Thought can't be reduced to a sequence of states, or functions acting on each other. I've tried to explain why in some other comments on HN. But let's grant that it can be so reduced for the sake of argument. I think even then, your position is impossible.
>> If there is no unchanging person having the thoughts, then there is no connection between the thoughts
> This is a non-sequitur.
You're right, I apologise. I should replace 'person' with 'thing' -- then it ceases to be a non-sequitur. I'll try to explain why:
> Thoughts can arise, like pure functions operating on their inputs, and returning some output into the global workspace.
This presupposes unity. Suppose, in case A, the thought "2+2" leads to the further thought "4". Let's suppose, further, that this is the case of a pure function operating on its input ("2+2") and returning the output ("4").
Suppose, in case B, exactly the same, but it returns the output "5".
I assume we agree that A is correct and B is incorrect.
You can affirm that the content of case A has some kind of unity underlying it, or you can deny it. (We could argue about the precise nature of the unity, but let us simply say that it is some kind of unity.) If you deny it, then you must say that there is no connection between 2+2 and 4. Connection presupposes something that connects. If there is no connection, then there is nothing that makes case A correct. That obviously undermines the possibility of any argumentation or logical thoughts. Alternatively, you can affirm the proposition. I think your position requires you affirm it, because by positing any kind of sequence, or function operating on an input and returning an output, you are positing unity. A sequence of any kind has a unity to it, otherwise it wouldn't be a sequence.
So in positing a sequence, you're positing unity. And in positing unity, you're positing something that unites, and that is different from that which is united. Such a thing must change from having the thought "2+2" to the thought "4", but it must persist as something underlying these changes in order for the changes to have any unity, and therefore for the arithmetic to have any coherence.
So we must logically get to the existence of something that persists while changing.
Obviously we could argue about what that thing is -- specifically, whether it's a person. We could also argue about when it comes in and goes out of existence. But the fact that there is a thing that persists in one sense, even as it changes in another, is all I'm trying to demonstrate here. I think once that's demonstrated, the position you're arguing is undermined.