I've scoured the Player's Handbook for an answer, but I still can't find it
Paladins do not have spells known like a sorcerer or warlock does. Paladins "know" all the spells on their list, which they are high enough level to cast. They then prepare spells in the same manner as other classes.
PHB p. 84 under Preparing and Casting Spells:
You prepare the list of paladin spells that are available for you to cast, choosing from the paladin spell list. When you do so, choose a number of paladin spells equal to your Charisma modifier + half your paladin level, rounded down (minimum of one spell). The spells must be of a level for which you have spell slots.
Additionally, a Paladin knows, and always has prepared, the spells that correspond with their chosen Oath.
PHB p. 85 under Oath Spells:
Each oath has a list of associated Spells. You gain access to these Spells at the levels specified in the oath description. Once you gain access to an oath spell, you always have it prepared. Oath Spells don’t count against the number of Spells you can prepare each day. If you gain an oath spell that doesn’t appear on the paladin spell list, the spell is nonetheless a paladin spell for you.