some sort of implication by suggesting bets that has some sort of negative connotation that I’m not picking up
That you don’t think the other party is capable of marshaling arguments to make you update, or of updating on your arguments.
What is your reasoning behind this conclusion?
An estimate of how much progress is made on this sort of problem per man-hour, and of how many man-hours will be devoted to the problem in the next ten years. But I am simply agnostic about whether or not a contradiction can be found “in principle.”
some sort of implication by suggesting bets that has some sort of negative connotation that I’m not picking up
That you don’t think the other party is capable of marshaling arguments to make you update, or of updating on your arguments.
The LW community probably considers betting on a disputed proposition to be much more normal, natural, and non-confrontational than most people do. This is likely because of our Overcoming Bias heritage and Robin Hanson’s work on prediction markets. Betting seems like a good quick way to get people to publicly quantify the probabilities that they assign to propositions. And this, ideally, could help the disputants approach Aumann agreement more quickly.
That you don’t think the other party is capable of marshaling arguments to make you update, or of updating on your arguments.
Ah, I see. That’s not an intended implication. I prefer constructing bets because it forces one (myself) to think carefully about how confident I actually am for a claim. But I see how one might think that.
An estimate of how much progress is made on this sort of problem per man-hour, and of how many man-hours will be devoted to the problem in the next ten years.
Ah, that makes a lot of sense.
But I am simply agnostic about whether or not a contradiction can be found “in principle.”
That make a lot of sense. Presumably this issue is connected to the problem that no one seems to have any idea how one would go about finding such a contradiction.
Incidentally, seriously thinking about these sorts of issues brings up strange issues of equiconsistency. I’m particularly now wondering about the equiconsistency statuses of Robinson arithmetic, the arithmetic hierarchy and, and PA. I don’t know of any result that says something morally like contradictions in PA can be imported into contradictions in Robinson arithmetic (or some extension via the arithmetic hierarchy), but this is pushing the bounds of my knowledge on these issues. Does anyone know if there are any results of that flavor or results in the other direction?
That you don’t think the other party is capable of marshaling arguments to make you update, or of updating on your arguments.
An estimate of how much progress is made on this sort of problem per man-hour, and of how many man-hours will be devoted to the problem in the next ten years. But I am simply agnostic about whether or not a contradiction can be found “in principle.”
The LW community probably considers betting on a disputed proposition to be much more normal, natural, and non-confrontational than most people do. This is likely because of our Overcoming Bias heritage and Robin Hanson’s work on prediction markets. Betting seems like a good quick way to get people to publicly quantify the probabilities that they assign to propositions. And this, ideally, could help the disputants approach Aumann agreement more quickly.
Ah, I see. That’s not an intended implication. I prefer constructing bets because it forces one (myself) to think carefully about how confident I actually am for a claim. But I see how one might think that.
Ah, that makes a lot of sense.
That make a lot of sense. Presumably this issue is connected to the problem that no one seems to have any idea how one would go about finding such a contradiction.
Incidentally, seriously thinking about these sorts of issues brings up strange issues of equiconsistency. I’m particularly now wondering about the equiconsistency statuses of Robinson arithmetic, the arithmetic hierarchy and, and PA. I don’t know of any result that says something morally like contradictions in PA can be imported into contradictions in Robinson arithmetic (or some extension via the arithmetic hierarchy), but this is pushing the bounds of my knowledge on these issues. Does anyone know if there are any results of that flavor or results in the other direction?