Clearly, since he died in April. And yet, if I'm not mistaken, he spoke out
against the view of QM uncertainties as being due to fundamental physical
uncertainties even when he was a "practicing physicist."
Also, we may be talking past each other a bit here. You speak as if the only
alternative views of probabilities are
1) some very subjective, vague "degree of belief"; or
2) an actual physical property.
But I don't think that the process of taking the incomplete, objective
information you have, and turning it into a probability distribution, can
reasonably be characterized as a "degree of belief". When you use the
macroscopic properties of a physical system to derive a probability
distribution over the states of the individual particles in a system, you are
not specifying some vague degree of belief; you are instead carefully encoding
the objective facts you do have available.
In my view, "degree of belief" probabilities are a fallback, something you use
when you have information (such as accumulated experience and expertise) that
you can't make explicit, or when you lack the time, mathematical tools, or
competence to do a proper job of turning the information you have into
probabilities.
> There is no dispute that the
> probabilities in quantum mechanics are objective.
Note that probabilities can be "objective" -- derived via an objective process
from the available information -- without being fundamental physical
properties and examples of indeterminacy in physical systems.
> Especially in light
> of Bell's theorems (which you should read, by the way).
I'd be happy to, if you would help me out by suggesting some specific papers,
books, or articles to read.
> >>>
> even if QM does in fact exhibit physical probabilities, this would
> be of little practical importance in most statistical problems, in
> which QM effects are negligible, and the physics of the situation is,
> to a high degree of accuracy, entirely deterministic.
> >>>
>
> [...] Do you
> happen to know what field of physics is responsible for the phenomena
> behind transistors? [...] do
> you happen to know what field of physics is responsible for the
> interplay between photons and the rods and cones in your retina?
Of course I do. I'm not suggesting that quantum effects are not important.
But quantum uncertainties don't often translate into any significant degree of
macroscopic uncertainty for the working engineer. For example, until the
scale gets very small, the *macroscopic* behavior of a transistor can be quite
accurately described via deterministic equations, and these deterministic
equations are what practicing engineers use in designing electronic circuits.
Furthermore, you'll note that I was specifically talking about statistical
problems. Where in the world do quantum uncertainties figure in predicting a
company's revenue over the next year, recognizing text or speech, or detecting
credit-card fraud?
> In any case, the important point is not whether the universe is based
> on objective probabilities, but that it *could be* and still be fully
> self-consistent mathematically.
Why is this the "important point"? Even if the universe does have objective,
physical probabilities at some level, this is of little practical importance
when you are dealing with a problem where this purported fundamental physical
uncertainty introduces no significant degree of uncertainty in the quantities
that interest you. For example, when rolling a pair of dice, of what
importance is the tiny degree of uncertainty introduced by QM in determining
the outcome?
Secondly, even if physical probabilities exist and play an important role in
some problem of interest, why do you insist that physical probabilities are
the *only* probabilities we can use? QM effects are not the only source of
uncertainty we have to contend with. We always have to deal with incomplete
information, and this introduces uncertainties of its own. Why deny us the
tools of probability theory in dealing with the limits of our information?
Thirdly, it's easy to get mathematical self-consistency; yet I never
encountered a satisfactory definition of what probabilities *mean* -- one that
avoids circular definitions at some point -- until I encountered Jaynes's
notion of probability distributions representing a state of knowledge.
> I.e., there is NO logical necessity to
> the degree of belief interprtation. The universe does not demand
> it. Rather it is (at most) a viewpoint imposed on the universe, by
> humans.
I think you're begging the question. Stating that "it is [...] a viewpoint
imposed on the universe" presupposes that statements about probabilities are
statements about the physical universe, i.e., that probabilities are physical
properties. I contend that probabilities are, rather, an intellectual tool to
be used in dealing with incomplete information.
Furthermore, there is in fact a logical necessity to non-frequentist,
non-physical probabilities. Cox showed us 50 years ago that any calculus of
uncertainty must be equivalent to probability theory to avoid logical
inconsistencies or various other pathologies. Thus, it is a logical necessity
that we represent all forms of uncertainties as probabilities, and reason
about them using probability theory -- including subjective uncertainties that
arise from the limits of our knowledge.
> >>>
> Perhaps you are confusing maximum a posteriori (MAP) methods with a full
> Bayesian analysis.
> >>>
>
> Um, in point of fact, I have several published papers explicating the
> dangers of using MAP rather than hierarchical Bayesian methods.
Then I really, honestly don't understand what you mean when you say that
Bayesians confuse their "guess" g for the truth with the actual truth t.
Would you care to explain in more detail.