Re: Is It True What They Say About Tarski?

Christian Whitaker (
Sat, 23 May 1998 23:59:01 PDT

>On Fri, 22 May 1998, Christian Whitaker wrote:
>> I suppose one could solve the vagueness of blue by assigning it a
>> definition. Blue is light with a wavelength of 550 nm. Given such a
>> definition, the truth value of the statement 'le ciel est bleu' must
>> no, as the value will be something other than precisely 550 nm, and
>> fluctuate across the horizon and from second to second as light is
>> marginally refracted by water vapor and other chemicals inthe
>> atmosphere. The only way to get a true Trotskian statement on sky
>> is to limit sky to a particular point in the sky to a particular
>> in time and find the precise wavelength. In practice this will not
>> very useful, because nobody says things like, 'le ciel est bleu at a
>> point 67 degrees and 35 minutes above and 23 degrees and 12 minutes
>> the left of my reference point at exactly 3:57 PM.', even in a
>> metalanguage.

On the contrary: rather, nobody uses metalanguages in day to day
conversation. (Lojban advocates, this is where you can pipe up if you
feel like it. :) ) If we did, however, you're right, this is the sort
thing we'd say.

Curiously, you could get away with this statement in ordinary language,
but in a metalanguage suitably precise for defining Tarskian truths this
sentence is nonsensical, because of problems drawing conclusions from
exact time. However, I'll make a couple other points before coming to
this one.

>> I like Bart Kosko's notion that Trotskian statements should be
>> assigned a fuzzy truth value.
>NO, and this is where me must take care. First, I presume you mean
>TARSKIAN statements. ;)

My mistake. I sometimes get my communists and atomists confused. They
are both idealists doing battle against an ambigous world.

Second, we may say that our INFORMATION is
>imprecise, but the TRUTH is not. When properly defined, the sky is or
>not blue; we may be only 99% certain of its blueness on a clear day at
>noon, but that is VERY different from saying that the sky is 99% blue
>(again, restricted by our formal metalanguage).
>We already quite often say in science that the wavelength of certain
>is 550 +/- 10 nm. This is not to say that the wavelength varies, but
>that our information is imprecise. So, to the extent that it is
>necessary, when we need to make clear how certain we are of something,
>will add the precision to which we think we know it.

This argument does not hold up because an increase in informatio will
actually increase the ambiguity, or at least make it more obvious. It
is certainly acceptable to assign blueness a range of 540-560 nm, but
there will still be certain situations in which it is impossible to say
whether the light is blue or not. For the moment I am going to abandon
the sky because the entire visible spectrum is present in what we
perceive as the blue sky. Imagine a satellite is beaming a laser down
on our instrumentation. We are trying to determine whether or not 'le
laser est bleu' has a true or false Tarskian value, based on a
definition fo blue between 540-560 nm. Presume using advanced
femtotechnology we have a wavelength detection instrument so precise
that it can measure the distance between each individual photon that
strikes the receptor down to the picometer scale or better. This
instrument will be able to detect wavelengths as precisely as physically
possible. Also presume that the laser on the satellite has been
calibrated as precisely as physically possible.
If the laser on the satellite has been calibrated to 550 nm, or
555, or 548, or any value in the middle of the blue range, we can quite
easily give it a true value. However, what if the laser is calibrated
at exactly 540 nm at it's source? As the laser shines through the
atmosphere, the photons will be slightly, randomly refracted so that the
time between photons striking the instrument will wobble slightly (The
instrument would measure wavelength between individual photons by
dividing the time between photon strikes by the speed of light). Slight
variations in temperature gradients throughout the atmosphere will slow
photons sufficiently to cause a wavelength change (this problem is
accerbated by the fact that both the position of the photons and the
atoms of the instrument are slightly ambigous because of quantum
uncertainty principles, but I shall ignore this factor for the moment).
The instrument would record the distances between individual photons as
Photon Number: 1 2 3 4 5 6 7 8

Distance Apart: (5) 39.97 40.03 40.01 40.04 39.99 39.95 40.04

In fact the variation from 540nm would be far, far smaller (not taking
into account quantum effects, because if one did you couldn't assign any
precise number at all), but it makes no difference in principle.
Because the wavelength of the light will inevitable wobble, the validity
of assigning a Tarskian truth value to the statement 'le laser est bleu'
is destroyed by the fact that neither a true or a false value can be
assigned at the borders of the definition (540 and 560 nm). The change
over time destroys any attempt at certainty.
One way to try to freeze the truth would be to freeze time, make the
precisely 5:34 P.M statement mentioned earlier. However, besides being
impractical in the real world, if time was frozen, light would not
travel and there would be no way for the instrumentation to measure any
value at all. If you froze time exactly at the point that a photon
struck the receptor, you would be able to tell whether the light was
blue in the past (540nm)/(186,000 km/sec)(I am suddenly struck by the
mortal terror that I have misremembered the speed of light. I will
fight my neurosis by sending it off as is). However, you would have
absolutely no basis for saying whether the light is blue NOW because
that will not become apparent until the next photon strikes the
receptor, and of course nothing at all can be said about the matter
until it is tested.
As a brief backtrack, I'll note the advantage of ordinary language
over metalanguage in that ordinary language allows just enough ambiguity
to avoid nonsense. When people use the term precisely, they allow for
that to include enough time so that light and sound waves can continue a
brief ways on their appointed rounds, thereby not striking the world
deaf and blind at that precise moment. I think the reason why common
language is so much more common than metalanguage is that it is much
more useful.

In fact, it seems that allowing for a discrete range of blueness
has made the ambiguity twice as bad. If blue was defined as light with
a wavelength of 550nm, at almost every point the Tarskian truth value of
the statement 'le laser est bleu' would be false, except at 550nm which
would be ambigous. By creating a range, there is an area of clear
truth, clear falsehood, and TWO ambigous points. It does not seem to me
that Tarskian logic is the path to finding absolute truth if there are
necesarily ambiguities wherever one tries to draw boundries. Indeed, the
only way to create a genuinely universal Tarskian logic statement would
be by defining blue as being the set of all wavelengths, i.e., an
infinite statement.

>We don't need "fuzzy truth" statements: the truth is binary,

I admire faith, and thus I choose not to argue against it. As bivalent
truth is the foundation of an information system, it cannot be supported
using the precepts of that system, any more than you can say that the
Pope is infallible because the infallible Pope said so. A foundation
cannot have foundations. I chose to allow for fuzzy truth because I
find it more relaxing philosophically and allows me to see more creative
possibilities. My support of fuzzy truth does not have any more logical
basis than your support of binary truth.

and we
>already have a means of communicating precision.

And the greater the precision, the more clear it becomes that it isn't
very clear.

-Christian Whitaker

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