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bogus comments on There just has to be something more, you know? - Less Wrong
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There is a big difference between decomposing consciousness into its constituent fragments, vs. simply identifying the degrees of freedom in your conscious experience. Drilling down into your introspection and identifying the smallest specks of experience which you can think of as being details of your consciousness is doing the latter. You can go about modifying any of these tiny details more or less independently, but your consciousness is still a self-contained object.
It's only after you isolate a single electron that you can talk about what its conscious experience would look and feel like.
I have no problem letting decomposition refer to details of mind that can be adjusted independently of others. I can imagine such things. But I do not know if such things actually exist in my mind.
I have a math background so I tend to think a bit like that. Here's a silly analogy: consider a linear transformation on a vector space. Sometimes there are invariant subspaces of the vector space called eigenspaces, but sometimes there are not. In this case, you cannot just analyze the effect of a linear transformation by examining a smaller subspace of the vector space since the transformation sort of forces all subspaces to interact with one another.
I can imagine that I adjust some detail of my mind's inner workings and I might imagine that this detail is somehow independent from all the other details. But perhaps, in reality, my mind has no eigenspaces. Perhaps adjusting one detail necessarily has an effect on all the other details of my mind. I can't really understand my consciousness unless I look at the whole thing at once.
Maybe this is embodied in the qualification you made: "more or less independently". Seems fair. But this is the sort of objection I think a non-reductionist might have.
They might also reject the notion of an electron having a conscious experience (as do I) for reasons mentioned elsewhere in the comments section.