Answer from the FAQ in the discord channel of the game:
Q: How to improve erudition?
Just communicate with the NPCs. With successful communication, the points necessary for improving erudition will be given to you by themselves and when you get the right amount, you will improve this attribute.
To see the number of points you need, just go to the diary located in your inventory, and then go to the category with the statistics of your character. To do this, just click on the categories in the right side of the diary.