From: Daniel Fabulich (daniel.fabulich@yale.edu)
Date: Sun May 24 1998 - 03:11:39 MDT
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
for contradictions.
Frankly, I think you have simply misspoken with respect to your point
about logic; in logic, things ARE either true or false. It's one of the
defining characteristics of logic. If you wish to adhere to fuzzy truth,
then you had best dump all pretenses of logic altogether and claim some
other higher ground; mysticism seems popular these days. However, one
thing we logicians have shown, time and time again, is that the mystics
cannot beat us on our own turf.
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