# Re: Programming is the Engineering Discipline of the Science that is Mathematics

Date: 11 Jun 2006 13:31:19 -0700

Message-ID: <1150057879.920774.144400_at_f6g2000cwb.googlegroups.com>

Bob Badour wrote:

*> vc wrote:
**>
**> > Bob Badour wrote:
**> >
*

> >>vc wrote:

*> >>
**> >>
**> >>>Keith H Duggar wrote:
**> >>>[Irrelevant stuff skipped]
**> >>>
**> >>>Assuming Bayesian treatment (which was not specified originally, mind
**> >>>you), the derivation is still meaningless. Let's try some argument
**> >>>from authority:
**> >>
**> >>[snip]
**> >>
**> >>Your whole dismissal, as I recall, depends on your observation:
**> >>
**> >> > P(B|A) def P(A and B)/P(A)
**> >
**> >
**> > It does in the frequentist probability interpretation, yes.
**> >
**> >> > the requirement for such definition being that P(A) <>0, naturally.
**> >>
**> >>Keith used the equivalent definition:
**> >
**> >
**> > In the Bayesian interpretation the product rule is a derivation form
**> > Cox's postulates, but even there P(B|A)P(A) is meaningful only when
**> > P(A) > 0.:
**> >
**> >>From the Jaynes book:
**> >
**> > "
**> > In our formal probability symbols (those with a capital P)
**> >
**> >
**> > P(A|B)
**> > ....
**> >
**> >
**> > We repeat the warning that a probability symbol is undefined and
**> > meaningless if the condi-
**> > tioning statement B happens to have zero probability in the context of
**> > our problem ...
**> > "
**> >
**> > Please see the book for details.
**>
**> And since Keith never relied on any meaningful value for P(A|B) in his
**> proof, I wonder what point you are trying to make.
**>
*

Consider a partial function f(x) defined on the set N of natural numbers as:

if x > 10 f(x) = 2*x

Now, what would be the value of x*f(x) given x = 0 ? It's not zero, it's undefined, it simply does not exist, there is no such thing as 'unmeaningful' values of f(x) given x outside the function domain. Likewise, P(A|B) is defined as probability of proposition A given proposition B is true, so if B is false P(A|B) is undefined (see Jaynes for details). Received on Sun Jun 11 2006 - 22:31:19 CEST