Sextus Empiricus in his Outlines, dealing with genus and its species, rips off an argument of the Parmenides. If we interpret the genus-species relation artificially in terms of ordinary geometric inclusion then obviously there will be problems. But there is nothing contradictory about several objects
But what if we question set theoretic equality and replace it with path-connectedness ? For instance
Consider the following set in the plane with the relative topology:
Then by our definition we have that
Also, what is a set of elements ? The elements must have a distinguishing property or relation prior to being organized into the set (this discussion needs to be greatly expanded).
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