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It isn't exposure to writing in itself that reduces remembering, but the difference in how literate people tend to behave, by relying more on "external storage" than their own memories. I first became aware of this possibility when I took a class in translating Homeric epic poetry, much of which has been shaped by its origin as an oral tradition. (For instance, it has been speculated that the many repetitive phrases the Homeric epics are aids to memory -- 'the swift-footed Achilles,' etc.)

It's well established that remembering is to some extent a skill. You can find sources with a cursory search. If you're interested in a longer treatment of the subject, "Moonwalking with Einstein" by a journalist named Josh Foer, who managed to win the largest memory competition in the US using mnemonics, is well worth the read.