Thanks Hal. I add that your link provide a way to recover my old conversation with Joel Dobrzelewski on the list (28 June 2001), which presents the simplest version of the Universal Dovetelair Argument (UDA), i.e. the argument showing that the computationalist hypothesis (in the bio/psycho/theo/-logical sciences) entails that physics is ultimately a branch of machine bio/psycho/theo/-logy. In particular it shows that physics can be presented as a probability or credibility measure on the relative computational histories (which are computation as seen from some first person perspective). The argument is presented in a step by step way, and begins here: http://email@example.com/msg01274.html You can then follow the step by clicking on the right arrow next "date", and skipping the many threads we were discussing simultaneously at that time. People interested can ask questions. Note that the lobian interview does not necessitate the understanding of the UDA, but this one provides the basic motivation for some of the Theaetetical variants of the modal logic G and G*. Bruno
I've had this question brewing for some time while I've been pondering the UDA. So now I've gone through the above thread and I still didn't find the answer to it.
In the UDA it is said that the Correct Level Of Substitution (I'll call is CLOS for short) is unknowable. I agree: Just intuitively, in a closed system, how could we know if something wasn't exactly right? It would result in the future being different than it would have been, but we wouldn't be aware of the difference. We would just accept that as reality.
Since the CLOS is unknowable, then we should be able to talk about an unknowable, yet true, probability P(CLOS) that each substitution is done at the CLOS. By the way, we know at least P(CLOS) < 1 because the doctor is guessing, and P(CLOS) = 1 would implies that the doctor knows and can actually implement it. But in fact I'd say that we really don't have any lower bound for P(CLOS), but that fact is beside the point I want to make.
OK, so now for my question. So when we talk about finding a probability measure on the 1-determinancy (I don't know if that's the exact right words), don't we have to multiply this probability measure by the unknown P(CLOS) to get the actual probability measure? But this would imply that the probability measure is impossible to find out to any degree that would be called scientific, since it is a function of P(CLOS), i.e. the step of faith in saying "Yes" to the doctor who doesn't know anything.
In fact, if each moment is equivalent to a substitution (not necessarily at the CLOS!), as comp says, then there would be an exponential decay of our identity, as sort of identity entropy.