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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?

  • If it is a belief you already "accepted" it, or you do not actually believe it. What I think you are asking is when it is reasonable to upgrade such intuitively gained belief to the status of knowledge, or some such. The general answer is that such a belief has to be obtained through a "reliable process". Sense perception and logical inference are two such processes, general conditions are studied under what is called process reliabilism. – Conifold Nov 29 '18 at 20:44
  • The title asks how it is possible to accept such beliefs, the question at the bottom how do you decide what beliefs can be accepted. These are not the same question, and I don't really understand the second one. I typically don't decide what to believe. I investigate and think and come up with conclusions with some level of belief, which may or may not be justified and/or accurate. Sometimes the beliefs are to some extent from intuition. What do you mean by deciding? – David Thornley Nov 29 '18 at 21:15
  • Simply ask whether such a belief can even exist in the future. If your new belief cannot exist in the future, then your more philosophical question has already been answered for you. – EternalPropagation Nov 29 '18 at 23:38
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    @bread ahhhh, thanks, that was the kind of answer I was looking for – BurnsBA Nov 30 '18 at 1:02
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Denying the distinction between rational and emotional process, since the brain is all of one piece, one can immediately answer by analogy: In the same way you decide whether to be scared or not when you are scared.

The answer to that question is equally inaccessible, but at least we accept that it is inaccessible. We are tempted to imagine rationality has rules that are significantly different from all other emotional processes. And in that we are deluded by centuries of history.

The first reasonable answer is that once you are scared, you are already scared, and you aren't making any choices. But that evades the question, because you do decide, once you realize the fear is affecting you, whether it is consonant with your view of yourself: Is it the kind of fear you are not suppose to have to begin with? Is it the kind of fear that one should act on immediately? etc.

This same sort of process, accessing your values and expectations, naturally occurs when you discover that you are acting on new information. But it is not the same across individuals, and it is deeply historical, so it is unlikely to be the kind of thing over which one has conscious control.

The only answer that can really be given is the Existentialist one "As authentically as you are able."

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  • Perception is fallible and limited. Everybody knows about optical and other sensory illusions, and there are other things that could affect your perception (hunger, sickness, PMS, various emotional states). Plus, our senses are limited, you cannot see small details in the distance, ears hear only certain frequencies etc ...

  • Logic is limited by premises. While pure mathematical binary Boolean logic seemingly does not fail, some sneaky assumption could turn things upside down. Example : France was stronger then Russia in WW1. Russia was weakened by revolution and civil war after WW1. France was defeated in WW2. Therefore, Russia should fall even faster. Try to find an error in judgment ;)

  • It is almost impossible to prove/disapprove transcendental things. While your original question ("Do I look good/bad in green shoes?") could be answered with let's say psychological research, religious question (about the nature of God for example) are based on some presumptions that could not be verified using the perception.

With all of this combined, you cannot 100% accept as true your "rational" knowledge, and also you cannot 100% reject as wrong your "mystical" knowledge that is not compatible with your "rational" knowledge. When you start building your perfect knowledge bullet proof system :) , you will soon end up like René Descartes during his
First Meditation.

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