On Tue, Nov 22, 2022 at 12:44 PM Brent Meeker <meekerbr...@gmail.com> wrote:
> On 11/21/2022 4:38 PM, Bruce Kellett wrote: > > On Tue, Nov 22, 2022 at 11:35 AM Brent Meeker <meekerbr...@gmail.com> > wrote: > >> >> But frequencies are how we test probabilistic theories. >> > > Testing is not a theoretical grounding of the theory. > > > It's not the axiomatic ground of Kolmogorov's theory. But so what? We > tested Euclid's theory of geometry by making measurements which weren't in > his axioms. That doesn't mean Euclid's wasn't a good theory of geometry. > I can see Deutsch crossing off Pythagora's theorem saying, "No matter how > precise our instruments they only yield rational quantities!" Physics is > not mathematics and it's never going to have data to infinitely many > decimal places. That frequencies only yield rational number approximations > to Born rule predictions doesn't seem like a big deal to me. > What is a probability? We can't define it as a limiting frequency, since repeats of a sequence of measurements of a spin are going to give a range of answers for the frequency of spin-up, and this sequence converges to some limit only in probability. That is then circular -- probability is defined in terms of probability. Perhaps 'probability' is a primitive concept -- not definable in terms of anything physical. Nevertheless, like language, it is essential for our understanding of our experience of the world. 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTvbeVt-pv8LPNXwi0JnT-nUzH5R1Bxu5DEftDRvju9ZA%40mail.gmail.com.
