Fuzzy Fallacies

["Peter L. Schuerman" <plschuerman@UCDAVIS.EDU>]

I wrote:

> >The dictionary definition of "tall" doesn't rely soley on measurement.
> >It includes the idea of comparison:  Having greater than ordinary
> >height.  You can't learn anything about tall by making a measurement,
> >unless you then compare it to something.

On Sat, 25 Nov 1995, Logical Language Group wrote:

> I'm not sure all dictionaries agree, and current thinking seems to be
> that most concepts are defined not with respect to something different
> (i.e. not-tall, as you describe above), but rather against some ideal of
> tallness.

There seems to be a continuing misunderstanding, which perhaps I can
correct here.  Tall is not defined with respect to "not-tall".  It is
defined against the speaker's criteria for tallness.  This criteria are
essentially the "ideal" that you refer to.  Note that different cultures
have different criteria, and even different people have different
criteria.  This may be very annoying, but it's the reality.  Fortunately,
most people within a culture have *similar* criteria for most words we
use... when our criteria are very different than the common criteria, it
makes us use words incorrectly; other people correct our usage, and we
adjust our criteria accordingly.  But the process does not result in an
exact duplication of criteria in all people.  We just tend to think
similarly.

> In that sense Steve is right.  For any person A that everyone agrees IS
> "tall", we can envision the possibility of someone B who is "more" tall.
> It is not clear whether we would mark the statement "A is tall" as being
> less than perfectly true MERELY because B exists.

The statement "A is tall" is a semantic shorthand for "A seems tall to me
based on the criteria I use to judge tallness."  If B is taller than A,
the statement "B is tall" does not in any way contradict or support "A is
tall" because it also means "B seems tall to me based on the criteria I
use to judge tallness."  This is true even if A is taller than B.

> Indeed, if this were
> possible, that the statement "x1 is tall" could change truth values with
> time though x1 did not change at all, simply by something else becoming
> taller.

If you expand "x1 is tall" into its implied meaning, you can see that the
truth value remains constant.

Ex:
Archeological evidence that people are taller now than they used to be.
If I am reading the wall of an Egyptian tomb, and the writing describes
the person buried there as "tall", I can then go and measure the mummy
and compare.  Even if the mummy is much taller than other similar
mummies, chances are, the mummy (after accounting for shrinkage over
time) is not going to seem tall to modern standards.  So, has the writing
on the wall changed its truth value?

The answer is no, because the assertion "X is tall" means "X is judged as
tall by a set of criteria."  If X is *still* tall according to those
criteria, then the statement is true.

> It is possible to define tallness as compared to something smaller.  But
> I dare say that unless there is agreement as to what the reference is,
> then it will be hard to get any consistency in values.

Which is why it is a mistake to use "tall" as a way of communicating
objective information about height.  That is why systems of measurement
were created in the first place!  You are right, that there must be
agreement as to what the reference is.  That's why we create references,
such as sticks with incremental marks on them and standard weights for
callibrating scales.

> Is my 9 year-old
> daughter tall?  She is 4'7 (140cm) - already fast approaching Nora's 5'2
> (158cm) even though still a couple of years from puberty.  In some
> contexts - against other 9 year olds - she is a bit taller than average,
> but not exceptional.  When Nora is thinking of her in terms of her
> imagining a grown Angela, Nora's relatively short height makes Angela
> subjectively taller for her when other girls are NOT present as when
> they are.  But when Angela wants to reach something on a high shelf,
> suddenly she is "short".  Likewise, I am tall to Nora, and am above
> average height.  But I don't tend to think of myself as tall at least
> partially because I have stubby legs (if my legs were proportionate to
> the rest of my body I would be 6'6 (2 meters).

"A is tall" is not useful as accurate communication unless the criteria of
the speaker are known.  For the *same* reason, "A is 5-tall" is *also*
not useful, unless the criteria of the speaker are known.

Of course, once the speaker and listener know what the criteria for these
descriptive words are, there is no longer a problem.  If you know that I
tend to give the value "tall" to people taller than me, you can get an
idea of A's height by looking at me.  Unfortunately, the omission of
criteria in discourse may lead to misunderstanding (perhaps A is a
building, and my criteria are based on some "average-height" building
which I am imagining).

So, even "5-tall" can be meaningful if the listener knows that it means
'between the heights of 5'8" and 5'11"' (for example).

The only problem with using numbers as descriptors in this way is that
they cease to function as numbers.  This in turn is not a problem, as
long as it is recognized that the numbers no longer have the same
semantic meaning.  When you do mathematical operations on numbers, you
get meaningful results.

Ex:
I have 5 boxes.  Each box has 6 objects inside.  5 * 6 = 30.  What does
30 represent?  30 represents the number of objects I have.

When you do mathematical operations on numbers-used-as-descriptors, you
get no meaningful results.

Ex:
A is 5-tall.  B is 6-tall.  5 * 6 = 30.  What does 30 represent?  What
would be the units for this number?

The rest of the examples you gave differed only in detail, and the same
arguments can be made for each.

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