Re: Is It True What They Say About Tarski?

Christian Whitaker (
Sat, 23 May 1998 23:14:50 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 enough, although nobody would do so, this statement would be
acceptable in ordinary lenguage, but is nonsensical in a precise
metalanguage, because of some problems encountered from specifying an
exact time. I'll make a few more points before I go back to this.
>> 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. ;)

Yes, I sometimes get my communists and atomists confused. They both are
idealists doing battle with 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
light is 550 +/- 10 nm. This is not to say that the wavelength varies,
>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,
we will add the precision to which we think we know it.

This is not a sustainable argument because the more information we had
the weaker this definition of blue would become. For the moment I am
going to shift the basis of the thought experiment away from the color
of the sky because that is too complex and diffuse; containing all
wavelengths of light to some degree. Let us presume that a man on the
moon is shining a laser down on our instrumentation, and we are trying
to determine on whether it is a Tarskian truth that 'le laser est bleu'
Presume that with advanced femtotechnology we have built the most
precise wavelength measuring instrument possible, one that can measure
the wavelength between individual photons being emitted by the laser
down to picometer scale or better. If the laser is calibrated at 550 nm
the light will certainly fall into the predefined range of blue.

>We don't need "fuzzy truth" statements: the truth is binary, and we
>already have a means of communicating precision.

Get Your Private, Free Email at