Bruno, John, Russell
I am half-way through Smullyan's book. It is an entertaining book for
someone motivated enough to do all these puzzles, but I think that what
is missing is a metalevel discussion of what all this means.
Mathematical fireworks occur because we are dealing with
self-referential systems. In the old days they may have called them
"reflexive." Reflection is, I think, an essential component of
conscious thought.
The type of reflection I have encountered so far in the book involves
"infinite" reflections which lead to paradoxes.
For example if someone says " I am a knave" then obviously we have a
paradox.
The human mind, however, does not have the capacity to deal with an
infinite number of reflections. (I think that you think that I think
that you think.....). If, however, self referential systems are limited
to a finite number of reflections, such as the human mind is capable of,
then these paradoxes may go away. With one reflection a knave would
says: "I am a knight." With two reflections he would say "I am a knave."
With three reflections, "I am a knight." With four "I am a knave." and
so on. With an infinite number of reflections he would remain "Forever
Undecided."
I am not sure if Physics is derived from an ideal infinite
self-referential systems or from a more human and messy finite system
and I cannot think of an obvious and clear-cut justification for either
approach. What do you think?
George
Bruno Marchal wrote:
> At 09:55 20/07/04 -0400, John Mikes wrote:
>
>> It all depends what do we deem: "POSSIBLE". According to what
>> conditions,
>> belief, circumstances? If we accept the "here and now"
>> as "the world", Stathis #1 may be right.
>
>
> This would mean Stathis first assumption was a first person
> assumption, but the
> whole point of Stathis seems (to me) third person. Also what would be the
> meaning of "physical" in a first person assertion.
> Perhaps Stathis could comment.
>
> Now you are right we should agree on what we deem "POSSIBLE".
> With the comp hyp I argued that POSSIBLE = arithmetically consistent, and
> then we can go back asking G and G* ....
>
> Giving that logic is not so well known apparently
> I will soon or later invite you all to Smullyan's knight
> knaves Island. It is the gentlest path to G and G* which are the
> propositional psychologies from which UDA shows how to
> extract the quantum measure in case (comp is true).
> And from which I have extract some bits of von neuman's quantum logic
> (but I am just beginning opening a vast and heavy doors here).
>
> Why not now? The native of that Island are all either knight or knaves
> and knight always tell the truth, and knaves always lie.
> You go there.
> Problem 1. A native tell you "I am a knight". Is it possible to deduce
> the native's type?
> Problem 2. You meet someone on the island, and he tells you
> "I am a knave". What can you deduce?
>
> I would be please to get answers, or critics.
> I think it will be useful if only by John Mike remark: we will not
> progress
> if we make not clear the word "possible" in our everything context ...
> Logic can help because it is the science of proofS, truthS, and
> possibilitieS
> (note the s).
>
> Bruno
>
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
Received on Wed Jul 21 2004 - 00:27:40 PDT