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Well, if faith in axioms is a negligible issue (because the probability distribution is so tight) then perhaps we should address common unscientific behavior of "scientists". Consider how many scientists in recent centuries would have bet their life savings that:
The Sun moves around the Earth
There aren't any tiny animals in a drop of pond water
Doctors washing their hands between patients is crackpottery
Space-time is Euclidean
A physics student presenting something like superposition to his professor should be kicked out of the school.
The question is, were these scientists guilty of something, or not? At the time, the scientists would have insisted these things were axioms with a very narrow probability distribution. Certainly the probability distribution widened when new information became available, but that new and extremely important information was greatly delayed by their faith in those axioms of admittedly narrow probability distribution. Part of the scientific method is learning from experience how to improve the scientific method. Let's learn from these mistakes that we should always spend at least a little time (not too much) on questioning whether 2+2 really does equal 4.
The Sun moves around the Earth
There aren't any tiny animals in a drop of pond water
Doctors washing their hands between patients is crackpottery
Space-time is Euclidean
A physics student presenting something like superposition to his professor should be kicked out of the school.
The question is, were these scientists guilty of something, or not? At the time, the scientists would have insisted these things were axioms with a very narrow probability distribution. Certainly the probability distribution widened when new information became available, but that new and extremely important information was greatly delayed by their faith in those axioms of admittedly narrow probability distribution. Part of the scientific method is learning from experience how to improve the scientific method. Let's learn from these mistakes that we should always spend at least a little time (not too much) on questioning whether 2+2 really does equal 4.