Personal Observation: Beliefs that live at the extreme are most probably false.
In retrospect, this seems like an obvious fact, until one introspects and finds that one of our own beliefs is extreme, and hence has a higher chance of it being false. Now we have a bit of cognitive dissonance, which needs resolving.
I came to this conclusion (that extreme beliefs are generally false) from very simple observations: people, experts, sometimes have opposing views on their own fields. The divide became more apparent in "softer" sciences than in STEM.
I myself found I hold some extreme beliefs, and it's hard to do the resolving. In the end, I settled to go with the more logical choice (in my opinion), that any and all extreme beliefs are probably false.
Much to my surprise, while reading this article, I came upon a proof of the above statement (under some weak assumptions). That the stronger a belief is, the weaker it's probability.
Let me phrase the statement (in my words):
The stronger the assumption, the weaker its chances of being true.
As given in the article above:
The stronger a statement is, the greater the risk of falsehood.
As I said above, this statement has a proof! In theory, it's known as the Theorem of Conjunction of Costs Probability. In the formal language of probability, one can write it as:
p(A) > p(A ^ B)
Or the probability of A being true, will always be greater then the probability of A and B being true. The only exception, is when adding B has no effect on A, in which case we get:
p(A) = p(A ^ B)
Stronger, more extreme statements are the product of multiple underlying assumptions, and as we get more extreme, the number of underlying assumptions only increases. This, according to the above theorem tends to only make the extreme statement more and more unlikely, or increases it's risk of falsehood.
The proof follows from a simple rule of probability:
p(A) = p(A ^ ~B) + p(A ^ B)
Hence, if p(A ^ ~B) > 0, p(A) will always be greater, otherwise it'll be equal to p(A ^ B).