To me, that is too complicated a theory.
Oh, ok. I have my own version of the anthropic principle:
The content of a first person "reality" of an observer is the minimum that is necessary and sufficient for the existence of that observer.
I am trying to include observer selection ideas in my definition of "anthropy". ;-) I conjecture that the "third-person" aspect could be defined in terms of a so-called "communication" principle:
An arbitrary pair of observers and only communicate within the "overlap"
or set theoretic intersection of their first person "realities".
I think "reality" is a structure/system that is a
set of paths through the plenitude, where those paths exhibit properties like self-consistency, coherence, locality, stability, energy etc.
That structure can contain observers that can observe the very structure they are part of, precisely because of those
properties of self-consistency, coherence, locality, stability
etc that the structure (i.e. those paths through a state-space
Every observer will see the structure from their own limited
point of view (from their place and time within it) so there will be disagreements about it, but fundamentally, the observers (those who can observe and communicate with each other) are within the same structure
and are viewing parts of the same thing.
If that is "physicalist" I don't know. It still seems purely mathematico-logical to me. But I'm just positing a larger structure that is a commons that is observed by parts of itself. I think this is "Tegmarkian" anthropy.
Look at it this way. The content of "reality" of an observer
is (their limited perspective on) the minimum (self-consistent
structure) that is necessary for themselves, and all the other observers they observe, and for the whole sustaining environment for them and the physics that produced it, to exist.
I wrote this just before much better and my email client
flipped out and killed it. So sorry for the sleepy, angry, more muddled version you got.
-- "We are all in the gutter, but some of us are looking at the stars." - Oscar Wilde