# Re: Is It True What They Say About Tarski?

Daniel Fabulich (daniel.fabulich@yale.edu)
Sun, 24 May 1998 05:11:39 -0400 (EDT)

On Sat, 23 May 1998, Christian Whitaker wrote:

Right; I'd thought your last post seemed a little too brief. :)

I am not certain your example is physically correct; EACH individual
photon has a wavelength all its own. That particles should have
wavelengths is odd, but true, as far as we can tell. For this reason, I
think we had best switch to referring to the distance between machine gun
pellets or some other Newtonian physical example; I know a little quantum,
but only very very little. :)

> The change
> over time destroys any attempt at certainty.

Hardly. We can see this from a macroscopic example: if I lead you in a
simple waltz on the Mexican border facing north, my left foot will be in
America during the first measure and in Mexico on 2 and 3 of the second
measure. (Ignore the fence.) It will truly be wherever it is at any
given time, however.

> 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.

Fortunately for us, we have calculus to illuminate our path. A particle
whose location at time t is given by the function x(t) is defined to have
an instantaneous velocity at time t given by the limit of [x(t + h) -
x(t)]/h where h approaches 0. Handy, yes?

> 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.

As noted, in light of the above definition, this discussion of ambiguity
is fishy. Since particles have a discrete location at a given time, and
since their instantaneous velocities ARE given by calculus, there's no
ambiguity at all on the Newtonian scale.

>
> >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.

Hardly. The truth of certain axioms is unquestionable; A=A leaps to mind.
You cannot logically support a position under which 0.99A=A, unless A is
0. In other words, if anything exists, then A = A; logic does not allow