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On Wed, 22 Nov 1995, Steven M. Belknap wrote:
> I would be interested to learn your interpretation of what fuzzy logic is abou
With regard to this discussion:
Fuzzy logic is an attempt to quantify words and experiences which possess
the quality of "continuousness." For instance, "sound" can be measured
across a continuum. It can be measured as the intensity of vibration, or
as frequency, etc. However, "loudness" or "quietness" cannot be measured.
Why not? Because these are subjective, and there is no fixed criteria.
What is loud for one person is not necessarily loud for another. Even if
we can get many, many people to agree that "greater than X intensity" is
"loud" and that "less than X intensity" is "not loud" this doesn't change
the fact that the determination is subjective, and that you are actually
measuring intensity and *calling* it loudness.
Another example: happiness. You can measure brainwaves, levels of
endorphins, heartrate, etc. all you want. You can correlate certain body
states with claims (by the person being studied) that they are happy. So
what? You are still only measuring body functions, not happiness.
Correlation is not identity, or so my statistics prof always used to say.
So while body functions may exist on a continuum, happiness does not. A
person is either happy, not-happy, or composed of elements which are happy
and not-happy (e.g. of two minds regarding his or her emotional state).
If your rich aunt dies and leaves you lots of money, but you really miss
your aunt, are you happy or not-happy? Without breaking this down any
further, it's hard to say. Part of you will be happy, part of you will
not, so what's the answer? The fuzzy logic people would say "you are 0.5
happy" or something equally stupid. Using conventional logic, one would
recognize that you have reason to feel happy and reason to feel sad, and
so would be expected to feel both emotions. Thus, you break down
(analyze) the statement. The answer to the question is "I am happy,"
because you are, in fact, happy, though for social reasons you would
probably want to explain that you are sad as well, so that you wouldn't
seem to be an unfeeling monster!
> 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.
And it sure as hell doesn't imply the idea that you can be 0.32-bald, or
6-bald, or any other such nonsense. All it implies is that baldness is a
lack of hair, with "lack" being judged by personal aesthetics. If you
want to count hairs to determine whether someone is bald, feel free, but
you *know* that this is not how people *really* make such judgements.
And, even if you do decide to put baldness on some sort of numerical
scale, you know it's no better than a system where you say
"not-bald/sorta-bald/kinda-bald/nearly-bald/bald/really bald/very bald"
(that is, the distinctions carry no real information except that the
speaker is being vague.)
> >> 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.
I would love to see an example of how numbers can illuminate logical
> >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?
OK, describe what I mean when I say that a restaurant was a 4.5 on a
restaurant-scale of 0 to 8.
> 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.
This is because people know what the words mean. How they may choose to
apply them will vary. Say you and I look at a beautiful woman. We both
know that "very beautiful" is more extreme than "beautiful". I say she is
beautiful, and you say she is very beautiful. Even if we both rank words
the same way doesn't mean we will apply them the same. Beauty is a word
(like bald, tall, happy, etc.) which is applied relative to some personal
criteria. In the example above, perhaps I have seen more beautiful women
than you have, thus my different reaction.
> 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.
Great! By all means, use them! :) When talking to a doctor about pain, I
am sure the patients learn to get the doctor to focus on certain pains
more than others by careful application of the numbers. This could also
be achieved by having the patient make simple statements, but doctors
don't tend to like patients to diagnose themselves... it's much better to
make a numerical guessing game out of it.
Patient: Doc, I need some Tylenol with codeine for my arm. It hurts!
Doctor: (irritated) So when did *you* go to med school?
Patient: ummm... I mean, I think there's something wrong with my arm.
Doctor: Come back tomorrow if it's worse.
Patient: Doc, my arm really hurts... can you make it stop?
Doctor: Well, hmmm... I don't know. How much does it hurt?
Patient: (thinking a moment) An 8?
Doctor: That's nearly a ten! Well, here's your Tylenol with codeine!
Patient: (to himself) Cool!
(okay, so I'm in a 7-silly mood... just ignore those, please :)
Anyway, for a patient to rank a pain higher than any others, he's simply
saying "this is the pain that's bothering me most." The highest pain
value probably is a good indicator of how "tough" the patient is... a
tough, macho guy is hardly going to admit to having "10" pain even if his
leg is broken!
> 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.
All I'm saying is that any description that anyone makes is based on
their own criteria. Is that so hard to believe?
> 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.
Discrete logics do model human thinking quite well, but tend to fail
when linguistically-unaware people use it. This is because logic is only
as good as the material it starts with... garbage in, garbage out. If
someone insists that such words as tall, bald and beautiful have some
sort of objective definitions, and then uses these words in statements
which are then logically analyzed, there will be some real problems
unless the statements are broken down into their actual meanings.
Bob is tall.
True or false? You can't say, not because the subject is "fuzzy" but
because the frame of reference isn't stated. Missing information. Bob is
either tall or not-tall, and we can agree on the truth or falseness of
this statement once we 1) agree on the criteria and 2) make an observation
that can be subjected to the criteria.
> 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.
A numerical basis for consciousness? How would this work... would you
measure qualities such as love, greed and wistfulness by the number of
neurons firing, or the rate of acetylcholine synthesis in certain
defined regions of the brain?
Of course, there *may* be numerical underpinnings for such things, but the
number of consciousness-elements involved in just "having an opinion about
something" is probably staggering, and if so, a 1-to-10 scale wouldn't
even be *remotely* adequate.
> And providing a mechanism for describing their intuitive
> understanding in a fuzzy way may be useful, even if such constructs are
> unwieldy in natlangs.
Fuzzy logic encourages one to stop analyzing, by oversimplifying. I
don't think too many people would disagree that to rate a person's
appearance on a scale of 1 to 10 is to oversimplify to the point of
> >> You are claiming that all such
> >> statements must be metareferences, which does not seem reasonable to me.
> >Why not?
> Sam is somewhat bald.
> It is somewhat true that Sam is bald.
> These are different statements, with different meanings. QED
Yes, one of the statements is, upon analysis, meaningless. I've already
explained that truth isn't scalar.
Peter Schuerman email@example.com
Co-editor, SPECTRA Online
for back issues: http://www.well.com/user/phandaal/