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  1. Structural Relativity and Informal Rigour.Neil Barton - forthcoming - In Objects, Structures, and Logics, FilMat Studies in the Philosophy of Mathematics.
    Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...)
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  • Maximally Consistent Sets of Instances of Naive Comprehension.Luca Incurvati & Julien Murzi - 2017 - Mind 126 (502).
    Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of set (...)
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  • Non-Wellfounded Set Theory.Lawrence S. Moss - 2008 - Stanford Encyclopedia of Philosophy.
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