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