"Captain," said Data.  "The Endometrians, in the Puta system,
have their own version of this paradox, which predates the Earth
version by--"
     "How very nice for them, Data.  Would you get me some tea? 
Earl Grey.  Hot."
     "Wankery," said Gauss, who then asked Fermat something which
Fermat did not answer.
     "Raymond," said Picard, "is it not true that for a given
series, 1 to n, if 1 has a certain predicate and n does not, then
there must be a least number, within the series, of course, which
does not have the predicate?  Ludwig, by 'predicate', I mean
'defining characteristic'."
     "That is basic, but the problem is--"
     "There are a number of schools of thought on this, Marilyn,"
said Picard.  "You are familiar, I take it, with classical logic?"
     She looked down, "Um, yeah.  Identity, excluded middle,
contradiction.  I miss any?"
     "No.  Now, some would argue that certain laws of classical
logic, particularly that excluded middle, should be discarded; 
others say any two-valued logic will yield the paradox; still
others say the problem is not articulated precisely enough to be
handled by formal logic."
     Ramanujan, who had appeared not to be listening, didn't look
up, but said, "Only in the West would such a problem arise.  In
ancient India, the Jains had a much more sophisticated attitude
toward the truth of a statement.

     To wit:
     (1)  maybe it is;
     (2)  maybe it is not;
     (3)  maybe it is, but it is not;
     (4)  maybe it is indeterminate;
     (5)  maybe it is but it is indeterminate;
     (6)  maybe it is not but it is indeterminate;
     (7)  maybe it is and it is not and is also indeterminate.

     The paradox of the sorites is not a paradox at all to the
Jains, and they're pretty goofy."
     "Thank you for that, Ram.  And we owe you for that whole zero
thing, but the paradox still raises, even after Cantor, deep
metaphysical problems."
     
     "How did Russell handle it?" asked young Wesley boy genius.
     "How would Macguyver?" said Riker.
     Data answered.  "Russell took a radical stance.  He said that
traditional logic assumes precise symbols are being employed,
therefore it is not applicable to this terrestrial life, but to an
imagined celestial existence."
     Marilyn was irate.  "You don't resolve a paradox by defining
it away.  That's just a language-game."
     "Language is a game," said Hollystone, in an uncharacteristic
burst of lucidity, "but the game is played."
     "Who said that?"
     "I did," answered a voice from the shadows.
     "Hey, look.  It's Wittgenstein."
     Wittgenstein seated himself at the corner between Gauss and 
Fermat.
     Hollystone whispered to Ludwig Plutonium, "Stay away from him. 
I heard he once killed a man with a guitar string."
     "Really?"
     "Either that, or my neurons are misfiring like flatulent dogs
again."
     Wittgenstein said, "If your 'paradox' is only a paradox
because you are reasoning with loose concepts, such as 'short'
'tall' 'bald', 'wealthy', 'nauseatingly earnest', then yes, you
*can* define it away.  Admittedly, 'frog' and 'tadpole' are not
vague in the same way that 'poor' and 'wealthy' are, but the
problem is analog--"
     "Language is a virus from the Hell," said Hollystone.
     "I like that," said Wittgenstein.  "Did I say that?"
     "I believe that was Burroughs," said Data, "later popularized
by Laurie Anderson."
     "Who?"
     "Laurie Anderson," said Data.  "Classically-trained violinist
and dimply performance artist.  Perhaps I can explain better in
song:

     "Paradise
      Is exactly like
      Where you are right now
      Only much much
      Better."

     "That's enough, Data.  We get the idea.  
     "But I'm not even up to the 'pain cry' part."
     "Pain cry?" said Wittgenstein.  "Tell me more."

     "Ludwig," said Picard, "I can't say I agree with Russell on
this one.  He'd have us exempt all reasoning with loose or vague
concepts from logical appraisal.  Surely, this is unsatisfactory."
     Marilyn nodded.
     Wittgenstein whistled an etude and said, "Russell was off the
mark on this one."
     "But you said--"
     "Did I?  Well, you were all being rather silly.  The point is
this:  If all empirical concepts are loose, as I think they are,
then Russell would prohibit us from *any* reasoning from empirical
premises."
     "Didn't I just say that?" said Picard.
     "If language is to maintain its fact-stating ability, we must
be able to draw recognizably valid inferences from empirical
premises."
     "For example?"
     "Unless we can infer from the statement 'Wesley is
nauseatingly earnest' the falsity of 'Wesley is sincere, but in a
good way' or the truth of 'Wesley is an asswipe', all these
statements will lose their power to convey information.  Russell's
implied prohibition would destroy ordinary language."
     Picard said, "Frege seemed to agree with Russell when he said
that 'a concept which is not sharply defined is wrongly termed a
concept'.
     "What a ballbuster," said Data.
     "Data!"
     "Captain," said the android, "the Myopians, on Glaucoma II,
believe that there is a precisely-defined moment where a boy
becomes a man, and have an elaborate ceremony to commemorate the
occasion.  The Vulcans, also--"
     Picard said, "Logic requires that such a moment exists.  It is
also true that this moment is forever elusive and unknowable."



          UN-altered REPRODUCTION and INSEMINATION of this
          IMPORTANT Information is a MORAL IMPERATIVE.

RICHH