Update: A few items from the archive added to the end.
Here goes…
Is there a clearer and stricter definition of ‘mental’ and ‘physical’ and what it means for something to be a mental state or a physical state?
Unfortunately, no. And there’s a reason too–it’s actually an extremely complicated topic, how the “physical” in “physicalism” should be defined (for those sleepless nights). Nonetheless, there is a sort of method to the madness here–at the end of the day, the theories are meant to illuminate basic and intuitive notions we already have. Those notions might need to be revised given a more rigorous analysis and empirical investigation, but they are the starting points. If we don’t already notice that some things have mind, or mental attributes, and others don’t, we won’t even be in this conversation at all. For our purposes, that more basic and intuitive understanding is thus all that we need to get the topic off the ground. It won’t stop there of course, if you are pursuing this more deeply.