Dr Brian King, Junior Research Fellow, Worcester College, University of Oxford
It is a straight-forward theorem of standard set-theory (ZF) that there is no set of all the sets, the so-called universal set. But why? I identify and critique some standard reasons we might offer for rejecting the existence of the universal set, and different (and incompatible) conceptions of set theory that support them. My conclusions suggest that the nature of ZF is worryingly guided, not by mathematical practice or philosophical principle, but by historical accident.