Dark Souls Remastered | Big Hat Logan, full dialogue on first encounter in cage in Sen's Fortress

After freeing Logan (aka Big Hat Logan), you'll find him back at Firelink Shrine offering to sell advanced sorceries.

Either the Cage Key or the Master Key will release him. Most Dark Souls fans agree the Master Key is the best starting gift to select with a new character. Not only does it unlock shortcuts, but it can be used in place of certain other keys, such as here. If you do not have it, you'll need to loot the Cage Key to release Big Hat Logan.

You can read more about the Master Key here:
https://darksouls.wiki.fextralife.com/Master+Key