Strong emergentists face a quadruple dilemma: accept the physical closure principle and deny strong emergentism, deny the closure principle and court either substance or property dualism, accept substance dualism and kill emergentism by accepting vitalism or accept property dualism and get locked into the fallacy of reconciling upward emergence with downward causation without the help of any external agency. Strong emergentists would most likely choose, and I seek to show that it contains contradictions that kill emergentism nonetheless. This is because (...) emergentists would ultimately have to admit the role of external agency or environmental input regarding upward/downward interaction. But once this happens, there seems no need to discuss emergence, since we are no longer entirely sure that properties alleged as emergent actually emerged from the base properties from which we would say they emerged. (shrink)