 Now bring this non-standard conception of ontological commitment to bear upon the envisaged infinite series of totality facts. It is impossible that the 2nd order totality fact comprising all the 1st order states of affairs exist and the 3rd order totality fact comprising all the 1st and 2nd order states not exist. So the 3rd totality fact—or any other state higher-order than it—is entailed by the existence of the 2nd order totality state. So all of these n &gt; 2 higher-order totality states supervene on it. That’s why Armstrong doesn’t think we need to take any of them with ontological seriousness.