fuzziness

["Steven M. Belknap" <sbelknap@UIC.EDU>]

la pitr cusku di'e
>
>It seems bizarre to divide a statement into 100 parts and then decide how
>many of those parts are true and how many are not.  It seems equally
>bizarre to divide it into seven parts, or nine parts, or any standard
>number of parts.
>

Spoken like a true Aristotlean. Perhaps you have misunderstood what fuzzy
truth values are. They are not collections of substatements some of which
are absolutely false and some of which are absolutely true. I have a friend
who has less hair than he did when he was younger. Using your Aristotlean
paradigm, when does my friend qualify as bald? When he has 100,000 hairs
left? 10,000? 100? None? If we had 30 men in a room in various states of
hair loss, we could probably agree on a rough ordering of the men from most
to least bald. Why do we throw this intuitive, natural understanding of the
world away? Although it might sound strange in English, we could describe
the baldness of the men on, (for example) a 0 to 7 scale. Note that I am
*not* suggesting that each man be assigned an exact baldness value, I am
describing the degree of baldness with a given granularity and fuzzy
position on this fuzzy scale. (Granularity refers to an 8 position scale in
this case, varying from 0 to 7)

Using a possible modification to the place-meanings of kerfa,

<X1> <kerfa> <granularity> <position>

>A statement is (according to a given set of criteria) either true, false,
>or made up of both true and false elements.

Now to me this sounds like a truly bizarre way of looking at the world. Who
says that everything must be true, false, indeterminate, or undecidable?
The tyranny of Boole. If you use this scheme, you will constantly be faced
with false dichotomies. When does a mountain become a hill? Lets say you
claim that the (arbitrary) cutoff between mountains and hills is 1000
meters, and we have a hill thats 999.9 meters high. In 15 minutes, I can
turn your hill into a mountain using a shovel! Absurd. 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.

>The number of elements in a
>statement is dependent on interpretation and analysis, so counting them is
>not going to give consistent results.  That is, true/false is not
>actually a scalar dichotomy... it only looks that way if a statement
>hasn't been properly analyzed.

O.K., Then show me the proper analysis:

<Bob is tall.>

>
>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.

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. You are claiming that all such
statements must be metareferences, which does not seem reasonable to me.

>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.

>The statement can be further analyzed as necessary to distinguish the
>elements and the truth or falsehood thereof.  Statements like "partly
>true"  and "partly almost true" make distinctions which are so subjective
>as to not convey any real information.
>

This turns out to be somewhat false. Several linguistics researchers have
asked people to order qualifiers, <quite, somewhat, extremely, partly,
almost, partly, etc> and find that there is actually quite good agreement
among different persons as to the order of these fuzzy operators. 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.

-la stivn


Steven M. Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria

email: sbelknap@uic.edu
Voice: 309/671-3403
Fax:   309/671-8413