I understand the the texts within the Voynich Manuscript are of an unknown language, and yet cryptographers are still working on it and still trying to decipher it. Does that mean that it is possible to crack any piece of writing even if it's in a language you don't know, and assuming you have no access to any tools that can translate the language? For example, let's say I see a piece of writing in Arabic, which obviously has no cohesion to English. Is it possible to translate it just by working on that piece of writing alone without nothing else? If so how would I go about this?
A core assumption of natural languages is that conceptual frequency and the grammar to construct and articulate concepts is not evenly and randomly distributed; so pattern discovery can occur.
However, two problems can quickly arise:
If I chose a novel in a language I don't know (say Russian) and converted it into Wingdings; my brain would still feel that the text "fits" my innate idea of written language without knowing why. Ilmari Karonen is correct that this problem is inherently cross-disciplinary.
The cryptanalytic curio is that a natural language isn't secure according to mathematical models but can still be completely unintelligible, thus serving the same outcome. This is a security-through-obscurity irritant that some cryptanalysts love to scratch. :-)
So yes, it is possible with the right provisos. If you can decipher a previously unknown natural language with a large corpus, yet disassociated from all other languages - you will probably win a Nobel prize in something.
The answer is yes, primarily because it has been done. Linear B, Akkadian, Sumerian, and hieroglyphics all had no persons with knowledge of them for centuries, and yet we can translate them today.