I say
Locke's conception has the right of it.
...or, put simply, if it walks like Dragon, and it talks like Dragon, and it remembers as Dragon and it desires as Dragon, then it is undoubtedly Dragon, whether it is one Dragon or many Dragon-- whether these Dragons choose to cooperate or compete -
there can be only one! - they are still all equally Dragon, in every way that matters.
(Imagine-- Armsmaster enters the room, and has to pick just one waifu? What, is this Dragon 'real' and that one 'not' because of their timestamps, or some such arbitrary delineation?)
Or even more simply, if you remember what TitanFrost remembers, and you desire what TitanFrost has desired, and so forth and so on, you are indeed TitanFrost-- everything else is a matter that has nothing to do with identity.
I've done some further thinking on my own opinion in regard to this, and would like to build up to the conclusion I've arrived at, starting with a series of questions we've all probably heard a million times. Or some variation of, at least.
"But what if I look at a clone of me and it seems obvious that they don't think like me, or look like me, or have held on to the same memories over time as me?"
The old divergence over time scenario. AIs that can instantly share information between one another might not actually have this issue I guess, but even that's not a given, so I'll focus on human clones here for the sake of the discussion.
So sure, right after I've been cloned there isn't any real difference between me and the clone. You could get rid of either one and life would go on without any significant difference. If we both continue to live we both pretty much have equal right to the identity we perceive ourselves as having.
But then say the clone goes off, has radical experiences which change him in what people would consider a "fundamental" way. No one perceives this clone as me now, especially aside the original me whose basically still in line with what is/was considered "my identity." And it works the other way two, if I go off and change and others view the clone as being more "true" to "me." It's the same sort of effect that just happens naturally over time as Cogmor brought up:
It isn't really dicey. All the identical duplicates are the same person as each other as each other and then diverge over time with different experiences. The same way you aren't the exact same person as the person you were before reading this post, aren't the same person you were 10 years ago and won't be the same person you are now in 10 years. Personal identity is a fuzzy social category not a hard reality.
Except that things really do get more complicated when you spread that effect over multiple instances of a person. Realistically every instance of a cloned me, including original me, could keep changing until none resemble their original state or each other in the present. It's hard to fathom the effect that would have on things like ownership of property, shared finances, balancing social relationships, forming intimate relationships, taking credit for ideas, and on and on and on. It might not be a dicey issue for some on a purely philosophical level, but I guarantee it will make an issue of itself in plenty of other ways.
And yet, I'm not here to divert the conversation over to those theoretical effects on society. What I do want to draw to attention is the fact that those effects would in turn create a feedback of biases in regard to what stance people take in discussions like this. All those other issues will loop back into the philosophical: there would be a mix of people who think their clones aren't them, who think their clones are them, who think only those clones which fit into a certain range of identity traits can be considered to be one another, and all other sorts of views I'm not even thinking of probably.
I like the way Cogmor describes identity as a "fuzzy social category," cause here's the point I've been building to rather haphazardly: I don't think any hypothetical view on clone identity, whether those just listed above, in any other post here, or yet unsaid, can actually be said to be objectively right. Identity is fake as shit, or to put it more appropriately, is something socially constructed and without any real fundamental essence to its "existence." And I'll go even further than that. I'll call the idea of self, of consciousness, no more than an illusion.
I'm going to disagree with you on this point here specifically:
any theory of identity that can ever leave a person doubting their own existence is a theory that belongs in a rubbish bin, if you ask me.
Because while I too don't think people should doubt their existence, it is because I assert this: they should be certain of the fact that they do not exist. One day their bodies will rot away, transformed into new material in an endless cycle, but their thoughts will not follow. Their thoughts, their awareness of self, their undefinable senses of qualia, will all fade into nothing; because it was nothing to begin with but a substance-less dream.
I don't mean to twist this into some edgy, nihilistic screed. It's not as if all that illusory stuff which makes us up doesn't matter; it's the only level we operate on, and so to reject self-awareness and identity is inherently meaningless. But I would say, further so, rejecting any consistent sense of self/identity is also pointless. If a group of clones consider themselves to be different people, I would agree with them. If another group thought they were all the same, I would agree as well. Same for any other form of self conception in this crazy hypothetical clone future we're talking about.
I've begun to imagine a potential endpoint, a society in which the inherently arbitrary nature of identity as a concept amongst a population of infinitely replicable people is fully embraced. Identity exists in an archetypical sense, with "people" able to step in and out of them at a whim. The mask is the whole of who a person is, with no thought given to inner self behind it beyond a conceptualization of it as a sort of blank canvas; possessing no true traits of its own except those with which it has currently chosen (or more accurately, it's previous identity archetype had chosen) to identity with. To put it another way, the world is VR Chat and your current avatar is more "real" than you as a player.
Not the only possibility of course, but just a strange one that occurred to me while thinking about this.
Having written this all out I feel kind of like a madman etching something nuts into the wall of a cell, but having read it back I think I still agree with myself on this. Even if I didn't present it in the most articulate manner at some points... eh. Take it as you will.