The use of null hypothesises is a pivotal tool for scientific endeavor and rational-skepticism in general. If you object to this practice, feel free to do so, but please note that what you’re objecting to is a necessary condition of the process of forming beliefs.
Yes, I am aware of how scientists use null hypotheses. But the null hypothesis is only a construct which exists in the context of significance testing, and significance testing does not reliably get accurate results when you measure small effect sizes, and also gives you different probabilities based on the same data depending on how you categorize that data; Eliezer already gave an example of this in one of the pages you linked earlier. The whole reason that people on this site in general have enthusiasm for Bayesian statistics is because we believe that they do better, as well as as it is possible to do.
The concept of a “null hypothesis,” as it is used in frequentist statistics, doesn’t even make sense in the context of a system where, as you have claimed, we cannot know that it is more likely that a coin will come up heads on the basis of it having come up heads the last hundred times you’ve flipped it.
I do not agree with the use of “justified knowledge” so ubiquitously. Furthermore, I have tried to establish a differentiation between belief claims and knowledge claims. The latter are categorically claims about “the territory”; the former are claims of approximation of “your map” to “the territory”.
If I say “it is raining out,” this is a claim about the territory, yes. If I say “I believe that it is raining out,” this is a claim about my map (and my map exists within, and is a part of, the territory, so it is also a claim “about the territory,” but not about the same part of the territory.)
But my claim about the territory is not certain to be correct. If I say “it is raining out, 99.99999% confidence,” which is the sort of thing I would mean when I say “it is raining out,” that means that I am saying that the territory probably agrees with this statement, but the information in my map does not allow me to have a higher confidence in the agreement than that.
Yes, I am aware of how scientists use null hypotheses. But the null hypothesis is only a construct which exists in the context of significance testing, and significance testing does not reliably get accurate results when you measure small effect sizes, and also gives you different probabilities based on the same data depending on how you categorize that data; Eliezer already gave an example of this in one of the pages you linked earlier. The whole reason that people on this site in general have enthusiasm for Bayesian statistics is because we believe that they do better, as well as as it is possible to do.
The concept of a “null hypothesis,” as it is used in frequentist statistics, doesn’t even make sense in the context of a system where, as you have claimed, we cannot know that it is more likely that a coin will come up heads on the basis of it having come up heads the last hundred times you’ve flipped it.
If I say “it is raining out,” this is a claim about the territory, yes. If I say “I believe that it is raining out,” this is a claim about my map (and my map exists within, and is a part of, the territory, so it is also a claim “about the territory,” but not about the same part of the territory.)
But my claim about the territory is not certain to be correct. If I say “it is raining out, 99.99999% confidence,” which is the sort of thing I would mean when I say “it is raining out,” that means that I am saying that the territory probably agrees with this statement, but the information in my map does not allow me to have a higher confidence in the agreement than that.