[extropy-chat] what is probability?

[Jef Allbright]

gts wrote:
> On Sun, 31 Dec 2006 20:00:26 -0500, Jef Allbright 
> <jef at jefallbright.net>
> wrote:
> 
> > gts wrote:
> >
> >> Which statement is most true?
> >>
> >> A) E is frequent because it is probable.
> >> B) E is probable because it is frequent.
> >
> > It would be helpful, highlighted by the example of (A), to 
> clarify the 
> > complementary usage of "probability" and "likelihood".  Once again, 
> > clear terminology is vital...
> 
> The purpose of my question is to help the reader discover on 
> his own which of the two objectivist interpretations of 
> probability he is likely to prefer (while leaving open the 
> question of subjective/epistemic interpretations).
> 
> I could write (A) as "E is frequent because it is has a high 
> propensity to occur" but this would at least partially defeat 
> the purpose of the exercise.
> 
> (But now the cat is out of the bag in any case. So much for 
> the Socratic method. :)
> 
> (A) seems most correct to me, but I wonder if perhaps others 
> here might disagree. Certainly frequency theorists would prefer (B).

I recall that you and I could never agree on the (in)validity of qualia
as a practical statement about "reality".  Do you think this is a
variation on that theme?

Your statement (A) seems to me to be flawed, i.e. it's not a matter of
preference between (A) and (B), since (A) doesn't even make sense.  If
(A) were rephrased as "E is frequent because it is likely", or better
yet "E is more frequent because it is more likely", then there would be
something meaningful to consider, but as it currently expressed it seems
to imply that an objective measurement is "because" of a subjective
assessment.

I have a different problem with (B) due to frequentist probability being
less complete than Bayesian probability.

- Jef