Actually, Bostrom did not argue that we are most likely living in a simulation. Instead, he argued that at least one of three propositions must be true, and one of those propositions is that "almost all people with our sorts of experiences live in computer simulations". But, since it is possible that one of the other two propositions could be true, it does not necessarily follow that we most likely live in a simulation.

In fact, Bostrom has stated that he believes that we are probably not simulated (see the second paragraph of this paper).

Of course, per your comments, it is possible that Bostrom only said that we are probably not simulated so as not to terminate the simulation :).

But if you don't know who is original or copy, you may start to worry about.

It seems to me that who is the original and who is the copy is irrelevant to my reaction in the leg amputation thought experiment. But, who is me and who is not me is very relevant. For example, suppose I am a copy of the original gpepper. In that case, I would be less unhappy about the original gpepper having his leg cut off than I would be about having my own leg cut off.

I understand that identity is too complex to figure out in this comment thread. However, any theory of identity that defines or approximates identity as "a member of a class" is apt to badly miss encapsulating most people's understanding of identity, as illustrated by the fact that my reaction to having my own leg cut off is going to be significantly different than is my reaction to a copy of me having his leg cut off. I wouldn't be happy about either situation, but I'd be much less happy at having my own leg cut off than I would about a copy of me having his leg cut off.

I agree that identity

is like "love" - everybody could feel it, as it evolved biologically and culturally, but if we try to give it short logical definition, we are in troubles

And, there are other things that most people experience but that are hard to define and can seem paradoxical, e.g. consciousness and free will.

However, you said that we can generalize your leg-amputation thought experiment as a principle: "I am a class of all beings from which I can't distinguish myself." I don't understand what you mean by this - your thought experiment involving 1,000,000 copies of a person seems equivalent to my thought experiment invovling 1,000,000 strangers. So, I do not see how being a member of a class from which I can't distinguish myself is relevant.

It seems to me that you have 1,000,000 different people, one of whom is going to get his/her leg cut off. The fact that they are all copies of one another seems irrelevant. The same relief that each of the 1,000,000 people in your example feels (in your step 3) upon learning that there is only 1/1000000 chance of loosing a leg would be felt by each of 1,000,000 randomly selected strangers if you:

• Told each individually that he/she would have his/her leg cut off
• Then told each that only one member of the group would be randomly selected to have his/her leg cut off

So I guess I do not see how this example tells us anything about identity.

Identity is complex social adaptation and it is directly connected with hard problem of consciousness.

I agree that identity is directly connected with the hard problem of consciousness. That identity is a social adaptation seems plausible (to me) but not certain.

So we can't finally solve any identity paradox on our current level of knowledge.

It seems to me that, per mwengler's observation, we already have past copies (your category number 1); identical twins are past copies that branched shortly after conception. Past copies, it seems to me, do not share a common identity and are distinct people with distinct conscious experiences. I'm not sure that I see any identity paradoxes involving past copies.

Current, mirror copies (your category number 2), cannot exist in a conscious state for any meaningful amount of time (except perhaps as EMs where the hosting environment ensures that they have identical stimuli, are kept in sync from a simulation standpoint, etc.), so mirror copies can be ignored, it seems to me.

Future copies (your category number 3) do seem to have some paradoxes (or at least they are unclear to me). Specifically,

1. if I know that I am going to be non-destructively copied in five minutes, should I care more about one future copy than I do the other? I suspect that I should not.

2. If I know that I am going to be copied but the original will be destroyed in the process, should this concern me? It seems like, per #1, it should not. But, somehow, I don't think that I'd be very eager to go through with a destructive copy process.

3. How can it be that the identity of a person and his/her future copy is the same (which seems plausible), but two past copies have distinct identities? It seems like personal identity should be transitive.

So it seems to me that future copies are paradoxical. And of course future copies will matter if/when uploading becomes possible, so we will eventually need to resolve (or accept) the paradoxes.

Thanks for the clarification. However when you say:

Suppose I am one of twins, but I don't know which twin I am. But I know that twin 1 will be hit in face in next 1 minute. In this case I am in the situation of so called indexical uncertainty and my best guess is that I have 50 per cent probability of being twin 1 and thus 50 per cent probability being hit in the future. After I will be hit, I will know with 100 per cent probability that I am twin 1.

This is really not unique to twins. Suppose I choose two strangers and tell them that I will flip a coin and punch one or the other of them in the face in one minute, depending on the outcome of the coin toss. Assuming the strangers stick around, they will be in the same position as the two twins in your example. So, I don't really see how this tells us anything interesting about identity, twins or copies.

Also, considering the first two of your three cases of copies, i.e. past copies and mirror copies, it seems to me that if I make a nondestructive copy of a person, the two will be mirror copies only for an instant; once the copy process completes and the two "wake up" (presuming that copying is done from an unconscious state), the two copies will immediately begin diverging based on different stimuli, etc., and will therefore become instances of case 1 (past copies). So, from a practical standpoint, there can be no instances of case 2 for any meaningful duration of time (that is to say, for enough time to interact with the copies).

any event which affect one of twins has 50 per cent situation to happen with them

I don't understand what that means. For example, if I were to punch one of a pair of identical twins, the twin that I punched would feel the pain, and the twin that I did not punch would not feel any pain. In this regard, the two twins would have no more of a shared consciousness than would two strangers.

I suspect that if someone were non-destructively copied, the situation would be similar, as mwengler suggests. The two would have a common set of memories up until the point that the copy was made, but from that point on they would have no common or shared consciousness; they would be two distinct people (albeit with an uncanny resemblance to each other).

The idea of the story is that there are no evidence.

But in the OP, you said:

she has known Adam very well and the Adam that she knew, wouldn't commit murder. She uses Adam's character and her personal relationship with him as evidence.

It seems to me that Adam's character as observed by Eve is evidence. Not irrefutable evidence, but evidence all the same. It seems to me that, baring evidence of Adam's guilt or evidence that Adam's character had recently changed, Eve is rational for beleiving Adam to be innocent on the basis of that evidence.

Cain provided no such evidence, so Eve is rational in her belief.

Even if you do not share your written thoughts with anyone, writing them down can help to organize your thoughts into a form that can be more easily analyzed and evaluated (by you).