On Tue, Nov 22, 2022 at 3:57 PM Jesse Mazer <[email protected]> wrote:
> What about the idea of grounding the notion of probability in terms of the > frequency in the limit of a hypothetical infinite series of trials, what > philosophers call "hypothetical frequentism"? The Stanford Encyclopedia of > Philosophy discussion of this at > https://plato.stanford.edu/entries/probability-interpret/#FreInt notes > the objection that the limit depends on the order we count the trials, but > it seems pretty natural to use temporal ordering in this case. Aside from > the philosophical objection that we don't have any clear a priori > justification for privileging temporal ordering in this way, are there any > objections of a more technical nature to hypothetical frequentism with > temporal ordering (scenarios where it would give you a different answer > from standard probability theory), or are the objections purely > philosophical? > The standard trouble with the hypothetical infinite series of trials is that we have to define the probability in terms of subsequences, since we can't actually realize an infinite series. In order for these subsequences to give (approximately) the same probability as the hypothetical infinite series, the subsequences have to be "typical", and "typical" can only be defined probabilistically, so we are back with the problem of circularity. Temporal ordering of the sequence is also somewhat arbitrary, since if we order a series of coin tosses according to magnitude (heads = 0, tails = 1), then most subsequences will not be "typical" and will give spurious results. Temporal ordering implies that we have actually completed an infinite series of tosses, and that is never possible. We then have to assume that the first N trials form a "typical" subset, and how do you ever justify that? Bruce -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQSx91DMcoNZfcGVWwJ_gMBd1pv2Xk%3DgBYQ3eij_owcvg%40mail.gmail.com.
