Hal Ruhl wrote:
>Turing's use of Cantor's diagonal argument results in the general lack of a
>decision procedure even if a FAS is countably infinite.
>
>Turing also tells us by the same approach that FAS cannot get any larger
>than that so such a FAS must be complete.
>
>Godel tells us that most FAS have to get that large to be complete.
This is vague. Completeness in logic is always completeness with respect
to a semantics (a class of models). In general complete means that
the theory (the Formal System) can prove what is true in all models of
the class. Be careful because "incomplete" is sometimes used with
respect to some standart model; so incomplete is not the negation
of complete.
>Godel tells us that most FAS have to get that large to be complete.
>
>I see Chaitin's work as saying that any FAS that has a theorem cascade must
>also get that large to be complete.
That could depend on the theory. This is a FAS dependent result.
>Unfortunately it therefore seems that most complete FAS are also
>inconsistent.
I can only guess what you mean here. It can be true or false. You should
try to be more explicit.
>The Everything ensemble proposal as I understand it encompasses the
>simultaneous existence of the complete collection of all possible FAS all
>in a complete state. If so it seems it must also be inconsistent.
What do you mean by "complete state" ? Why should the Everything ensemble
proposal be inconsistent ? It is not even a theory, but a semantically
based
proposal (so it is consistent by very definition). The concept of
consistency
applies to syntax, not semantical structure.
(Having (at least one) model is equivalent
with consistency *only* for *first* order logics).
>So it seems we must either accept inconsistency for most universes or
>abandon the idea of the Everything ensemble as containing all FAS in a
>complete state.
>
>My Superverse is an attempt at a consistent, but incomplete i.e. dynamic,
>yet all possible FAS ensemble.
>
>Its characteristics are a work in progress.
Could you by chance make a comparison between your superverse and UD* ?
(cf UD* = the extended execution of the universal dovetailer i.e. the
program which generates and executes all possible programme written in all
possible programming languages (I use Church's thesis).
How do you manage the distinction between subjective (first person)
and objective (third person) descriptions ?
Have you read?
http://www.escribe.com/science/theory/m1726.html
Bruno
Received on Wed Nov 15 2000 - 03:55:31 PST