I seriously don't know whether subjective experience is mostly independent of hardware implementation or not. I don't think we can know for sure.

However: If we take the position that conscious experience is strongly connected with behaviour such as writing about those conscious experiences, then it has to be largely hardware-independent since the behaviour of an isomorphic system is identical.

So my expectation is that it probably is hardware-independent, and that any system that internally implements isomorphic behaviour probably is at least very similarly conscious.

In any event, we should probably treat them as being conscious even if we can't be certain. After all, none of us can be truly certain that any other humans are conscious. They certainly behave as if they are, but that leads back to "... and so does any other isomorphic system".

No, it isn't.

the mathematical structure itself is conscious

If I understand it correctly, that's the position of, e.g. Max Tegmark (more generally, he thinks that "to exist" equals "to have a corresponding math structure").

So there should be some sort of hardware-dependence to obtain subjective experience

My (and, I think, a lot of other people's) intuition says something like "there is no hardware-dependence, but the process of computation must exist somewhere".

Don't think there is a conclusion, just more puzzling situations the deeper you go:

"Scott Aaronson: To my mind, one of the central things that any account of consciousness needs to do, is to explain where your consciousness “is” in space, which physical objects are the locus of it.  I mean, not just in ordinary life (where presumably we can all agree that your consciousness resides in your brain, and especially in your cerebral cortex—though which parts of your cerebral cortex?), but in all sorts of hypothetical situations that we can devise.  What if we made a backup copy of all the information in your brain and ran it on a server somewhere?  Knowing that, should you then expect there’s a 50% chance that “you’re” the backup copy?  Or are you and your backup copy somehow tethered together as a single consciousness, no matter how far apart in space you might be?  Or are you tethered together for a while, but then become untethered when your experiences start to diverge?  Does it matter if your backup copy is actually “run,” and what counts as running it?  Would a simulation on pen and paper (a huge amount of pen and paper, but no matter) suffice?  What if the simulation of you was encrypted, and the only decryption key was stored in some other galaxy?  Or, if the universe is infinite, should you assume that “your” consciousness is spread across infinitely many physical entities, namely all the brains physically indistinguishable from yours—including “Boltzmann brains” that arise purely by chance fluctuations?"
Link

The point here is that you could have a system that to an outside observer looked random or encrypted but with the key would be revealed to be a conscious creature. But what if the key was forever destroyed? Does the universe then somehow know to assign it consciousness?

You also need to fully decide when replaying vs computing apparently conscious behavior counts. If you compute a digital sim once, then save the states and replay it the 2nd time what does that mean? What about playing it backwards?

Boltzmann brains really mess things up further.

It seems to lead to the position then that its just all arbitrary and there is no objective truth, or uncountable infinities of consciousness in un-causal timeless situations. Embracing this view doesn't lead anywhere useful from what I can see and of course I don't want it to be the logical conclusion.

Unless I misunderstand the confusion, a useful line of thought which might resolve some things:

Instead of analyzing whether you yourself are conscious or not, analyze what is causally upstream of your mind thinking that you are conscious, or your body uttering the words "I am conscious".

Similarly you could analyze whether an upload would would think similar thoughts, or say similar things. What about a human doing manual computations? What about a pure mathematical object?

A couple of examples of where to go from there:
- If they have the same behavior, perhaps they are the same?
- If they have the same behavior, but you still think there is a difference, try to find out why you think there is a difference, what is causally upstream of this thought/belief?
 

If you think consciousness is a real existent thing then it has to either be in:

The Software, or

The Hardware.

Assuming to be in the hardware causes some weird problems. Like "which atom in my brain in the conscious one?". Or "No, Jimmy can't be conscious because he had a hip replacement, so his hardware now contains non-biological components".

Most people therefore assume it is in the software. Hence why a simulation of you, even one done by thousands of apes working it out on paper, is imagined to be as conscious as you are. If it helps, that simulation (assuming it works) will say the same things you would. So, if you think its not conscious then you also think that everything you do and say, in some sense, does not depend on your being conscious, because a simulation can do and say the same without the consciousness.

