The full quote from Socrates is:

“…this discovery of yours will create forgetfulness in the learners’ souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves. “ (Dialogues of Plato, Phaedrus, pp. 275).

Is it ironic that you are reading this quote about Socrates on this blog? Seems like the ability to read may dull our individual memories, but that it greatly strengthens the memory of our species.