> But, like I said, you are manipulating the input to control the value
> returned by the function; you are not manipulating the function.
But that's what we mean by "manipulating the function." Since the
whole discussion seems to be about settling upon a common set
of conventions about how to use words, it seems to me that my
invocation of ordinary language meaning is pertinent.
> The only
> way to manipuluate a function (say x-squared) is to turn it into say
> x-cubed. Remember a function, by definition, is a set of ordered pairs.
That's problematic. How can you be manipulating "a" function here?
It seems to me that x^2 and x^3 are two functions rather than one.
So this appears not to be a possible way of talking about manipulating
functions.
As for my terminological preference for "random variable" or "uncertain
quantity" talk, I prefer consistency with Savage's usage (i.e., RV),
since I fail to see a reason to change. Although I'm no reactionary,
I'm prepared to let the dead hand of convention win, when there's
no positive reason to change.
About physical vs. subjective probabilities I again differ...
> 1) In a Bayesian application we manipulate probabilities. If we claim they
> are physical (relative frequencies), then we need to include our confidence
> in them and compute our confidence in the inferred probabilities (it is not
> same).
First, relative frequencies aren't probabilities at all, even if
they provide evidence for probabilities. Physical probabilities are
a distinct kind of beast. I believe the best treatment of the
relation between physical and subjective probability is that
of David Lewis -- "A Subjectivist's Guide to Objective Chance,"
in R. Jeffrey (1980) Studies in Inductive Logic & Probability, II.
I'd be interested in your response to that.
There is, of course, the need to have subjective probabilities about
our objective probabilities, just as we need (as inductive
agents) to have subjective probabilities about any of our theories
about the physical world.
> 2) Even if (1) is overcome, we now have a problem when the probability is
> clearly not physical....
I can't see how there's a problem here; but then I'm hardly
a frequentist, even if I fail to live up to born-again expectations.
> I really do not want to discuss physical verses subjective probabilities
> anymore. I have had that discussion 1000 times.
I think there's plenty to be said in this general area that hasn't
yet been said. I'm working on a paper (partially) on the subject, in fact.
Cheers, Kevin