The fighter archetype titan fighter allows the character to use 1 size larger weapons. With that in mind, can a medium size titan fighter use a bastard sword that is 2 size bigger assuming he has the exotic weapon proficiency bastard sword?
linky
No. A bastard sword is not a 2 handed weapon, so it is not affected by the Titan Fighters special abilities.
Edit: also once you go 2 size categories larger you also go outside of most of the titan fighters abilities.