Well, first I want to be clear that I’m not trying to be belligerently argumentative here. Arguing is how I figure things out.
Second, both parts being required is specifically not in the rules, either the Brown book or that .pdf. In fact, it specifically mentions under the 3rd belief guidelines of the .pdf that some of the best and most interesting rules don’t explicitly specify any goal or action that falls out of them. They’re the moral or philosophical stances that can motivate any number of different kinds of goals/actions. It does say that those beliefs can be hard, but that the key to them is to make sure they’re motivating and controversial, that they can be contradicted. Goals can be opposed or supported, which correlates to validating them and undermining them, but they cannot be contradicted or verified, such a concept literally doesn’t make sense.
It does say that it can be a good idea to put them in there, and I don’t dispute that, at least, not very much. Beliefs should definitely be motivating, and there should be clear Goals that fall out of them given the scenario, but adding those goals only serves to direct the players in manifesting the “fact-claim + disposition” part of the Belief, and direct the GM in challenging that Belief, should the Players and the GM need that direction. I tend to think, however, that if they do need that direction, then that’s evidence that there needs to be better lines of communication opened up between the GM and the Players overall, and that more effort needed to be spend on the set-up, where players and GM decide what kind of game they want to play, what sorts of things they want to pursue, and what “feel” they want their game to have.
And adding a specific Goal half to the Belief that can be rapidly achieved, then swapped out for a new Goal such that the core fact-claim and disposition towards that fact aren’t changed, solely for the purpose of farming Persona points, seems cheaty to me. Ultimately, though, this comes down to GM approval of the Beliefs in the first place. “Dulcinea is beautiful and pure, I must win her heart by picking her some flowers from the Count’s garden” turns into “Dulcinea…I must pick the lock to her bedchamber to leave the flowers for her to discover” turns into “Dulcinea…I must remain undiscovered behind her curtains so that I don’t make her father mad at me” and so on, earning Persona points at each change. That seems excessive to me, given all the other ways Persona points can be earned.
Further, the Persona section mentions Beliefs just once under the Personal Goals heading, where it says that they should be “clearly described in a character’s Beliefs, or should be an explicitly stated goal for the group.” “Clearly described” =/= “explicitly stated.” A clear description of a goal can be attained by having a highly motivating Belief of a “fact-claim” form together with a clear and well-defined setting. “Count Vladd deserves to die, and can only be defeated by an expert swordsman wielding the Blade of Woe” can be viewed as having three clear goals described within it, as long as it’s very clear in the setting that the character is the only one in a position to do anything about those facts. “Kill Count Vladd,” “Become an expert swordsman,” and “Get the Blade of Woe.” Doing any of those things can earn a Persona point as well, as long as it’s clear from the set-up and scenario that those are the goals of that character that follow from that belief. If the set-up and scenario are different, the character might have the same belief, but goals of “Find an expert swordsman to wield the Blade of Woe, which I already have, and convince him to kill Count Vladd with it.” Specifying the goals serves only to highlight the point where the character wants to earn their Persona, and that specification can be equally clearly made in the set-up of the scenario and the meta-communication between Players and GM.
Further, it seems to me that Fate points are pretty explicitly aimed at the “fact-claim + disposition” part of the Beliefs. They’re awarded for “manifesting” those beliefs, not for “making progress” on them. If they were about making progress towards a goal, then how much progress is a Fate point worth? If my goal is to “discover the murderer” and I find a clue, do I get a Fate point for that even if the clue turns out to be a dead end? Do I get Fate points only when I find a clue that turns out to further the investigation? How will I know until the investigation’s done? Do I get Fate points for trying to find clues, whether I find them or not? I don’t suppose I can get a Fate point for claiming to be going out to investigate the murders, but ending up in a bar drinking myself into a stupor and happening to overhear the murderer bragging to his friends?
On the other hand, a Belief like, “The murderer killed my sister, and must be found before he strikes again” is clearly manifested in any number of ways. When I convince the Duke to hang the murderer as soon as he’s found, without a trial, I’m manifesting the (implicit) disposition I have towards the death of my sister. When I beat up the fences and snitches hanging out in the alleys to get a lead on the guy, I’m manifesting the fact that I think he must be found. When I Torture the murderer’s accomplice Quickly to find out where his hideout is, I’m manifesting the fact that I think he must be found before he strikes again, and when I search the hideout Carefully to discover clues as to where he fled, I’m again manifesting the fact that I think he must be found. It seems to me that a Belief that can only earn Persona Points, but cannot be manifested in a clear way to earn Fate Points is at least an incomplete belief.