Re: Summary

From: Marchal <marchal.domain.name.hidden>
Date: Tue Oct 5 07:58:55 1999

>I agree Bruno, I don't know much about modal logic and I'll try to brush up
>on it. From what you wrote above, you are saying that LIP (Leibniz
>Indistinguishability Principle) comes in two flavors.
>
>The first is the non-modal extensional version which says that if two
>particular items appear indistiguishable to an observer, then in so far as
>this observer is concerned, these two items are one and the same. However,
>he
>cannot conclude that these two items will appear indistinguishable, and
>hence
>be identical to other observers. This conclusion is very much in keeping
>with Relativity Theory.
>
>The second version of LIP is the modal intensional version. It says that if
>two items appear to be indistinguishable to an observer, then these two
>items, not only are identical insofar as the observer is concerned, but are
>also indistinguishable and identical to other observers. This version
>supports a view of the world which is absolute.

You can see it this way, although analytical philosophers would object
that the intensional/extensional distinction can itself be made in
purely extensionnal ways. After all that is what Kripke Semantics
is about.

Some philosopher like Quine have pretented that this pure extensional
analysis breaks down at the first-order logical level (with the ``for all"
and ``it exists" quantifiers). But here, as Boolos himself enmphasizes,
this critics is nullified by the Gödelian provability logic.


>It seems that if we extrapolate the above, we are heading toward having to
>decide whether reality is subjective and relative, or objective and
>absolute.

You can call that an extrapolation indeed. I am not sure I follow you.
Reality still could be subjective and absolute, or objective and relative.
But unless we formalise just a little bit, we will not known if we are not
playing with words, here. (I suspect it).

>Extrapolating still further, we are led to having to make a choice
>between a Many-Perspectives Interpretation and a Many-Worlds interpretation.
>The Many-World Interpretation would support an objective world independent
>of
>the consciousness that inhabits it; and the Many-Perspective Interpretation
>would consider each SELF as the center of its own universe (perception) -
>kind of like a distributed solipsist point of view. The only absolute entity
>in the Many-Perspective Interpretation would be the Plenitude itself.

I agree a lot.

Moreover it is not difficult to guess (and even to prove) that if we are
digital machine the Plenitude is no more distinguishable from the
Arithmetical Plenitude. Or if you prefer:
Machines cannot distinguish between Plenitude and Arithmetical Plenitude.
My work can be seen as leading toward a ``Many-Perspective Interpretation (by machines) of Arithmetical Plenitude.

Physical reality emerged from what you call the ``distributed solipsist
point of view" once you define the SELF in the traditionnal
post-gödel-turing-kleene-...-informatical way.

Bruno
Received on Tue Oct 05 1999 - 07:58:55 PDT