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:
On 11/21/2022 4:33 PM, Bruce Kellett wrote:
On Tue, Nov 22, 2022 at 11:08 AM Brent Meeker
<meekerbr...@gmail.com> wrote:
He's wrong that frequentism does not empirically support
probability statements. He goes off on a tangent by
referring to "other gamblers". Nothing in physics is
certain, yet Deutsch takes a bunch of definite assertions and
claims they alone are the real physics.
His critique of frequentism is just a recap of arguments that are
well known -- you cannot ground probability theory in
frequentism, or the idea that probabilities are nothing more than
ratios of long-run frequencies. Long-run frequencies might
approximate the probabilities, but they cannot be used to ground
probability theory -- for well known reasons. I agree that he
goes off on a number of irrelevant tangents, and he is wrong to
suppose that frequentism is a main-stream theory of
probability (at least, these days).
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.
Brent
Bruce
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