|Both Michaels are making good points here.|
Popper called the wrong approach the "Who should rule?" problem and said most political philosophy argues about who should rule, when it should be focussing a lot more on how to set up political systems capable of correcting mistakes about who gets to rule.I agree that asking the question "Who should rule?" is wrong-headed, but that is because it presumes that a man should rule other men -- which is wrong. You can call it a 'smuggler's question' because it tries to smuggle-in a wrong notion about mankind. Importantly, it can be known to be wrong without special empirical investigation into the matter -- it can be known to be wrong from just common empirical input (like the kind you get from merely living as a human being). People sometimes brandish this as "a priori" but there is never anything purely a priori. All reasoning starts not ex nihilo, but instead from a pool of common human experience.
What about epistemology? "Which ideas should we start with?" is a bit like "Who should rule?" You're never going to get it perfect and it shouldn't be the primary focus of attention. Instead you want to set things up so if you start with the wrong ideas you can find out the mistake and fix it quickly, easily, cheaply.
error correction is (a lot) more important than starting in a good place.
But the question "Which ideas should we start with?" is not like the question "Who should rule?" -- and this is a terribly important distinction. When examining things such as the science of knowing (epistemology), you have to keep context, and part of the context is to note your first principles and your final ends (aims). First principles and final ends tell you how to start in a good place. In the case of the smuggler's question above, the wrong first principle adopted is that a man should rule over other men, and the final end or aim is to trick others into allowing tyranny.
Like Rand said, anyone talking like that is, or wants to be, the dictator. So, on the basis of its false first principles and its morally-wrong final ends -- we can dispense (for all time) with the question: "Who should rule?"
You cannot do this with the epistemological question "Which ideas should we start with"? Questions imply answerability (the potential of there being a correct answer). What was wrong with the political "Who should rule?" question is that it implies that there is a correct answer -- when there is actually not a correct answer. In the case of epistemology, however, there is a correct answer. The final end or aim of epistemology is to answer the 5-word question: "How do you know that?" and some of the first principles of epistemology will involve things like the principle of non-contradiction.
Because there is a known path and a known destination, it can also be known whether you are starting in a good place or not. If this could not be known beforehand -- because of disbelieving that existence is identity, for instance -- then error correction would be a lot more important than starting in a good place.