1. There is only one consciousness. Under this scenario then 'states of affairs' which are coherent and justified by 'evidence' become objectively if they indicate the existence of an external (to the single consciousness) world that is governed by universal laws. Whether or not there is in fact a world that is external to the single consciousness is perhaps uncertain, but from the point of view of the single consciousness it probably doesn't matter so long as it seems that way.
2. There are multiple conscious entities and they agree on certain states of affairs (at least by their apparent behaviour). Again, the existence of an external physical world is probably not important. What is important is that the beliefs are coherent and indicate the existence of universal laws or at least apparent consistency in the way that the external world is.