George Levy

>> Yes but Einstein was still confusing the methodological evacuation
>> of the subject with the idea that the subject cannot be handled
>> scientifically.
>
>I don't understand. Do you mean the "methodological evaluation of the
>subject..."? Which subject was Einstein evaluating or believed could not
>be handled scientifically? 


Evacuation. Nagel has written a paper about that. The idea that
science should talk only on 3-person propositions. Those are verifiable,
refutable like "if you look in that direction with a telescope 
you will see a planet" or like "there is no biggest prime", etc.

I agree science should *use* on 3-propositions, but this does not prevent
science on talking on
*on* 1-propositions, once you got a 3-theory about the 1-propositions.

Ultimately what remains are the arithmetical 3-theory. The 3-physics
is transformed into a 1-psychology of number.

Einstein like most physicist talk only on 3-propositions, but Galileo
Einstein and Everett have deepened the perspectival role of the
observer, but still abstracting the 1-person away.


>> And I guess you forget I am using comp, and this include that
>> the set of provable arithmetical truth is a 3-person sharable
>> objective set.
>
>I guess this is the crux of the difference between us. Your starting
>point is axiomatic and logical/mathematical and you believe that the set
>of provable arithmetical truty is a 3-person sharable objective set. My
>starting point is relativistic and I feel comfortable with a
>relativistic generalization of the first/third person concept. It would
>be nice if we could bridge that gap.


I limit myself intentionaly to a "scientific" dialog with the machine.
I oblige her to prove in a verifiable formal sort of way any of her
assertion. (it is 3-person by construction).

As a mathematician I limit myself to dialogs with sound (correct) machine,
although I have no algorithm for distinguishing a priori correct machine
from uncorrect one. Still I can study the *mathematical* logics of the
discourse of the correct machine. Here appears the logics G and G*.

Only *then* I use G and G* (and Platon) to define in those (meta)logics
the notion of 1-discours.

>I guess one way to begin is to specify what are the axiomatic logical
>constraints A for a set of provable arithmetical truth to be 3-person
>sharable.

They are easily sharable. Even between us and any program emulating
an algorithmic extension on Peano Arithmetic or Zermelo Fraenkel theories.
The truth of the theorem are not sharable, but the theoremhood is sharable
by definition of "provable".

 
>Second question is: Are there several logical modes of A for which this
>set is sharable. 


Yes. (by mode I understand modal variation of provability).


>If yes, then each mode corresponds to a "frame of
>reference." 

Mmh ... does not fit my interpretation of mode. Still for each
mode I have a Kripke frame. So perhaps ...

>Observers possessing identical logical modes would belong to
>the same frame of reference and would experinece the same arithmetic
>truths. Observers in different logical modes would experience different
>loogical truths.

In my modal variation, the set of provable arithmetical proposition
does not vary, G* says but G ignore, so the machine obeys to different
logic in different mode, although the base proposition are the same.
That is true but unprovable by the machine.

G* proves ([0]p <-> [1]p)
G* proves -[0]([0]p <-> [1]p)  and G* proves -[1]([0]p <-> [1]p)

with for exemple [0]p = provable (p) and [1]p = (provable(p) & p), the
simplest Thaetetic mode variant of the provability, my first defintion
of first person (the knower).

>If three such modes can be demonstrated, then the first/third person
>concept becomes insufficient to express the relationships between the
>observers. We may have to fall back on a relativistic concept.


Those mode are abstract and help to characterize the logic invariant
for any solitary observers. Your relativity would need in my framework
multimodal logic. I'm afraid that will be for later. You can look
to bimodal logic (two mode at once) in Boolos 93.


>I am fascinated by the parallelism between social systems and axiomatic
>systems. Please allow me some poetic license. Each social system becomes
>inconsistent given certain conditions. For example, Ghandi showed that
>the British system could not possibly be "civilized" and deal with
>non-violent protest in a "civilized" non-violent manner. By
>demonstrating that the British presence in India was inconsistent, he
>was able to kick the British out. 
>
>It may be that the rise of christianity in ancient Rome happened when
>judaism monotheism exposed the inconsistency of the Roman religious
>beliefs.
>
>Modern terrorists take advantage of our freedoms (economic, legal,
>etc..) to perform their evil acts. These may be our inconsistencies.  
>
>The big question is this: is it possible to expose the inconsistencies
>of terrorists and terrorist organizations? What are their
>inconsistencies? What methods should we use to get rid of them, that
>will remain consistent with our own system?


Well, a typical G*-like answer would be: we will get rid of terrorism
when we will stop trying to get rid of terrorism.
This is also in the spirit of Alan Watts "The Wisdom of Insecurity".
Terrorist are not inconsistent (although some of their beliefs can be 
inconsistent with our beliefs), but they indeed prove some inherent
and intrinsical possibility of inconsistency of our democraties. But,
that "possibility of inconsistency" is what we must learn to live with.
For the same "deep" reason we can expect there will never be universal
vaccin in medecine.

We can perhaps hope to temperate the nuisance of terrorism, and diseases.
We can sublimise (if it is english) those thinks (I wish!).

Also, I agree with your sentence to Charles Goodwin. But be careful,
because such sentence are often misunderstood (my experience).

>In summary, I think that someone can believe in evolution, can believe
>that God did "nothing" and yet be intensely mystical and believe in a
>higher God.


Bruno

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