spoon-discuss: Re: spoon-business: new proposal: ptime

[Rob Speer <rob@xxxxxxxxxxxx>]

On Sun, Feb 03, 2002 at 02:06:52AM -0500, Donald Whytock wrote:
> Has anyone noticed that we still don't have a paradox resolution rule?  Or maybe it's just me...

There isn't anything to notice. A paradox resolution rule is impossible.
Paradoxes arise from the effects of rules coming into conflict. If there
is a rule about paradoxes, either:

* It has no effects (i.e. it is useless).
* It has effects (specifically, effects based on the effects of other
  rules). This will only serve to move paradoxes to a higher level.

A paradox rule cannot eliminate all of its own potential paradoxical
effects, either; I believe this follows from Godel's Incompleteness
Theorem, or at least a similar argument.

To illustrate this, I will present Douglas Hofstadter's wonderful
analogy. In his analogy, the records and the record player were
mathematical theorems and mathematical systems, but here consider them
to be game effects and rules about paradoxes.

Mr. Crab buys a record player, "Record Player 1", which the salesman
claims can reproduce any sound. Mr. Tortoise hears Crab bragging about
this, and gives Crab a record named "I Cannot Be Played On Record Player
1", which contains precisely the sound which will cause Record Player
1's machinery to break. Crab plays it. It does.

Crab is undaunted, and buys Record Player 2, which he is assured will
not break when it makes that sound. Tortoise produces "I Cannot Be
Played On Record Player 2" which breaks Record Player 2.

Eventually, Crab catches on and comes up with Record Player Omega, which
optically scans a record for the sound it will produce, and if it
determines that the sound will cause it to break, a special part of the
record player disassembles the record player and rebuilds it into a
record player that will not break when it plays that sound. Feeling
invincible, Crab plays the next record Tortoise gives him, "I Cannot Be
Played On Record Player Omega", which happens to be one that breaks the
disassembling machinery.

The only way Crab could escape this loop would be to get an imperfect
record player, a record player which cannot play its own breaking-sound.
This would be the equivalent of a paradox rule that does not actually
prevent any paradoxes.

-- 
Rob Speer