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PETER SULLIVAN, MICHAEL POTTER, Hale on Caesar, Philosophia Mathematica, Volume 5, Issue 2, June 1997, Pages 135–152, https://doi.org/10.1093/philmat/5.2.135
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Abstract
Crispin Wright and Bob Hale have defended the strategy of defining the natural numbers contextually against the objection which led Frege himself to reject it, namely the so-called ‘Julius Caesar problem’. To do this they have formulated principles (called sortal inclusion principles) designed to ensure that numbers are distinct from any objects, such as persons, a proper grasp of which could not be afforded by the contextual definition. We discuss whether either Hale or Wright has provided independent motivation for a defensible version of the sortal inclusion principle and whether they have succeeded in showing that numbers are just what the contextual definition says they are.