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How do you differentiate between knowledge and belief?
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Belief is seeing that the light is green even when it isn't.
Knowledge is accepting that the light is red when it is.
Believing that the light is green will not help you when you get flattened by a truck. Knowing that the light is red will keep you from dying pointlessly.
Knowledge is the first step on the path to wisdom. Belief is delusion.
If you cannot demonstrate, or point to a demonstration, then all you can do is guess. You can make an educated guess based on other demonstrations, but if you cling to your guesswork as if it were demonstrated to be true, and you internalize your guesswork as part of your identity, and you refuse to let go of it when confronted with contradictory demonstrations, then you are a fool.
Your description makes belief sound like willful ignorance.
It sounds like the real challenge is knowing when you have enough information to convert your educated guess into full-blown knowledge
Maybe, maybe not. In the absence of evidence, belief may be harmless, though somewhat pointless in the sense of Hitchen's razor:
and Newton's flaming laser sword:
It certainly becomes willful ignorance if the believer avoids and/or actively rejects contradictory evidence.
The educated guess (hypothesis) becomes knowledge when it can be demonstrated by direct experiment rather than inferred/constructed from related knowledge. Also it's important that the educated guess be testable/disprovable somehow, at least in theory (Popper's falsifiability principle):
So, belief is benign when it exists in an untested/untestable area and the believer is not bound to the belief emotionally. Belief is malignant when it exists in a tested area or when the believer clings to the belief emotionally. Belief is either harmless or extremely damaging, but in either case of no practical value.