Ever try to delete your recycle bin (if you use Windows) or Wastebasket (if you use a Mac)? In some sense it seems like it ought to work (since these are just objects in the system) but in some other sense it seems like it would cause a paradox and destroy the univese (or at least prevent you from being able to delete other things, or crash the machine). Computing brings us many other paradoxes like "compiling the first compiler" and "paging out to disk the code that pages code back in to RAM".