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## Munich Center for Mathematical Philosophy (MCMP)

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Colloquium Mathematical Philosophy, John Wigglesworth (MCMP/LMU) gives a talk at the MCMP Colloquium (16 July, 2015) titled "Mathematical Structuralism and Metaphysical Dependence". Abstract: The notion of dependence plays various roles in non-eliminative mathematical structuralism. Of particular interest is the dependence relation that is said by some structuralists to hold between an abstract mathematical structure and the various realisations that exemplify that structure. This dependence relation can be used to distinguish between different versions of non-eliminative structuralism. Ante rem structuralists say that the abstract structure is prior to and independent of any realisation of that structure. In re structuralists claim that the realisations are prior, and so the abstract structure is dependent on there being some realisation of that structure. But very little has been said about this notion of dependence. In this talk, I evaluate one account of dependence that can be found in the literature. I then propose an alternative account and use it to assess the dependence claims made by ante rem and in re structuralists.

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