Beliefs in Burning wheel are of the following form: I believe in A, and the next thing I will do about it is B. When the belief is seen in play the player gets fate artha (metagame points that improve rolls) and if the character accomplishes B, they get persona artha (stronger metagame points). There is also more, but let us stick with this simplified model for now.
Pathfinder, as it is usually played, is a game where the player characters act as a party that either has goals and tries to accomplish them within a relatively free sandbox environment or is driven by the game master's more-or-less explicit railroad.
In both of these situations, the party is the entity that usually takes action; in Burning wheel, characters having their own goals, acting by themselves and maybe even conflicting is assumed and usual.
Direction to Pathfinder play
Supposing you are playing Pathfinder in a fairly usual manner but the party is floundering, you may want to institute a party-wide goal or several and make them explicit. If the setting is a sandbox with lots of player choice, allow the players to set their goal. Choose an explicit story experience award to make the goal concrete and tell it to the players. Allow them to negotiate the reward, but make sure it remains in proportion to the challenges involved. (You may even want to only use such player-set goal experience, giving nothing on merely fighting enemies.)
The experience, and the game master participating in the process, makes it explicit that the goal is suitable for the game and possible to accomplish. It gives players the permission to focus on that goal or those goals and make them the point of play. I think the Pavlovian reward is secondary here.
If you driving a train with the players as passangers, then it is up to you to make the group goal explicit and helpful in moving to the next station. Maybe level the entire party up, once the goal is accomplished?
More character-driven Pathfinder play
If you institute personal beliefs, as in Burning wheel, then you move the game a little towards character-driven play. If the entire group is not enthusiastic, I would be very careful with this maneuver.
You should discuss the role of the beliefs with the entire group. Maybe they would mostly be used to inspire banter and discussions; this would not be disruptive. But if they are seen to drive play, then you risk party splitting and inter-character conflict. These are completely valid components of interesting roleplaying, but do make sure all the players agree and are prepared for this. Also, if you do railroad, then keeping the characters on rails will require work (that I consider unpleasant; YMMV) or excellent planning.
Discuss, with the entire group, what your (plural) goals in roleplaying are and what kind of play you (plural) want. Tailor the system accordingly.