I didn't already know what illusionism argues, so I tried to understand it by skimming two related wiki articles that may be the ones you meant.
https://en.wikipedia.org/wiki/Illusionism_(philosophy) - this one doesn't seem like what you were talking about; it's relevant anyway, and I think the answer is undefined
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https://en.wikipedia.org/wiki/Eliminative_materialism#Illusionism this seems like what you're talking about. The issue I always hear is, an illusion to whom? and the answer I give is effectively EC Theory: consciousness to whom is a confused question, "to whom" is answered by access consciousness ie the question of when information becomes locally available to a physical process; the hard problem of consciousness boils down to "wat, the universe exists?" which is something that all matter is surprised by.
As for anthropics: I think anthropics must be rephrased into the third person to make any sense at all anyhow. you update off your own existence the same way you do on anything else: huh, the parts of me seem to have informed each other that they are a complex system; that is a surprising amount of complexity! and because we neurons have informed each other of a complex world and therefore have access consciousness of it, to the degree that our dance of representations is able to point to shapes we will experience in the future, such that the neuron weights will light up and match them when the thing they point to occurs, and our physical implementation of approximately bayesian low-level learning can find a model for the environment -
well, that model should probably be independent of where it's applied to physics; no matter what a network senses, the universe has the same mechanisms to implement the network, and that network must figure out what those invariants are in order to work most reliably. whether that network is a cell, a bio neural net, a social net, or a computer network, the task of building quorum representation involves a patch of universe building a model of what is around it. no self is needed for that.
So, okay, I've said too many words into my speech recognition and should have used more punctuation. My point about anthropics boils down to the claim that the best way to learn about anthropics is by example. Most or all math and physics works by making larger scale systems with different rules by arbitrarily choosing to virtualize those rules, so a system can only learn about other things that could have been in its place by learning what things can be and then inferring how likely that patch of stuff is and where it is in the possibility-space of things that can be.
This is a lot of words to say, you can do anthropic reasoning in an entirely materialist-first worldview where you don't even believe mathematical objects are distinctly real separate from physics. you don't need self-identity, because any network of interacting physical systems can reason about its own likelihood.
Alright, I said way the hell too many words in order to say the same thing enough ways that I have any chance in hell of saying what I intend to be. Let me know if this made any sense.
That sounds like a plausible theory. But, if we reject that there is a separate 1st person perspective, doesn't that entail that we should be Halfers in the SBP? Not saying it's wrong. But it does seem to me like illusionism/elimitivism has anthropic consequences.