We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue.
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Acknowledgements ES was the primary author of Sects. 1 and 2; SCF and PP were the primary authors of Sect. 3 and provided edits of all sections. ES would like to thank Robert Batterman, John Earman, and John Norton. All authors thank the contributors to this special issue and the partipants of the Munich Center for Mathematical Philosophy’s June, 2016 conference on the same topic. SCF acknowledges partial support from a Marie Curie Fellowship (PIIF-GA-2013-628533).
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