How do you measure the distance from false to true? I know there are standard metrics in various fields, such as engineering and statistics. Can anybody think of a few?

How do you measure the distance from false to true?
 
I know there are standard metrics in various fields, such as engineering and statistics.
 
Can anybody think of a few?
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I was reading a little about https://en.wikipedia.org/wiki/Gibbs_paradox yesterday again and then this came to mind today.
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Amazing responses. So many things touched upon. A few were in the range of my intention and many were not but fascinating just the same.I look forward to more answers and I’ll start providing a few samples of how I’m thinking. [and maybe I’ll take on a challenge to map a “closer to and further from true” from those examples that don’t fit neatly into my presuppositions.
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