(thank you for the terminology correction in the last post)
That's not exactly what it is. It's a conceptual correction. I'm just using terminology to distinguish the concepts. That being said, the terminology does have precedent. Just to clarify though, in case this confusion arises, when I say identity in this sense, I mean something other than personal identity.
But the problem is: what matters for personal identity? Because the brain state of a single brain changes continuously, so we should find something that doesn't change and keeps the personal identity.
Sure. I, in practice, have my own set of experiences which establishes a relation to a particular environment, my own particular beliefs about that environment, my own particular desires, and my own particular goals. When I say that I am a different individual than you, what I mean is that you don't think my thoughts nor remember them; you don't see what I'm seeing; and your behaviors are potentially directed to different goals than mine. When I say that I'm the same individual I was in the past, what I mean is that I remember not only what I did, but I remember some of these things that make me say that I'm a different person than you are.
Before introducing a difference in the environment of W and E, they have exaclty the same brain state X. after introducing the difference, W have the brain state Y, and E have the brain state Z.
You cannot describe the states as different, because I specifically set up the problem such that you don't know if there is a difference or not. This is critical, but realistic; we do not come with a gods-eye view of the world, only a subjective one. So we can only infer things based on what we know. All I did in this scenario was set up a situation where it's plausible that the brain states are equivalent in every way. From there, we have to figure out if they are.
That's where the main problem arises with the above invariants. I can infer facts about my environment, because I'm connected to it. But I cannot infer facts about the environment in the other laboratory. Does E see the same thing I do? The fact that I answer
maybe instead of
yes highlights the critical difference; it is the same exact difference that compels me to think that you are a different individual than I am.
1) The personal identity varies with brain state, so W and E in brain state X have the same personal identity (simultaneusly) but W in state Y has another personal identity and E in state Z has another one (Empty Individualism)
What you're trying to say here is simply that if W and E are in the same brain state that they are equivalent under the concept of personal identity. You're better off just saying that directly, because what you in fact said does not follow. What you said was that personal identity varies with brain state; in other words, if W and E are not in the same state, then they are not equivalent under the context of personal identity. It does not follow from this that if they are in the same then they are.
2) The personal identity doesn't depend (only) by the brain state but by something more: maybe the space/time location or by specific elementary particles, or another external condition that may avoid dualism somehow, or some dualistic soul.
It's unclear what you mean here.
3) As you wrote in your successive post, we can consider the causal chain. But in your experiment must we consider it identical for W and E until you introduce a difference or it is differenced only in that moment?
Let's say before the split, we'll call you P. So P causally leads to W, and P causally leads to E. W remembers "being" P, in the sense that W remembers things about P that we already claimed was part of the distinction between P and other people, such that we would grant P with a meaningful concept "personal identity". So we can say that W is the same person as P.
In like fashion, we can say that E is also the same person as P.
But we cannot say that W is the same person as E, because, again, given how we came up with the meaningful concept of "personal identity", W and E are distinct individuals. Note that this means that equivalence, in this sense, is not transitive. That's fine--don't panic. We get to have systems like this.
In the second case, we have to presuma the at least one of W and E changes his personal identity in that moment.
There are changes not only in that moment, but all of the time, constantly. This is what ANTpogo meant when saying that it's dynamic. What we're describing by personal identity is simply what changes constitute something we're going to call the same person, and what changes don't constitute that.
4) The personal identity is illusory.
Illusory in which sense though? There are very specific implications to the concept of personal identity that I outlined, and we even make use of them; even you make use of them. That's why you're trying to convey something to me in this very thread; you believe you have to phrase it just right in order for me to understand it, because you believe I'm not privy to your thoughts. But you believe that you have figured this out over a period of time, so you believe that there's something persistent about your thoughts.
Do you believe the entire act of developing your view of open individualism is illusory? Do you believe you are attempting to convince me of this view, or that this is illusory as well?