What does a chimpanzee know about genes, gravitational waves or prime numbers? Nothing.
What could a very smart chimpanzee, guided by human trainers who even teach it sign language, know about these things. Nothing.
Quite obviously, there are areas of reality that are inaccessible to the knowledge of even the smartest chimp, and in principle.
The question now is: Are there also areas / aspects of reality "out there" that are as inaccessible to us as gravitational waves are to the monkey? Areas of reality that are not only unknown, but in principle un-knowable?
Or has evolution produced a potentially all-knowing organ - the human brain?
And what ability would it be that allows humans - unlike all other animals - to really see, know and understand even the most distant corner of reality?
But above all: how could we recognise / know that we are potentially omniscient?
Shouldn't we be omniscient in the forst place only to answer this question?
One way to look at it is to ask. Are there some things which are inherently unknowable, however great the intelligence. Which it seems there are.
For examples. 1. Anything which is infinite, such as the mathematical development of Pi, or 2. the largest prime. 3. Anything more complex than the brain trying to do the understanding, which is only the brain plus one. 4. Anything beyond the distance covered by light waves since the beginning of the universe.
The more you think about it the more examples you come up with. So I would say . No we can never be omniscient.
It seems to me that at this point in our brief developmental history we've barely scratched the surface of awareness about the universe, beginning with our own planet, the depths of which we've yet to explore. In other words, we don't even know what we don't know. Furthermore, knowledge itself--which can range from simple awareness to mastery--isn't static, as change occurs over time.
It is said that omniscience is the capacity to know everything, as opposed to the learning of it. If we assume it is possible that there could come a time--should our species or the artificial intelligence that we create continue to evolve in its capacity--when all that it known of cosmology, biology, mathematics, physics and disciplines yet to be discovered might inform us of what we've yet to learn, will there ever come a time when we have achieved unqualified mastery? In an infinite universe--or perhaps multiverse--it would seem unlikely, IMHO.
Thank you for this excellent thought exercise!
The difference between ignorance and knowledge is that knowledge is limited.