Achieving "neither P nor not P"

["Fred E.J. Linton" <fejlinton@usa.net>]

Here's a thought that may seem a bit off-topic, having more to do, 
at first glance, with "paradoxical" logic than with categories.

Eleven years ago, for a conference in Bangalore [1], I was trying to 
present natural-seeming examples of statements P each illustrating 
another of the four distinct, mutually exclusive, jointly exhaustive, 
and individually indispensable "logical possibilities" thought available 
for P in the logic of the Hindu catuskoti, or Tetralemma principle: that,
given P, one have either P, or ~P, or both P and ~P, or neither P nor ~P.

(Note that an Aristotelean would hold that already P and ~P are mutually 
exclusive and jointly exhaustive, so that the last two are simply false,
hence utterly dispensable.)

The only illustrations I could come up with back then for a P with 
"neither P nor ~P" always struck me as somewhat artificial; so that 
I was greatly heartened, recently, to stumble on a far more natural 
illustration as outgrowth of a discussant's sardonic comment, concluding 
his remarks on how contemporary web page design strategies needed to be 
modified to take into account the fact that *touch* is more and more 
replacing *mouse cursor and click* as the user interface of choice: 

"Change is good."

Well, he didn't mean it, of course: he said it entirely tongue-in-cheek. 
But it hit me: that's a superb illustration of a P with "neither P nor ~P":
for, in fact (in my view), such "change" is neither good nor not good -- it 
just is, and may need to be accommodated :-) ).

Enjoy! And cheers, -- Fred
---
[1] pp. 62-73 of ISBN 81-85931-58-5, www.hindbook.com, 2005 (esp. pp. 70-71);
cf. http://www.hindbook.com/images/book_content/Emch.pdf ; or
www.hindbook.com/index.php/contributions-to-the-history-of-indian-mathematics





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