However, your P1 statement already implies the most important parts of K1 and K2; as just by inserting the adjective “hundred-sided” into P1 loads it with this knowledge.
I disagree.
For example, I can confirm that something is a hundred-sided die by the expedient of counting its sides. But if a known conman bets me $1000 that P1 is false, I will want to do more than count the sides of the die before I take that bet. (For example, I will want to roll it a few times to ensure it’s not loaded.) That suggests that there are important facts in K2 other than the definition of a hundred-sided die (e.g., whether the die is fair, whether the speaker is a known conman, etc.) that factor into my judgment of P1.
In other words, your probability estimate in the dice analogy is only high confidence because of the confidence in understanding how dice work, and that the object in question actually is a hundred sided die.
And a bunch of other things, as above. Which is why I mentioned K1 and K2 in the first place.
...your probability estimate in the dice analogy is only high confidence …
Wait, what?
First, nowhere in here have I made a probability estimate. I’ve made a prediction about what will happen on the next roll of this die. You are inferring that i made that prediction on the basis of a probability estimate, and you admittedly have good reasons to infer that.
Second… are you now saying that I can be confident in P1? Because when I asked you that in the first place you answered no. I suspect I’ve misunderstood you somewhere.
First, nowhere in here have I made a probability estimate. I’ve made a prediction about what will happen on the next roll of this die. You are inferring that i made that prediction on the basis of a probability estimate, and you admittedly have good reasons to infer that.
Yes. I have explained (in some amount of detail) what I mean by confidence, such that it is distinct from probability, as relates to prediction.
And yes, as a human you are in fact constrained (in practice) to making predictions based on internal probability estimates (based on my understanding of neuroscience).
Confidence, like probability, is not binary.
You can have fairly high confidence in the implied probability of P1 given K1 and K2, and likewise little confidence in a probability estimate of P1 in the case of a die of unknown dimension—this should be straightforward.
Second… are you now saying that I can be confident in P1? Because when I asked you that in the first place you answered no. I suspect I’ve misunderstood you somewhere.
Yes, and the mistake is on my part: wow that first comment was a partial brainfart. I was agreeing with you, and meant to say yes but … I’ll edit in a comment to that effect.
I disagree.
For example, I can confirm that something is a hundred-sided die by the expedient of counting its sides.
But if a known conman bets me $1000 that P1 is false, I will want to do more than count the sides of the die before I take that bet. (For example, I will want to roll it a few times to ensure it’s not loaded.)
That suggests that there are important facts in K2 other than the definition of a hundred-sided die (e.g., whether the die is fair, whether the speaker is a known conman, etc.) that factor into my judgment of P1.
And a bunch of other things, as above. Which is why I mentioned K1 and K2 in the first place.
Wait, what?
First, nowhere in here have I made a probability estimate. I’ve made a prediction about what will happen on the next roll of this die. You are inferring that i made that prediction on the basis of a probability estimate, and you admittedly have good reasons to infer that.
Second… are you now saying that I can be confident in P1? Because when I asked you that in the first place you answered no. I suspect I’ve misunderstood you somewhere.
Yes. I have explained (in some amount of detail) what I mean by confidence, such that it is distinct from probability, as relates to prediction.
And yes, as a human you are in fact constrained (in practice) to making predictions based on internal probability estimates (based on my understanding of neuroscience).
Confidence, like probability, is not binary.
You can have fairly high confidence in the implied probability of P1 given K1 and K2, and likewise little confidence in a probability estimate of P1 in the case of a die of unknown dimension—this should be straightforward.
Yes, and the mistake is on my part: wow that first comment was a partial brainfart. I was agreeing with you, and meant to say yes but … I’ll edit in a comment to that effect.
Ah!
I feel much better now.
I should go through this discussion again and re-evaluate what I think you’re saying based on that clarification before I try to reply .