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Peter Schuerman wrote:
>> Perhaps you have misunderstood what fuzzy
>> truth values are.
>Let's just say I have my own interpretation of what fuzzy logic is about,
>as compared to the interpretation of adherents of this discipline.
I would be interested to learn your interpretation of what fuzzy logic is about.
>You are redefining a word to suit your purposes... something that is very
>common in the "fuzzy logic" camp. The word "bald" does not refer to
>"having X hairs on the head." The word actually means "lacking hair on
>the top of the head." Now, "lacking" is a subjective term. If you lack
>something, then you do not have what you desire. Thus, baldness is
>perceived by someone who looks at someone's head and sees that the amount
>of hair they think should be there, isn't. :)
I am not redefining the word bald. American Heritage Dictionary defines
bald as "lacking hair on the head" Dictionaries are generally agnostic on
the question of whether a discrete or continuous logic is being used.
Certainly the AHD definition of bald does not imply a two-valued logic.
>> Although it might sound strange in English, we could describe
>> the baldness of the men on, (for example) a 0 to 7 scale.
>It's not strange, it's just pretense. Scalar logic is just a way to
>dress up subjective interpretations as objective determinations.
I'm willing to be thought pretentious. I would point ought that the
rational numbers have proven to be quite useful in other areas. Perhaps
they are useful in logic.
>No one will understand what 6-baldness is unless you show them. For all
>the usefulness of this linguistic construction, you might as well point
>and grunt. :)
On what basis do you make this assertion? From my (non-expert) reading of
the linguistic research that has been done, people can order the adjectives
they use according to intensity, and this ordering is fairly consistent
among subjects. I often use a 1 to 10 scale with patients & experimental
subjects, and they seem to understand what I mean, and provide useful,
reproducible responses when we have objectively quantified them.
>> Consider another
>> scheme, in which hillishness is 100 meters high & mountainish is 1000
>> meters high. Any geographic feature between 100 meters and 1000 meters high
>> is then to some extent a mountain and to some extent a hill. Higher than
>> 1000 meters is all mountain and not-at-all hill, so you haven't lost
>> anything for definite mountains.
>Again, I agree. This is very stupid.
You provide no explanation of why you think fuzzy definitions are not
useful in resolving the obvious absurdity of a hill suddenly turning into a
mountain. Claiming, "its all subjective" seems nihilistic to me. I believe
it may be possible to improve understanding among people by enriching
language in certain ways, such as a better understanding of fuzzy sets, and
a better understanding of how people actually think. My hypothesis is that
discrete logics do not model human thinking very well. Perhaps this
hypothesis is wrong, but you fail to shed any light on the discussion by
simply agreeing that the illustrative example I gave is absurd. Of course
it is, that is why I used it as an example!
>> >Scalar interpretation of truth boils down to making statements like "On a
>> >truth scale of 1 to 10, that's a 4." How useful is that?
>> This is not the only potential way of making fuzzy statements:
>> I'm a little hungry.
>> I'm somewhat hungry.
>> I'm quite hungry.
>> I'm extremely hungry.
>These statements are based on internal criteria. If the person says they
>are extremely hungry, and this is consistent with their internal criteria,
>it is true. If it isn't they're lying and it's false... they might only
>be "quite hungry."
>> Speakers of these statements do *not* necessarily refer to some position on
>> a truth scale. They are talking about positions on a hungry scale, which
>> can be assigned a fuzzy hungry value.
>No it can't. The criteria are not numerical.
A squirrel which weighs 2.3 kgs does not know he weighs 2.3 kgs. People who
accurately use fuzzy sets in their daily discourse may not consciously use
numerical criteria. Yet such criteria may accurately model their thinking
and discourse. And providing a mechanism for describing their intuitive
understanding in a fuzzy way may be useful, even if such constructs are
unwieldy in natlangs.
>> You are claiming that all such
>> statements must be metareferences, which does not seem reasonable to me.
Sam is somewhat bald.
It is somewhat true that Sam is bald.
These are different statements, with different meanings. QED
>> >It seems to me that, even though you *can* say these things in Lojban,
>> >that all anyone *actually* needs is true, false, and part-true/part-false.
>> O.K. That sounds fine, as long as you also provide the lojban speaker with
>> a means of expressing granularity and ordinality.
>As long as those aren't numerical, sure.
No one is compelling you to use fuzzy logic. But those of us who find it
useful may find fuzzy numerical scales useful I am seeking a way to express
fuzzy statements concisely & elegantly in lojban. I have thought about this
for several months, and currently believe that fuzziness is best expressed
in a way which allows granularity and ordinality. (Ordinality is numerical
by definition.) Perhaps this idea is wrong. How would you express fuzzy
logic in lojban?
>Correlation is not the same as identity. There might be a *relationship*
>between hair number and baldness rank, but they aren't the same thing.
Presumably speaker and listener would agree, either explicitly or
implicitly on what criteria are to be used to assess baldness. I see no
>> I would
>> agree that the ordering could be made more explicit and more objective by
>> using ordinality. Perhaps you are confusing subjectivity with fuzziness.
>> They are quite different.
>Fuzziness is an attempt to transcend subjectivity, which doesn't
>succeed. It uses numbers, so it sure *looks* good though! :)
Again, you are confusing subjectivity with fuzziness. Fuzziness has been
successfully used in areas where subjectivity was not the problem. I wrote
a computer program that used a fuzzy logic engine to model how an expert
general internist selects antihypertensive medication. The program works
surprisingly well. Subjectivity was not an issue. A panel of experts agreed
on their analysis, but were unable to clearly explain why in a way that
could be simply implemented on a computer. The fuzzy logic approach worked.
Better than other approaches I've tried. I guess I'm just a utilitarian.
Steven M. Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria