Circular Discernment in Completely Extensive Structures and How to Avoid such Circles Generally

Studia Logica 100 (5):947-952 (2012)
In this journal (Studia Logica), D. Rizza [2010: 176] expounded a solution of what he called “the indiscernibility problem for ante rem structuralism”, which is the problem to make sense of the presence, in structures, of objects that are indiscernible yet distinct, by only appealing to what that structure provides. We argue that Rizza’s solution is circular and expound a different solution that not only solves the problem for completely extensive structures, treated by Rizza, but for nearly (but not) all mathematical structures
Keywords Structuralism  Structure  Identity-criterion  Discernibility
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DOI 10.1007/s11225-012-9442-7
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Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.

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