In many discussions I'm pulled back to the distinction between not-guilty and innocent as a way to demonstrate how the burden of proof works and what the true default position should be in any given argument. A lot of people seem to not have any problem seeing the distinction, but many intelligent people for some reason don't see it.
In this article I explain why the distinction exists and why it matters, in particular why it matters in real-life scenarios, especially when people try to shift the burden of proof.
Essentially, in my view the universe we are talking about is {uncertain,guilty,innocent}, therefore not-guilty is guilty', which is {uncertain,innocent}. Therefore innocent ⇒ not-guilty, but not-guilty ⇏ innocent.
When O. J. Simpson was acquitted, that doesn’t mean he was found innocent, it means the prosecution could not prove his guilt beyond reasonable doubt. He was found not-guilty, which is not the same as innocent. It very well could be that the jury found the truth of the matter uncertain.
This notion has implications in many real-life scenarios when people want to shift the burden of proof if you reject a claim when it's not substantiated. They wrongly assume you claim their claim is false (equivalent to innocent), when in truth all you are doing is staying in the default position (uncertain).
Rejecting the claim that a god exists is not the same as claim a god doesn't exist: it doesn't require a burden of proof because it's the default position. Agnosticism is the default position. The burden of proof is on the people making the claim.
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Notes -
0/0: 0.5±∞
5/5: 0.5±0.034
50/50: 0.5±0.003
5000/5000: 0.5±0.000
If I ask for the probability that Putin is dead tomorrow, I'd say that fixes the date. You don't move "tomorrow" along with you so it never arrives. After the next coin flip happened, it either was heads or it wasn't, there's nothing left.
There is that word "probability" in the question, so of course how one interprets that word changes the question. If you disagree, give an argument. Instead, you are just repeating that your way of interpreting the word is the only way. I'd ask you to rephrase the question without using the words "the probability/chances/odds" or any such synonym. Then ask how a Bayesian would answer that version of the question, and see if the disagreement persists.
I know the definitions of probability, I know what probability is according to a Bayesian, I know what a likelihood function is, and I know what the actual probability of this example is, because I wrote a computer simulation with the actual probability embedded in it.
You are just avoiding the facts.
You know what probability is according to a Bayesian, and you think they are factually wrong. The rest of of the problems stem from that. I'd suggest at least you focus your arguments to why you think they are objectively wrong. Instead, you inject your understanding of probability into their statements and conclude factually wrong things like how they don't consider uncertainty when they do.
Then a Bayesian would be willing to answer the question of what your that parameter you embedded in your simulation is, with answers like beta(51,51).
That is not what I'm saying.
False. You know what they answer, and it's a single number.
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