Re: Is It True What They Say About Tarski?

Daniel Fabulich (daniel.fabulich@yale.edu)
Sat, 30 May 1998 19:58:22 -0400 (EDT)

On Sat, 30 May 1998, Michael Lorrey wrote:

> Yes, while the frequency of each photon cannot be measured with certainty, you
> can measure their average wavelegth with a certain amount of precision, with
> variance depending on the accuracy of your instrument. If the accuracy of your
> instrument that measures the average wavelegnth is less than +/- 1 nm, then you
> have created a bivalent situation, where there is Truth and Falsity.

It would be more precise to say truth OR falsity. If we define blue to be
a single photon with a wavelength above a certain threshold, Measuring an
average to within +/- 1 nm means that some of the particles will be above
the threshold and some below, or that some of the light is truly blue and
some is not. For an individual particle, however, it would be wrong to say
that the statement is true and false. Fortunately, since we're talking in
a metalanguage here, we can imagine statements sufficiently well defined
to eliminate ambiguity such as "the light is blue" would cause in this
example.

To return to my waltzing example, on the first beat of each measure my
average location will be on the border of Mexico and America. If "in
Mexico" is defined to be located anywhere from the border south, then I am
in Mexico and I am in America. This is not the same as saying Truth AND
Falsehood, unless we posit the illogical premise that "If one is in
America, one cannot be in Mexico." Clearly, since you are in America and
in Mexico when you are on the border, the premise is false; it would be
true if one was in Mexico if and only if one was SOUTH of the border, in
which case I would be in neither America nor in Mexico when I was standing
on the border; again, this is only a problem if we posit that "One must be
in either Mexico or America," an obviously false premise under these
definitions.

> The human eye tends to make its 'color' determinetion based on the peak of the
> bell curve, or in the case of multiple substances, like nitrogen and oxygen
> having offset bell curves with differing amplitudes, its a matter of averaging
> the two peaks together....

True, but take this example to its logical extreme: 450 +/- 300nm would
hardly be called blue by most, despite the fact that its peak may lie in
the blue range.

At any rate, if we say that something is blue or not depending on what the
probability curve looks like rather than the wavelength of the individual
particle, then you NEVER have ambiguity of the sort described here:
quantum DOES allow you to describe the shape of the probability curve for
location and for momentum with perfect precision; you never even have to
have uncertainty in a well defined example of this sort.