The scientific realm is unlimited. However, the scientific reach is limited. It will always be limited. And that is exactly what Gödel showed us.

Any time we use a formal system, and science is a formal system, the completeness of that formal system is limited to that formal system.

Anytime we walk up to the largest of all levels, all formal systems will show up as Incompletenesses.

The example I often use is the word blue. The meaning of the word blue depends on the context in which it is used.

Blue in the paint store means something else than blue on the couch with the shrink.

We cannot take blue to the overall level, because we will bump into our own limitations. The first one is that the word can have different meanings (scientists do not like that). Then, there is the issue of language. In other languages the word blue is not blue but something of their own making.

Also, the human brain experiences blue in potentially different manners than other species, while for a good number of species blue is a non-word because they don't see that color at all.

Long story short: Science is only capable of seeing things the scientific way as long as scientists stay within the scientific formal system.

In other words, it is not important that scientists have a hard time with investigating consciousness. It is part of the scientific discourse to bump into the boundaries of the scientific axioms.

Thank you for an otherwise good article. I just missed your consciousness about the inherent nature of science not having much business diving into this subject matter. Science cannot peer all that much outside its own box. The scientific reach is (much) shorter than the scientific realm.