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So plausibility isn't the only dimension for assessing how "good" a belief is.
A or not A is a certainty. I'm trying to formally understand why that statement tells me nothing about anything.
The motivating practical problem came from this question,
"guess the rule governing the following sequence" 11, 31, 41, 61, 71, 101, 131, ...
I cried, "Ah the sequence is increasing!" With pride I looked into the back of the book and found the answer "primes ending in 1".
I'm trying to zone in on what I did wrong.
If I had said instead, the sequence is a list of numbers - that would be stupider, but well inline with my previous logic.
My first attempt at explaining my mistake, was by arguing "it's an increasing sequence" was actually less plausible then the real answer, since the real answer was making a much riskier claim. I think one can argue this without contradiction (the rule is either vague or specific, not both).
However, it's often easy to show whether some infinite product is analytic. Making the jump that the product evaluates to sin, in particular, requires more evidence. But in some qualitative sense, establishing that later goal is much better. My guess was that establishing the equivalence is a more specific claim, making it more valuable.
In my attempt to formalize this, I tried to show this was represented by the probabilities. This is clearly false.
What should I read to understand this problem more formerly, or more precisely? Should I look up formal definitions of evidence?