# Re: Thomas' Fuzziness and Probability

From: Herman Rubin (hrubin@odds.stat.purdue.edu)
Date: Fri Aug 24 2001 - 16:43:04 MET DST

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In article <9luacg\$olf\$1@zeus.polsl.gliwice.pl>,
Andrzej Pownuk <pownuk@zeus.polsl.gliwice.pl> wrote:
>> > Btw, I doubt that the fact that you know something is reflected by
>> > probabilistic logic, without your formalizing it in any way.

<> That is =EXACTLY= what Bayesian probability theory is all about !!!
<> In Bayesian probability theory, _ALL_ probabilities are conditional
<> on the knowledge base one is willing to apply to the problem at hand.
<> The conditional probability P(A|{B}) in Bayesian theory is the degree
<> of confidence one has in the truth of Boolean proposition 'A', given
<> that the set of Boolean propositions {B} (the knowledge base one is
<> willing to apply to the problem) is assumed to be true. The Laws of
<> probability and Bayes theorem provide all the tools one needs to reason
<> about such `uncertain' Boolean propositions, as well as to incorporate
<> new data into one's knowledge base. See G. Larry Bretthorst's paper
<> ``An Introduction To Model Selection Using Probability Theory As Logic''
<> <http://bayes.wustl.edu/glb/model.ps.gz>, or the draft of E. T. Jaynes'
<> magnum opus ``Probability Theory: The Logic of Science''
<> <http://bayes.wustl.edu/etj/prob.html>.

>Probability theory is related
>with the question
>"how often something happened".
>When in each experiment we get the same results,
>then this problem is not related with theory of probability.
>We know the answers with probability one.

This is confusing probability with limiting relative
frequency. One NEVER has this situation, and in any
case, limits tell one nothing for finite samples.

One cannot "repeat" an experiment; the situation is
always different. So probability has to be looked
at otherwise. The only reasonable approach I have
seen is that it exists, and the properties are as
described. The assumptions one makes, such as
independence, similarity of moments, etc., are far
more precise than any observations can yield.

>When I see that knowledge
>of my students is related with probability,
>(For the same question I got
>different response.)
>then I doubt about their knowledge.

This happens all the time.

```--
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
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