On Tue, Nov 22, 2022 at 12:44 PM Brent Meeker <[email protected]> wrote:
> On 11/21/2022 4:38 PM, Bruce Kellett wrote: > > On Tue, Nov 22, 2022 at 11:35 AM Brent Meeker <[email protected]> > 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTvbeVt-pv8LPNXwi0JnT-nUzH5R1Bxu5DEftDRvju9ZA%40mail.gmail.com.
