conceptual

First of all, because the singleton of Socrates does not exist. Singletons of concrete objects are not bona fide mathematical objects. Set theory is a well established and perhaps fundamental mathematical theory and so its objects are as well established part of our ontology as any other mathematical objects, but this mathematical theory contains no singleton of Socrates, it only contains pure sets and so it so its only singletons are singletons of other sets. Carlos Romero reminds me that ZFC-U is a bona fide mathematical theory [Thanks Carlos!!], which is completely true; however I am not sure that Socrates is an ur-element of the sort that are the proper objects of ZFU. I suspect there is a distinction here between being an ur-element and playing the role of being an ur-element – to borrow a useful distinction from Stewart Shapiro. We cannot get    singleton of Socrates via some sort of indispensability argument from the application of set theory with concrete ur-e...