# Re: Thomas' Fuzziness and Probability

From: Herman Rubin (hrubin@odds.stat.purdue.edu)
Date: Thu Aug 16 2001 - 00:19:46 MET DST

• Next message: Earl Cox: "Re: Thomas' Fuzziness and Probability"

In article <%yKc7.52091\$m8.16672957@news1.rdc1.md.home.com>,
Earl Cox <earldcox1@home.com> wrote:
>I suppose the statements:

>>The important distinction is not
>> between bivalent logic and multivalent logic, but between
>> meta-language and object language. A bivalent logic in the
>> meta-language is perfectly adequate for the purpose of modeling the
>> fuzziness in the object language.

>must make sense to someone. But any metalanguage
>that can convert two-valued logic into continuous valued
>logic must be, at heart, fuzzy logic (since this is exactly
>what fuzzy logic, via the extension Principle, does.)

I repeat, nobody has been able to make anything sensible
in the form of a linear continuous truth-value system.
Probability is not a truth-value system, but a scale
resting on a Boolean one.

In any truth-value system, the truth of a statement made
by combining other statements with logical operators
depends only on the truth-values and the operators. The
truth-value of A OR B depends ONLY on those of A and B.
If A has truth-value 1/2, and B has truth-value 1/2, the
truth-value of A OR B is the same if B=A or if B = ~A.

Probability is NOT truth-value, and does not try to be.
Fuzziness tries to be.

```--
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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