There is an important technicality here. If I am simulating a projectile then the real projectile has mass, and my simulation software doesn't have any mass. But that doesn't imply that the projectiles mass does not matter. My simulation software has a parameter for the mass, which has some kind of mapping onto the real mass. A really detailed simulation of every neuron in your brain will have some kind of emergent combination of parameters that has some kind of mapping onto the real consciousness I assume you possess. If the consciousness is assumed to be software, then you have two programs that do the same thing. I don't think there is any super solid argument that forces you to accept that this thing that maps 1:1 to your consciousness is itself conscious. But there also isn't any super solid argument that forces you to accept that other people are conscious. So at some point I think its best to shrug as say "if it quacks like consciousness".

You don’t have to be a substance dualist to believe a sim (something computationally or functionally isomorphic to a person) could be a zombie. It's a common error , that because dualism is a reason to reject something as being genuinely conscious,it is the only reason --there is also an argument based on physicalism.

There are three things that can defeat the multiple realisability of consciousness:-

1. Computationalism is true, and the physical basis makes a difference to the kinds of computations that are possible.

2. Physicalism is true, but computationalism isn't. Having the right computation without the right physics only gives a semblance of consciousness.

3. Dualism is true. Consciousness depends on something that is neither physics nor computation.

So there are two issues: what explains claims of consciousness? What explains absence of consciousness?

Computationalism is a theory of multiple realisability: the hardware on which the computation runs doesn't matter, so long as it is adequate to run the computation, so grey matter and silicon can run the same computations...and a lot of physical details are therefore irrelevant to conscious.

Computationalism isn't a direct consequence of physicalism.

Physicalism has it that an exact atom-by-atom duplicate of a person will be a person and not a zombie, because there is no nonphysical element to go missing. That's the argument against p-zombies. But if actually takes an atom-by-atom duplication to achieve human functioning, then the computational theory of mind will be false, because there CTM implies that the same algorithm running on different hardware will be sufficient. Physicalism doesn't imply computationalism, and arguments against p-zombies don't imply the non existence of c-zombies-duplicates that are identical computationally, but not physically.

So it is possible,given physicalism , for qualia to depend on the real physics , the physical level of granularity, not on the higher level of granularity that is computation.

A computational duplicate of a believer in consciousness and qualia will continue to state that it has them , whether it does or not, because its a computational duplicate , so it produces the same output in response to the same input. Likewise, a duplicate of a non believer will deny them. (This point is clearer if you think in terms of duplicates of specific individuals with consistent views, like Dennett and Chalmers, rather than a generic human ).

@JuliaHP

Instead of analyzing whether you yourself are conscious or not, analyze what is causally upstream of your mind thinking that you are conscious, or your body uttering the words “I am conscious”.

Since an effect can have more that one cause that isn't going to tell you much.

I suspect there's a fair amount of handwaving involved, but generally as I understand it, the common belief is that "true" isomorphism does include everything necessary for subjective experience.  There's a TON of weight put on the idea of "relevant pieces" of the brain/CNS, and IMO there's a serious disconnect among those who claim it's anywhere near feasible today.

You'll have to define "conscious" and "subjective experience" more operationally before anyone can even guess what parts of the computation are relevant to those things.  It does seem very likely that everything is physics, and a sufficiently accurate simulation will have all the properties of the original.  Note the circular definition of "sufficient" there.

Keep in mind that intuition is a bad guide for what a subjective experience even is.  We have zero positive or negative experiences outside of the very limited singleton that is ourselves.  There's nothing to have trained or evolved an intuition on.

Sorta? Usually the idea is that the presence or absence of hardware determines the anthropic probability of being that conscious process, otherwise you would expect to be some random arbitrary Boltzmann brain-like conscious.

Also this is an immediate corollary of the mathematical universe hypothesis, which says our universe is a mathematical structure.

An isomorphism isn't enough. Stealing from Robert (Lastname?), you could make an isomorphism from a rock to your brain, but you likely wouldn't consider it "conscious". You have to factor out the Kolmogorov complexity of the isomorphism.

conscious in the way that we are conscious

Whether it's the same way is an ethical question, so you can decide however you want.

So there should be some sort of hardware-dependence to obtain subjective experience.

I certainly don't believe in subjective experience without any hardware, but no, there is no much dependence except for your preferences for hardware.

As for generally accepted conclusions... I think it's generally accepted that some preferences for hardware are useful in epistemic contexts, so you can be persuaded to say "rock is not conscious" for the same reason you say "rock is not calculator".