Abstract
In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the role diagrams play as means of discovery and understanding. Alternatively, this paper purports to show that the view that the method of mathematics is the analytic method is capable of dealing with diagrams qua diagrams, and of accounting for such role.
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Acknowledgements
I am grateful to Otávio Bueno, Jessica Carter, Miriam Franchella, Gila Hanna, Robert Thomas, Fabio Sterpetti, Francesco Verde, and two anonymous reviewers for their comments and suggestions.
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Cellucci, C. Diagrams in Mathematics. Found Sci 24, 583–604 (2019). https://doi.org/10.1007/s10699-019-09583-x
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DOI: https://doi.org/10.1007/s10699-019-09583-x