[FoRK] The quantum-logical theory of truth and irony

Bill Stoddard wgstoddard at gmail.com
Fri Jan 22 09:08:20 PST 2010


On 1/22/10 12:00 PM, Jeff Bone wrote:
>
> On Jan 22, 2010, at 10:02 AM, Jeff Bone wrote:
>
>> One small lemma in the theory, worthy of note:  anti-anti-irony is 
>> not +1 irony, but rather -4/3 irony.  Anti-anti-anti-irony = -2 
>> irony.  However, anti-anti-meta-anti-irony = +2 irony, yet 
>> quasi-meta-anti-meta-anti-meta-anti-irony (or any of its well-formed 
>> tangles) = negative infinity +/- 2/3.  (Dimensional analysis reveals 
>> this number, intriguingly, to be unitless.)
>
> You're probably confused.  I know what you're thinking:  "shouldn't 
> anti-anti-anti-irony = +2 irony, not -2 irony?"
>
> This tripped me up at first, too.
>
> However, recall "Seinfeld's Law":  in any linear composition of 
> anti-ironic applications to collapsed quantum-logical products, the 
> sign-twist result of every other application is implicitly reversed.  
> In practice, this means that any odd number of sequential applications 
> of anti- to an unmodified truson with positive intensionality and any 
> whole-number extensionality has negative sign-twist.  (Hence, 
> "sign-folding.")  However, when the number of such applications has 
> been "lifted" transfinitely via the application of e.g. meta or other 
> operators, the sign becomes unknowable.  Only the linear subsequences 
> of such applications have deterministic sign.
>
> In practice this is not a problem for most common speech-act 
> applications.  The primitive expression of the typed truson calculus 
> using positional operators does, however, permit disambiguation;  
> consider the twist-type signature of the following tangle, for 
> example:  (anti-)-(anti)(-anti)-(anti-)-(-anti-) X.
>
> I hope this clarifies things and therefore preemptively avoids a 
> shit-storm of confusion and debate on this issue.

Russell,
You're in Austin, right?  Need to go over and talk Jeff down...

Bill


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