Assume an epistemological foundation of sorts that admits rational intuition and empirical evidence. Then you can gain new beliefs through experience/sense perception, or extrapolating from prior beliefs.
Suppose that through the course of normal events (lived experience, etc) you learn new things and adjust your base belief system. For example, say your political beliefs evolve over the span of decades. Call these "the rational beliefs", the ones being contrasted by the title question.
Then suppose that, through no fault of your own, one day your brain state changes (divine intervention, mental illness, or benign reasons) and you discover a new belief (the "non-rational belief" of the title). This could be anything:
- You believe something benign ("you look bad in green shoes")
- You believe something religious; it is implied this contradicts at least some of your rational foundation
- You believe your should do something immoral (say, causing yourself or others harm)
- You believe your beliefs are (partially) wrong ("the rules of logic do not apply to subject XYZ")
(I did say "through no fault of your own" in order to keep things simpler, but there are ritualistic uses of mind altering drugs in some cultures that may have similar effects.)
How do you know whether to accept this new belief or not, especially in light of the fact that you already accept other new beliefs on some kind of rational/empirical basis?
At first glance, this looks like a rather trivial problem: don't accept contradicting beliefs (some benign and some religious beliefs would be allowed). But I think it would be possible to engineer a series of rather benign beliefs that end up leading to one of the other (irrational, immoral, or inconsistent) choices. If so, then which benign choices should be allowed, and which not? The ones that don't contradict your belief system at time X, or your belief system at time Y? And how to determine X and Y? etc.
Question: How do you decide what new beliefs can be accepted into an existing belief system?