On Friday, April 22, 2022 at 2:13:43 PM UTC+3 johnk...@gmail.com wrote: > On Thu, Apr 21, 2022 at 6:04 PM George Kahrimanis <geka...@gmail.com> > wrote: > > >> > Strictly speaking, zero information implies "undefined probability", > > > Sure, but[...] >
Sorry, but if it is undefined then there is no "but". You remind me of myself a few decades ago, when I was in love with Bayesian inference and I defended the use of artificial priors. Later I understood that BI is just a heuristic method, not sound inference (unless the prior is true). A flat prior, or probabilities 1/2 in this case, are only tools in a heuristisc method, not proper descriptions of ignorance. Anyway, my point in this example was only that probability is a very tricky subject. > For the instrumentalists among us (glad to have you, BTW): the question >> of interest to me is not about which way is best to derive probability from >> QM -- that would be a pointless discussion, > > > It would be pointless because we have known from experiment for nearly a > century that the best way to obtain probability from quantum mechanics is > to take the square of the absolute value of a particle's wave-function, > a.k.a. the Born rule. > Not only I do not argue with this, but I emphasise it: this is one of the ways in which QM appears "workable". But my point was to prepare the reader for a version of the Born rule concerning large samples only, instead of single outcomes. Surely the experimental evidence is from large samples; the probability for a single case is an extrapolation which is "a matter of course" for a certain way of thinking, but not technically obligatory. > > >> >The question is whether all of them beg the question, so that we have >> to think of a rational decision theory without probability. >> > > Even in the days before quantum mechanics, as soon as physicists started > thinking about thermodynamics they knew that a rational decision theory > without probability was not viable. > In my anwer to Brent (my previous message) I gave an example. > Although Everett's argument (whose improvement I have proposed) grants >> that in the long run (that is, large samples) the Born Rule is practically >> certain to apply, this is not technically the same as probability for each >> single outcome -- though I admit that it works the same, > > > I would argue that if X works the same as Y then technically X is Y. > Careful! You trimmed off the end of my sentence: "... it works the same, to trigger an instinctive impulse". Sorry for my sloppy syntax: I meant "it works the same, with regard to triggering an instinctive impulse". Noy always, not necessarily. Instead of "technically" you should have "practically", in the sense "a technical distinction without a practical difference". > > > for a RATIONAL decision theory this probability is not granted, > > > *IF* that's true *THEN* a RATIONAL man will consistently make predictions > about the outcome of an experiment that are inferior to the predictions > that an IRRATIONAL man would make. So there would be no point to > rationality or being "rational". *THEREFORE* I conclude that your above > statement is not true. > (I emphasised "rational" as opposed to an experimentally derived decision theory.) A good point, but I am an inadequate amateur in the subject you bring up. Surely it is more fun to be irrational, for a while at least, and we all do it. Besides, there is no point in being rational about taking an umbrella in the morrning, unless there are grave consequences to reckon with. Moreover, rationality is about organising certain basic irrational pursuits, typically thinkgs like security, food, sex, and entertainment; priorities are for to the agent to define. Not a black-or-white dichotomy, therefore. And I did not say that there are rational versus irrational predictions. My concern is about the interpretation of probability for a single outcome. If it is a matter of pleasure without any worrying consequences, then the irrational interpretation is fine, even from the rational point of view, At least we agree on the MWI! The other issues will be resolved, I hope. George K. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/e85c3c27-a813-4c25-a7b4-95104349e97dn%40googlegroups.com.
