacetime I: Spacetime State Realism.” British Journal for the Philosophy of Science 61 (4):697–727. http://bjps.oxfordjournals.org/content/61/4/697.CrossRefGoogle Scholar