Achieving "neither P nor not P"

Achieving "neither P nor not P"

[Fred E.J. Linton]

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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Re: Achieving "neither P nor not P"

[Vaughan Pratt]

Fred, I don't believe you can reliably conflate the propositions "change
is not good" and "not(change is good)".

In fact I believe you can't reliably conflate them.

Vaughan

On 12/13/2014 1:19 AM, Fred E.J. Linton wrote:
> "change" is neither good nor not good


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Re: Achieving "neither P nor not P"

[Steve Vickers]

Dear Fred,

The Tetralemma principle is too simplistic. In reality, P may be
interpreted in a variety of situations, with different analyses.

Some good examples come from typos theory. Consider P as "changing y to
o [is good]". In the context of the string "gyyd" it is good, for the
string "definitely not" it is definitely not, while for "typos" it
depends on further analysis.

There is a typology induced on the strings by the amount of "further
analysis" that is needed, and in boundary cases it can be infinite. For
these we effectively have neither P nor ~P.

Typos theory is very formal, but you can clearly see the same principle
in your example, "change is good". It depends on the context. In some it
evidently is good, in some it evidently is not, and in some (as with the
remark attributed to Mao Tse Tung about the French revolution) it seems
always to be too early to tell.

Merry Christmas,

Steve.

On 13/12/2014 09:19, Fred E.J. Linton wrote:
> 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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Re: Achieving "neither P nor not P"

[Vaughan Pratt]

On 12/15/2014 2:03 AM, Steve Vickers wrote:
> In reality, P may be
> interpreted in a variety of situations, with different analyses.
> Some good examples come from typos theory.
> Consider P as "changing y to o [is good]".

A triple entendre (change y to o in "typos")!  Very gyyd, Steve.  And a
theory rendered commendable by the absence of tedious debate about the
plural of "typos".  "Sketches of a giraph" for the definitive wyrk?

Vaughan


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Re: Achieving "neither P nor not P"

[Fred E.J. Linton]

Vaughan Pratt wrote:

> Fred, I don't believe you can reliably conflate the propositions "change
> is not good" and "not(change is good)".

Careful, Vaughan, could you simply be conflating one of those, 
and not the other, with "change is bad"? I can't do that, myself. 

> In fact I believe you can't reliably conflate them.

Well, that belief's a good reason for you not to "believe you can", 
but I don't seem to share that belief yet :-) .

Or perhaps, once the novelty of the example wears off, I'll come to realize
it limps as badly as the earlier examples adduced in that Bangalore piece.

Cheers, -- Fred



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