Ah, the ever returning question of identity.
Two objects which are identical down to the quantum level share a certain sameness. However, they are two objects. Does the principle of Identity of Indiscernables tell us when and how we can tell when TWO objects (2, count em, TWO) are the "same?"
No, actually, it doesn't. The principle of Identity of Indiscernables is making a statement about *physical states.* Specifically, that if we take two indiscernable objects (which is to say that we take a PAIR of objects, two of them!) and switch them, the state of the universe following this switch is perfectly identical to the state of the universe before the switch. I repeat, the state prior to the switch is identical in every way to the state following the switch.
Now, of course, only objects which are extremely similar (that is, indiscernable down to the quantum level) can satisfy the requirements for this principle. And, since this principle is an "if or only if" statement, we might be inclined to run it in reverse: if you could switch two objects and get a physical state indiscernable from the original state, then the objects must be identical.
But despite the fact that these two objects (dos, duo, not 1 or 3; four is
right out!) are identical, they are not the "same object." They are:
*two* *indiscernable* objects.
To say that two indiscernable objects are really the SAME object, we'd have to imagine some metaphysical object off in Plato's heaven, an object of which the two things we see are mere instantiations. Even then, however, they'd still be *two* instantiations of one thing.
How does this relate to consciousness? Well, consciousness IS the one of those things that exists only in Plato's heaven. Being a metaphysical object, it obeys all kinds of rules and laws that we'll never know about and that science can never truly understand, ya da ya da. Of course, skepticism probably isn't what this debate needs right now. We know a little about consciousness, don't we? So let's just assume that you've got some and I've got some and that if either of us died at this moment, the dead one wouldn't have any.
Now, let's try to remember why we started thinking about this question in the first place. In fact, the question was essentially pragmatic/ethical: If an identical copy of me existed, would it be OK if the copy died? Would "I" continue living so long as one copy of me continues living?
Now, here, people have falsely applied Identity of Indiscernables to say "Yes, definitely. If the I.o.I. principle is true, then the two copies are the same person." Well, again, this requires us to assume that there is a "person," a "consciousness" off in Plato's heaven, of which the two copies are instances. We have two instances, obviously, but so long as they're both instances of the same person, it should be fine if one of them dies. The true form of you exists so long as one of your copies exists.
Now, I'm going to make the big leap here. Many of you will disagree. But here we go:
There is no true form of a person. There is no Plato's heaven.
OK, where does this leave us? This means that the two copies are two identical people. Since it's obviously a bad idea for a person to die, we'd better not kill either copy, right?
Well, not necessarily. It's a faulty ethical assumption to presume that death is always a bad idea, particularly when the person dying doesn't mind. (Here's the libertarian in me showing through. If you're into deontology, you won't like this a bit.) While it seems inherently unwise for a person to kill themselves, I think it takes an even bigger leap than I just made to presume that it is universally morally wrong for them to do so.
I personally see no reason to kill myself, and would strongly advocate against any of you trying this at home. That being said, I can think of reasons why a person might believe that their own interests would be best served by their own deaths. Under those circumstances, and presuming that they don't trample on other peoples' rights in the process, such people can and should be allowed to risk or even sacrifice their own lives for whatever reasons they see fit.
This brings me back to the copies. It seems not at all unreasonable that the copies might be willing to die so that the other one would live. We see this all the time in parents willing to give their own lives for their children. Indeed, by a simple extension of evolutionary psychology, we should expect that the copies would be at least as willing to die for one another as two siblings might be, if not more so. I'd be inclined to think that they'd be MUCH more willing to do so, since (at least for a fraction of a second) they'd even satisfy the conditions for Identity of Indiscernables: for a brief moment, they'd be identical *in every way*.
So I answer the question this way: If the copies don't mind dying so long as one of the other copies still lives (or so long as another copy can be made,) then it's fine for them to do so. If you make many such copies, you'll have many people who place a low value on their lives individually but great value on the permanence of at least one copy. Ethically speaking, if it's fine with them, it should be fine with us.
You might be asking yourself "Now, that's all good and well, but should
*I* be willing to die so long as one of my copies still lives?" If
Plato's heaven doesn't exist, then this is a question which no one can answer for you. I don't think I'd mind. You might. If so, then there's no arguing with you. No one can tell you that you shouldn't mind, any more than they can tell you that you shouldn't feel what you feel.