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On being right and avoiding being wrong
The two goals: 1) having true beliefs, 2) not having false beliefs may seem to be equivalent or something like that, but they in fact result in different optimal strats.
Not having false beliefs
If one has only goal (2), the optimal strat is to believe as few things as possible, suspending belief about most things. Even if one meticulously checks the evidence to avoid being wrong, one will make mistakes once in a while perhaps simply because the current best available evidence about the subject is misleading (i.e. indicates that a particular thing is true that is actually false). So, the optimal strat is to believe nothing at all, but it is hardly possible to live like that. Unfortunately acquiring beliefs is more or less automatic in the sense that if one is exposed to evidence one will automatically form the relevant beliefs without making a choice about it.1 So, one needs to avoid exposing oneself to any evidence relevant to things that one does not already believe. Perhaps spending one's time meditating is the optimal strat here.
Having true beliefs
If one has only goal (1), the optimal strat is to acquire lots of information and believe all sorts of things about it. I'm not entirely sure about the exact optimal strat. Perhaps the optimal strat is to set the evidence requirement for a belief as low as possible becus this makes it possible to form lots of beliefs, even on bad evidence. However, even this takes some time and since one wants to maximize the number of true beliefs, not just any beliefs, one shud probably gather at least some evidence. However, gathering evidence takes time and effort which cud be spend gathering evidence about some other subjects and forming beliefs about them as a result. So, some equilibrium will emerge about the optimal evidence requirement. Gathering evidence about a particular subject is a diminishing returns strat for having true beliefs.
The kind of thing that one shud gather evidence about matters. It is best to stick to areas where there is consensus about the experts and so that one can simply appeal to their authority and be right (most of the time). For subjects where there is much disagreement among experts, one wud need to gather some better evidence oneself to find out what the truth is. This probably means that one shud employ the heuristics mentioned in the previous link and stay away from subjects that fail at one or more of them. So, basically, one shud avoid all the subjects that i like. :P
However, as the number of one's beliefs keep rising, one will run out of consensus subjects to study, in which case one will need to study non-consensus subjects and form beliefs about them too, even the 'worst' and less socially acceptable/politically correct subjects. Perhaps one shud keep these beliefs to oneself.
It is also a good idea to find other people with the same goal so that one can share evidence about things with them to speed up the progress.
Both having true beliefs and avoiding having false beliefs?
What about someone who has both goals and perhaps with different importance ratings? Here it is more difficult to give advice about the optimal strat. Perhaps one shud set the evidence requirement pretty high, but not impossibly high so that no amount of evidence is enuf. This shud take care of most of the false beliefs. However, there are more ways to get rid of false beliefs. There are many debunking sites around and lists of common misconceptions about all kinds of stuff. One shud read those to get rid of pesky beliefs that got thru the 'evidence defense', perhaps at some time before one was a critical thinker. Beliefs tend to stick around. Here are some good things to read to get rid of misconceptions about various things:
There are plenty more of such skepticism material around which brings me to the next point: One shud study critical thinking and logic with a focus on fallacies so that one can avoid making them and thus acquiring wrong beliefs. It is also a good idea to know about cognitive biases so that one can try to compensate for them. A strong command of mathematics, especially statistics, is also a good idea. This helps assess much of the science as most of that employ statistics now a days.
Then, one shud spend alot of time gathering good quality evidence about subjects. Since it takes time to read stuff, one shud read the highest quality stuff in that it offers the best evidence about the particular subject. This probably means reading science in journals and textbooks to begin with to learn the things about the subject that there is consensus about.
Other relevant literature
1As a side note, this is why pragmatic arguments for the belief in something are not very useful. One cannot just will oneself to start believing in something that one thinks that there is no evidence for, e.g. the xtian god. See http://www.infidels.org/library/modern/theodore_drange/sobel.html