JQuinton mentioned that he uses this to argue about falsifiability. I’d like to hear that explained more. I think the >example is meant to show that a hypothesis that “can explain anything” (the 8 sided die), should lose probability if >we obtain evidence that is “better explained” by the more specific hypothesis (the 3′s only die).
Yes, that’s correct. The thing I was trying to illustrate is that some hypotheses are more falsifiable than others. A hypothesis that can explain too much data (e.g. a 1,000 sided die) would lose probability to a more restricted hypothesis like a 6 sided die if the numbers 1 − 6 are rolled. The compliment to that is if the numbers 7 − 1,000 are rolled this refutes the idea that the 6 sided die was rolled. Accounting for too much data and falsifiability are two sides of the same coin; explaining too much data tends towards unfalsfiability.
Yes, that’s correct. The thing I was trying to illustrate is that some hypotheses are more falsifiable than others. A hypothesis that can explain too much data (e.g. a 1,000 sided die) would lose probability to a more restricted hypothesis like a 6 sided die if the numbers 1 − 6 are rolled. The compliment to that is if the numbers 7 − 1,000 are rolled this refutes the idea that the 6 sided die was rolled. Accounting for too much data and falsifiability are two sides of the same coin; explaining too much data tends towards unfalsfiability.