1. Non-indexical conditioning is not “a way to do probability theory”; it is just a policy of not throwing out any data, even data that appears irrelevant.
2. No, you do not usually do probability theory on centered propositions such as “today is Monday”, as they are not legitimate propositions in classical logic. The propositions of classical logic are timeless—they are true, or they are false, but they do not change from one to the other.
3. Nowhere in the analysis do I treat a data point as “there exists a version of me which has received this data...”; the concept of “a version of me” does not even appear in the discussion. If you are quibbling over the fact that Pdt is only the stream of perceptions Beauty remembers experiencing as of time t, instead of being the entire stream of perceptions up to time t, then you can suppose that Beauty has perfect memory. This simplifies things—we can now let Pd simply be the entire sequence of perceptions Beauty experiences over the course of the day, and define R(y,d) to mean ”y is the first n elements of Pd, for some n“—but it does not alter the analysis.
Nowhere in the analysis do I treat a data point as “there exists a version of me which has received this data...”;
This confuses me. Dacyn’s “There exists a version of me which has received this data as well as all of the prior data I have received” seems equivalent to Neal’s “I will here consider what happens if you ignore such indexical information, conditioning only on the fact that someone in the universe with your memories exists. I refer to this procedure as “Full Non-indexical Conditioning” (FNC).” (Section 2.3 of Neal2007)
Do you think Dacyn is saying something different from Neal? Or that you are saying something different from both Dacyn and Neal? Or something else?
None of this is about “versions of me”; it’s about identifying what information you actually have and using that to make inferences. If the FNIC approach is wrong, then tell me what how Beauty’s actual state of information differs from what is used in the analysis; don’t just say, “it seems really odd.”
I responded to #2 below, and #1 seems to be just a restatement of your other points, so I’ll respond to #3 here. You seem to be taking what I wrote a little too literally. It looks like you want the proposition Sleeping Beauty conditions on to be “on some day, Sleeping Beauty has received / is receiving / will receive the data X”, where X is the data that she has just received. (If this is not what you think she should condition on, then I think you should try to write the proposition you think she should condition on, using English and not mathematical symbols.) This proposition doesn’t have any reference to “a version of me”, but it seems to me to be morally the same as what I wrote (and in particular, I still think that it is really odd to say that that it is the proposition she should condition on, and that more motivation is needed for it).
There are several misconceptions here:
1. Non-indexical conditioning is not “a way to do probability theory”; it is just a policy of not throwing out any data, even data that appears irrelevant.
2. No, you do not usually do probability theory on centered propositions such as “today is Monday”, as they are not legitimate propositions in classical logic. The propositions of classical logic are timeless—they are true, or they are false, but they do not change from one to the other.
3. Nowhere in the analysis do I treat a data point as “there exists a version of me which has received this data...”; the concept of “a version of me” does not even appear in the discussion. If you are quibbling over the fact that Pdt is only the stream of perceptions Beauty remembers experiencing as of time t, instead of being the entire stream of perceptions up to time t, then you can suppose that Beauty has perfect memory. This simplifies things—we can now let Pd simply be the entire sequence of perceptions Beauty experiences over the course of the day, and define R(y,d) to mean ”y is the first n elements of Pd, for some n“—but it does not alter the analysis.
This confuses me. Dacyn’s “There exists a version of me which has received this data as well as all of the prior data I have received” seems equivalent to Neal’s “I will here consider what happens if you ignore such indexical information, conditioning only on the fact that someone in the universe with your memories exists. I refer to this procedure as “Full Non-indexical Conditioning” (FNC).” (Section 2.3 of Neal2007)
Do you think Dacyn is saying something different from Neal? Or that you are saying something different from both Dacyn and Neal? Or something else?
None of this is about “versions of me”; it’s about identifying what information you actually have and using that to make inferences. If the FNIC approach is wrong, then tell me what how Beauty’s actual state of information differs from what is used in the analysis; don’t just say, “it seems really odd.”
I responded to #2 below, and #1 seems to be just a restatement of your other points, so I’ll respond to #3 here. You seem to be taking what I wrote a little too literally. It looks like you want the proposition Sleeping Beauty conditions on to be “on some day, Sleeping Beauty has received / is receiving / will receive the data X”, where X is the data that she has just received. (If this is not what you think she should condition on, then I think you should try to write the proposition you think she should condition on, using English and not mathematical symbols.) This proposition doesn’t have any reference to “a version of me”, but it seems to me to be morally the same as what I wrote (and in particular, I still think that it is really odd to say that that it is the proposition she should condition on, and that more motivation is needed for it).