Coincidence and cardinality

Coincidentalism is the view that distinct material things can be composed of the same microphysical simples at the same time. The existence of distinct coincidents is incompatible with any microphysical criterion of identity over time of material composites. This incompatibility constitutes a problem for the coincidentalist only if the coincidentalist needs a microphysical criterion of identity over time. What does the coincidentalist need such a criterion for? I will show that the coincidentalist needs such a criterion for an explanation of cardinal supervenience, of the thesis that facts concerning how many composite material things exist supervene on facts about microphysical simples.
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