>>17804760 (OP)That quote comes from Plato's Phaedrus, specifically in the part where Socrates recounts a myth about the Egyptian god Theuth (or Thoth) presenting the invention of writing to King Thamus.
Here's the essence of the passage:
Theuth claims writing will improve memory and wisdom.
Thamus disagrees, saying it will produce forgetfulness in learners' souls, because they will rely on external marks rather than internal memory.
The fuller version of the quote is something like:
"For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practice their memory. They will trust to the external written characters and not remember of themselves." — Plato, Phaedrus 275a-b