After Popper science isn't about establishing truth or the right hypothesis.
I am not familiar with Popper but I would agree anyway. I will be more careful with my terms. Would 'scientific fact' work though? I think it does but I am open to being corrected.
If you can do better than a random guess (the dart throwing monkey) than you have knowledge in the Bayesian sense.
[1] What if a rational assessment of inconclusive data weighs you towards the wrong direction. Wouldn't you then start doing worse than the dart throwing monkey?
There could be situations where you really don't know more than the dart throwing monkey and were it thus doesn't make sense to speak about probability but in most cases we know at least a little bit.
I would challenge your 'in most cases' statement. I would also challenge the contention that a little bit is better than nothing according to [1].
Would 'scientific fact' work though?
No. Everything in science is falsifiable and open to challenge.
[1] What if a rational assessment of inconclusive data weighs you towards the wrong direction.
It's certainly possible to be completely deceived by reality.
Whenever you act where an outcome matters to you, you will take the expected outcomes into account. Even if you say "I don't know" you still have to make decisions about what you do about an issue.
Maybe http://slatestarcodex.com/2013/08/06/on-first-looking-into-chapmans-pop-bayesianism/ ...
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