The probability is the prior times the evidence ratio, so the higher the prior probability, the less evidence you need. If there’s a lottery with one million numbers, and you have no evidence for anything, you’ll think there’s a 0.0001% chance of it getting 839772 exactly, a 50% chance of it getting 500000 or less, and a 99.9999% chance of it getting something other than 839772. Thus, you can be pretty sure it won’t land on 839772 even without evidence.
The ultimate prior is maximum entropy, aka “idk”, aka “50/50: either happens or not”. We never actually have it, because we start gathering evidence for how the world is before our brains even form enough to make any links between it.
That prior doesn’t work when there is a countable number of hypotheses, aka “I’ve picked a number from {0,1,2,...}. Which?” or “Given that the laws of physics can be described by a computer program, which?”.
Your knowledge of the rules of probability is evidence. It’s not evidence specific to this question, but it is evidence for this question, among others.
The probability is the prior times the evidence ratio, so the higher the prior probability, the less evidence you need. If there’s a lottery with one million numbers, and you have no evidence for anything, you’ll think there’s a 0.0001% chance of it getting 839772 exactly, a 50% chance of it getting 500000 or less, and a 99.9999% chance of it getting something other than 839772. Thus, you can be pretty sure it won’t land on 839772 even without evidence.
I think knowing a prior constitutes evidence. If you know that the lottery has one million numbers, that is a piece of evidence.
You need a prior to take evidence into account. If the prior is evidence, then what is the prior?
Hm… You make a good point. I’m not sure I understand this conceptually well enough to have any sort of coherent response.
The ultimate prior is maximum entropy, aka “idk”, aka “50/50: either happens or not”. We never actually have it, because we start gathering evidence for how the world is before our brains even form enough to make any links between it.
That prior doesn’t work when there is a countable number of hypotheses, aka “I’ve picked a number from {0,1,2,...}. Which?” or “Given that the laws of physics can be described by a computer program, which?”.
Your knowledge of the rules of probability is evidence. It’s not evidence specific to this question, but it is evidence for this question, among others.