Logic Is A Two-Edged Sword
Is it possible to perceive a world which is external to our perceptions?
Actually, Earthborn has a valid point.
Asking: "Is it possible to perceive a world which is external to our perceptions?"
is essentially the same thing as asking "Can we detect something that is undetectable?"
Something beyond our perceptions cannot be perceived by definition.
So the question is logically invalid, since we cannot possibly proceed to answer a question given in that form because it makes no logical sense.
I think I understand the answer you're seeking, but that's not the correct way to ask the question.
Unfortunately, the logical answer to the projected assumption is 'NO'.
The reason is because if we can perceive a 'thing', then by definition that 'thing' IS within our perceptions or we would have no actual knowledge of it whatsoever and its existence would be pure belief or speculation without any tangible foundations upon which to rest.
We can only call what we perceive 'knowledge' if it has at least one kernel of substantial, perceptible fact at its core. The difference between superstition and knowledge is the existence of this factual core as a foundation.
Simply put, we can't
know anything that we can't perceive or is beyond our perceptions. Think very carefully about it.
All the knowledge that we have is perceptible, but not all the knowledge that exists is within our perceptions.
That doesn't prove that the world you seek to explore doesn't exist, but it does mean that if it exists, you have no way of knowing - without delving into supernatural beliefs - and please let's not go there, you're too bright for that, thus logically invalidating the question.
You ask a forever unanswerable question.
In computer logic terms, the question is an infinite loop, and in this case, an irresolvable question means the same as 'NO'
I'm sticking explicitly to the parameters of the question and making minimal external assumptions, so it may not be the answer you are seeking if we are on different pages of abstract thought.