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Re: scalar polarity

On Wed, 22 Nov 1995, Steven M. Belknap wrote:

> 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.

This has nothing to do with Aristotle, you name-dropper  ;)

> 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.

> 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?

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.  :)

> 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.

We could order them in terms of how much hair they seem to have.  Since
having few hairs can be interpretted as "lacking", we'd probably order
them similarly.  However, a person with a big head would rank as being
"more bald" than someone with the same number of hairs and a smaller
head.  The same problem would be created by differences in hair density,
and even hair color.

> Why do we throw this intuitive, natural understanding of the
> world away?

We don't... as your example shows, we *can* order things on subjective
scales.  It's just that so few words rely directly on number for their

> 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.

> 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)

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.  :)

> >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.

Absurd, indeed. You demonstrate quite nicely why words are not defined
numerically.  Only a fool would claim that a certain number of inches
makes you tall, a certain number of hairs makes you bald, or a certain
number of meters makes something a mountain.

> 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.

> >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.>

Keeping in mind that this is a subjective statement, relative to some
notion of "average", then this is true if the person has greater height
than average. It's not true if the person does not have greater height
than average.  See?  Why get fuzzy headed about it?

> >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.

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

Why not?

> >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.

> >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.

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.

> 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!  :)

Peter Schuerman                                    plschuerman@ucdavis.edu
                        Co-editor, SPECTRA Online
          for back issues: http://www.well.com/user/phandaal/