Another example is what’s the probability that our physical constants are what they are, especially the constants that seem tuned to life?
The answer is if the constants are arbitrary real numbers, the answer is probability 0, and this applies no matter what number you pick.
This is how we can defuse the fine-tuning argument, that the cosmos’s constants have improbable values that seem tuned for life, since any other constant has probability 0, no matter whether it was able to sustain life or not:
I think anytime you say “what is the probability that”, as if it were an objective fact or measure, rather than an agent’s tool for prediction, framed as “what is this agent’s probability assignment over …”, you’re somewhat outside of a bayesean framework.
In my view, those are incomplete propositions—your probability assignment may be a convenience in making predictions, but it’s not directly updatable. Bayesean calculations are about how to predict evidence, and how to update on that evidence. “what is the chance that this decider can solve the halting program for this program in that timeframe” is something that can use evidence to update. likewise “what is the chance that I will measure this constant next week and have it off by more than 10% from last week”.
“What is true of the universe, in an unobservable way” is not really a question for Bayes-style probability calculations. That doesn’t keep agents from having beliefs, just that there’s no general mechanism for correctly making them better.
I’ll give 2 examples:
What’s the probability that the program you are given contains a solvable halting problem for your decider:
The answer is it has probability 1, but that doesn’t mean that we can extend the decider of the halting problem to cover all cases.
https://arxiv.org/abs/math/0504351
Another example is what’s the probability that our physical constants are what they are, especially the constants that seem tuned to life?
The answer is if the constants are arbitrary real numbers, the answer is probability 0, and this applies no matter what number you pick.
This is how we can defuse the fine-tuning argument, that the cosmos’s constants have improbable values that seem tuned for life, since any other constant has probability 0, no matter whether it was able to sustain life or not:
https://en.wikipedia.org/wiki/Fine-tuned_universe
I think anytime you say “what is the probability that”, as if it were an objective fact or measure, rather than an agent’s tool for prediction, framed as “what is this agent’s probability assignment over …”, you’re somewhat outside of a bayesean framework.
In my view, those are incomplete propositions—your probability assignment may be a convenience in making predictions, but it’s not directly updatable. Bayesean calculations are about how to predict evidence, and how to update on that evidence. “what is the chance that this decider can solve the halting program for this program in that timeframe” is something that can use evidence to update. likewise “what is the chance that I will measure this constant next week and have it off by more than 10% from last week”.
“What is true of the universe, in an unobservable way” is not really a question for Bayes-style probability calculations. That doesn’t keep agents from having beliefs, just that there’s no general mechanism for correctly making them better.