This is the sentence in question from The Cambridge Companion to Chomsky by James McGilvray:
Evidence for both kinds of modularity comes from the independence one from the other of the various modules, as seen most clearly in double dissociation.
Which appears in this context below:
[...] there are two different notions of modularity: one according to which the language faculty is a module of the mind, distinct from moral judgment, music, and mathematics; another according to which the language module itself divides up into submodules, relating to sound, structure, and meaning. Evidence for both kinds of modularity comes from the independence one from the other of the various modules, as seen most clearly in double dissociation.
At the outset my reading is there is a missing "of" between "independence" and "one", but when I tried to look closer I felt that this "one from the other" is standing alone not without a reason, so I went on to search Linggle, SKELL and COCA, which, with considerable hits, yielded such results as:
Arden Green was a sprawling place, kitchen and garden far removed one from the other.
Both cases offer a unique experience one from the other.
places during her life, none of them seemed too different, one from the other.
These categories were said to be wholly distinct one from the other.
Women are all different one from the other.
These examples strike me as evidence that "one from the other" might be an adverbial phrase in its own right, pointing to the possibility that I have found something trivial without realizing I'm reinventing the wheel. Therefore I referred to what dictionaries I have access to like M-W, OED, in whose entries I didn't find what I expected to, be it under "one", "from" or "other". [edit: in the light of the answer provided by @ruakh I found now there's to one the other under one in OED]
It seems now that adverbial "one from the other" exists, though occluded in large measure by its ordinary usage (like differentiate one from the other) in online corpora.
I'm not sure if it means that this is really insignificant and cannot be counted as a full-fledged phrase.