I am confused how you got to the point of writing such a thoroughly detailed analysis of the application of the math of infinities to ethics while (from my perspective) strawmanning finitism by addressing only ultrafinitism. “Infinities aren’t a thing” is only a “dicey game” if the probability of finitism is less than 100% :). In particular, there’s an important distinction between being able to reference the “largest number + 1″ and write it down versus referencing it as a symbol as we do, because in our referencing of it as a symbol, in the original frame, it can be encoded as a small number.
Another easy way to just dismiss the question of infinite ethics that I feel you overlooked is that you can assign zero probability to our choice of mathematical axioms is exactly correct about the nature of infinities (or even probabilities).
You’ll notice that both of these examples correspond to absolute certainty, and that one may object that I am “not being open minded” or something like that for having infinitely trapped priors. However, I would remind readers that you cannot chose all of your beliefs and that, practically, understanding your own beliefs can be more important than changing (or being able to change) them. We can play word games regarding infinities, but will you put your life at stake? Or will your body reject the attempts of your confused mind when the situation and threats at hand are visible?
I would also like to directly claim, regardless of the truth of aforementioned claims, that entities and actions beyond the cosmic horizon of our observable universe are forfeit for consideration of ethics (and only once they are past that horizon). In particular, I dislike that your argument relies on the notion that cosmologists believe that the universe is infinite, while cosmologist will also definitely tell you that things beyond the cosmological horizon are outside of causal influence. Your appeal to logos only to later reject it in your favor is inconsistent and unpalatable to me.
I also am generally under the impression that a post like this should be classified as a cognitohazard, as I am under the impression that the post will cause net harm under the premise that it attempts to update people in the direction of susceptibility to arguments of the nature of Pascal’s Wager.
I’m sorry if I’m coming off as harsh. In particular, I know from reading your posts that I think you generally contribute positively and I have enjoyed much of your content. However, I am under the impression that this post is likely a net negative, and directly conflicting against the proposition that we “help our species make it to a wise and empowered future” because I think that this contributes towards misleading our species. I have found myself, and obviously others may find otherwise, that as far as I can tell there is ingrained in my experience of consciousness itself that assigns zero probability to our choice of axioms as being literally entirely correct (the map is not the territory). I also claim that regardless of the supposed “actual truth” of the existence of infinities in ethics, that a practical standpoint suggests that you should definitely reject the idea, as I believe practically having any modicum of belief is more likely to lead you astray and likely to perform worse in exceptional case that our range of causal influence is “actually infinite” though clearly this is not something I can prove.
I don’t understand or disagree with a lot in your comment, but I don’t think I’d say much different from Joe. However, my meta-level principles say I should respond to
I also am generally under the impression that a post like this should be classified as a cognitohazard, as I am under the impression that the post will cause net harm under the premise that it attempts to update people in the direction of susceptibility to arguments of the nature of Pascal’s Wager.
I disagree for two independently dispositive reasons:
I think that if anything, readers would update in the opposite direction, realizing that the bullets to utility-maximizing are harder to swallow than they thought. Joe shows that infinity makes decision theory really weird, making it more appealing (on the margin) to just do prosaic stuff. (I’m relatively fanatical, but I would be much more fanatical and much more comfortable in my fanaticism if not for issues Joe mentions.) And Joe doesn’t advocate, e.g., pressing the red button here, and his last section has good nuanced discussion of this in practice.
Discussions related to this topic have expected benefits in figuring out how to deal with Pascal’s Wager/Mugging outweighing expected costs (if they existed) in individuals making worse decisions (and this “expectation” is robust to non-fanaticism, or something).
I am confused how you got to the point of writing such a thoroughly detailed analysis of the application of the math of infinities to ethics while (from my perspective) strawmanning finitism by addressing only ultrafinitism. “Infinities aren’t a thing” is only a “dicey game” if the probability of finitism is less than 100% :). In particular, there’s an important distinction between being able to reference the “largest number + 1″ and write it down versus referencing it as a symbol as we do, because in our referencing of it as a symbol, in the original frame, it can be encoded as a small number.
Another easy way to just dismiss the question of infinite ethics that I feel you overlooked is that you can assign zero probability to our choice of mathematical axioms is exactly correct about the nature of infinities (or even probabilities).
You’ll notice that both of these examples correspond to absolute certainty, and that one may object that I am “not being open minded” or something like that for having infinitely trapped priors. However, I would remind readers that you cannot chose all of your beliefs and that, practically, understanding your own beliefs can be more important than changing (or being able to change) them. We can play word games regarding infinities, but will you put your life at stake? Or will your body reject the attempts of your confused mind when the situation and threats at hand are visible?
I would also like to directly claim, regardless of the truth of aforementioned claims, that entities and actions beyond the cosmic horizon of our observable universe are forfeit for consideration of ethics (and only once they are past that horizon). In particular, I dislike that your argument relies on the notion that cosmologists believe that the universe is infinite, while cosmologist will also definitely tell you that things beyond the cosmological horizon are outside of causal influence. Your appeal to logos only to later reject it in your favor is inconsistent and unpalatable to me.
I also am generally under the impression that a post like this should be classified as a cognitohazard, as I am under the impression that the post will cause net harm under the premise that it attempts to update people in the direction of susceptibility to arguments of the nature of Pascal’s Wager.
I’m sorry if I’m coming off as harsh. In particular, I know from reading your posts that I think you generally contribute positively and I have enjoyed much of your content. However, I am under the impression that this post is likely a net negative, and directly conflicting against the proposition that we “help our species make it to a wise and empowered future” because I think that this contributes towards misleading our species. I have found myself, and obviously others may find otherwise, that as far as I can tell there is ingrained in my experience of consciousness itself that assigns zero probability to our choice of axioms as being literally entirely correct (the map is not the territory). I also claim that regardless of the supposed “actual truth” of the existence of infinities in ethics, that a practical standpoint suggests that you should definitely reject the idea, as I believe practically having any modicum of belief is more likely to lead you astray and likely to perform worse in exceptional case that our range of causal influence is “actually infinite” though clearly this is not something I can prove.
I don’t understand or disagree with a lot in your comment, but I don’t think I’d say much different from Joe. However, my meta-level principles say I should respond to
I disagree for two independently dispositive reasons:
I think that if anything, readers would update in the opposite direction, realizing that the bullets to utility-maximizing are harder to swallow than they thought. Joe shows that infinity makes decision theory really weird, making it more appealing (on the margin) to just do prosaic stuff. (I’m relatively fanatical, but I would be much more fanatical and much more comfortable in my fanaticism if not for issues Joe mentions.) And Joe doesn’t advocate, e.g., pressing the red button here, and his last section has good nuanced discussion of this in practice.
Discussions related to this topic have expected benefits in figuring out how to deal with Pascal’s Wager/Mugging outweighing expected costs (if they existed) in individuals making worse decisions (and this “expectation” is robust to non-fanaticism, or something).