Hi Vaden, thanks again for posting this! Great to see this discussion. I wanted to get further along C&R before replying, but:
no laws of physics are being violated with the scenario “someone shouts the natural number i”. This is why this establishes a one-to-one correspondence between the set of future possibilities and the natural numbers
If we’re assuming that time is finite and quantized, then wouldn’t these assumptions (or, alternatively, finite time + the speed of light) imply a finite upper bound on how many syllables someone can shout before the end of the universe (and therefore a finite upper bound on the size of the set of shoutable numbers)? I thought Isaac was making this point; not that it’s physically impossible to shout all natural numbers sequentially, but that it’s physically impossible to shout any of the natural numbers (except for a finite subset).
(Although this may not be crucial, since I think you can still validly make the point that Bayesians don’t have the option of, say, totally ruling out faster-than-light number-pronunciation as absurd.)
Note also that EV style reasoning is only really popular in this community. No other community of researchers reasons in this way, and they’re able to make decisions just fine.
Are they? I had the impression that most communities of researchers are more interested in finding interesting truths than in making decisions, while most communities of decision makers severely neglect large-scale problems. (Maybe there’s better ways to account for scope than EV, but I’d hesitate to look for them in conventional decision making.)
Hi Vaden, thanks again for posting this! Great to see this discussion. I wanted to get further along C&R before replying, but:
If we’re assuming that time is finite and quantized, then wouldn’t these assumptions (or, alternatively, finite time + the speed of light) imply a finite upper bound on how many syllables someone can shout before the end of the universe (and therefore a finite upper bound on the size of the set of shoutable numbers)? I thought Isaac was making this point; not that it’s physically impossible to shout all natural numbers sequentially, but that it’s physically impossible to shout any of the natural numbers (except for a finite subset).
(Although this may not be crucial, since I think you can still validly make the point that Bayesians don’t have the option of, say, totally ruling out faster-than-light number-pronunciation as absurd.)
Are they? I had the impression that most communities of researchers are more interested in finding interesting truths than in making decisions, while most communities of decision makers severely neglect large-scale problems. (Maybe there’s better ways to account for scope than EV, but I’d hesitate to look for them in conventional decision making.)