This one of the beauties of my proposal, is that if we do not have to assign probabilities to possible universes, we don’t have to limit ourselves to an uncountable infinity.
Hmm. Seems like your caring-about measure should still sum to 1. If you’re just comparing two universes, all you need to know is their relative importance, but if you want to evaluate policies over the whole set of universes, you’re going to want a set of weights whose sum is bounded.
However, even if the multiverse is infinite, or not even a set, I as a finite mind can only look at finite pieces of it. My caring function looks at a small piece of the multiverse, because it cannot comprehend the whole thing. This is sad. However, it does not feel arbitrary to me. The caring function has limitations of finiteness, or limitations of set theory, but that is MY limit function. There is a big difference to me between me having a limited caring function, and thinking that the universe has built in a limited probability function.
I see. :) You can do that, and it’s psychologically plausible.
I’m old-school and still believe there’s some fact of the matter about what the multiverse is. Presumably this fact of the matter is representable analytically (though not necessarily by human minds). If we found a better mathematical way to capture this, presumably your limitations would expand and you would then care about more than you do now.
I’m old-school and still believe there’s some fact of the matter about what the multiverse is.
I enjoyed this sentence.
If we found a better mathematical way to capture this, presumably your limitations would expand and you would then care about more than you do now.
Only to a point! Suppose Coscott has a policy for accepting new math which applies a critical eye and only accepts things based on a consistent criteria. That is: if he would accept X upon inspection, then, he would not have accepted not-X via his inspection.
Then consider the “completion” of Coscott’s views; that is, the (presumably uncomputable) system which is Coscott in the limit of being taught arbitrarily many new math techniques.
Now apply Tarski’s Undefinability. We can construct a more powerful math which Coscott could never accept.
Therefore, if Coscott is a sufficiently careful mathematician, then his math powers seem to have ultimate limits already, rather than mere current limits.
On the other hand, if there is no such limit, because Coscott could accept either X or not-X for some X depending on which is presented to him first, then there is hope! A “stronger” teacher could show Coscott the way to the more powerful math. Yet, Coscott is also at risk of being misled.
Here’s a riddle: according to Coscott, is there any way Coscott could be mislead? Coscott has established that physical existence is meaningless to him; but is there mathematical truth beyond provability? Is there a branch of the multiverse in which the axiom of choice is true, and one where it is false? (It seems clear that there is a subset of the universe where the axiom of choice is true, and one where it is false, but I don’t think that’s what I mean...)
However, even if the multiverse is infinite, or not even a set, I as a finite mind can only look at finite pieces of it. My caring function looks at a small piece of the multiverse, because it cannot comprehend the whole thing.
Your limitation does not inherently prohibit you from having a caring function that looks at the entire multiverse. The constraint is on how complex the pattern of evaluation of the features of the multiverse can be.
Hmm. Seems like your caring-about measure should still sum to 1. If you’re just comparing two universes, all you need to know is their relative importance, but if you want to evaluate policies over the whole set of universes, you’re going to want a set of weights whose sum is bounded.
Great point.
However, even if the multiverse is infinite, or not even a set, I as a finite mind can only look at finite pieces of it. My caring function looks at a small piece of the multiverse, because it cannot comprehend the whole thing. This is sad. However, it does not feel arbitrary to me. The caring function has limitations of finiteness, or limitations of set theory, but that is MY limit function. There is a big difference to me between me having a limited caring function, and thinking that the universe has built in a limited probability function.
I see. :) You can do that, and it’s psychologically plausible.
I’m old-school and still believe there’s some fact of the matter about what the multiverse is. Presumably this fact of the matter is representable analytically (though not necessarily by human minds). If we found a better mathematical way to capture this, presumably your limitations would expand and you would then care about more than you do now.
I enjoyed this sentence.
Only to a point! Suppose Coscott has a policy for accepting new math which applies a critical eye and only accepts things based on a consistent criteria. That is: if he would accept X upon inspection, then, he would not have accepted not-X via his inspection.
Then consider the “completion” of Coscott’s views; that is, the (presumably uncomputable) system which is Coscott in the limit of being taught arbitrarily many new math techniques.
Now apply Tarski’s Undefinability. We can construct a more powerful math which Coscott could never accept.
Therefore, if Coscott is a sufficiently careful mathematician, then his math powers seem to have ultimate limits already, rather than mere current limits.
On the other hand, if there is no such limit, because Coscott could accept either X or not-X for some X depending on which is presented to him first, then there is hope! A “stronger” teacher could show Coscott the way to the more powerful math. Yet, Coscott is also at risk of being misled.
Here’s a riddle: according to Coscott, is there any way Coscott could be mislead? Coscott has established that physical existence is meaningless to him; but is there mathematical truth beyond provability? Is there a branch of the multiverse in which the axiom of choice is true, and one where it is false? (It seems clear that there is a subset of the universe where the axiom of choice is true, and one where it is false, but I don’t think that’s what I mean...)
What do you mean by “psychologically plausible?”
I mean it’s a plausible way to describe how people actually feel and make decisions when acting.
Your limitation does not inherently prohibit you from having a caring function that looks at the entire multiverse. The constraint is on how complex the pattern of evaluation of the features of the multiverse can be.
Fair enough. I was aware of that, but did not bother to write it out. Sorry.