Thank you, happy new year to you, too!

On Dec 27, 8:36 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 26 Dec 2010, at 22:51, Brian Tenneson wrote:
>
> > "Limits To Science: God, Godel, Gravity"
>
> >http://www.science20.com/hammock_physicist/limits_science_god_godel_g...
>
> > Here is my comment:
> > An important question is whether or not a TOE will be finite in
> > length.
>
> Of course, this is a matter of definition.
Indeed.


>
> > I am taking 'TOE' to be, as a working definition, a complete
> > description of reality or a complete description of everything that
> > exists.
>
> That does not exist. Arithmetical truth is already not recursively  
> enumerable.

If a complete description of arithmetical truth is not possible, what
exactly are we talking about?



> > Then one *might* consider this program which generates a TOE to
> > arbitrary precision to be "the" TOE, a compression of an infinitely
> > long document into a finitely long document, thus showing that reality
> > at its core does not possess the trait of Kolmogorov randomness. Being
> > that reality contains the uncomputable, it *seems* unlikely that
> > everything can be finitely describable.
>
> This is simply wrong.

That's good!


> > The argument is made that a TOE can be in the form of a logical
> > structure which is a tuple consisting of an underlying set, a set of
> > distinguished constants (like zero), functions (like successor), and
> > relations (like less than) on this underlying set. Making the
> > additional assumption that if there is a structure such that *all*
> > logical structures can be "embedded" within it, then this type of
> > universality endows such a structure with the same structure as
> > reality. Thus this sort of ultimate structure would be in an intuitive
> > sense like ultimate reality. Thus a description of this ultimate
> > structure would be a description of reality.
>
> You have to distinguish the outside and inside view of the ultimate  
> reality.

What is the outside view of the ultimate reality?  How is it possible
to have an outside view of the ultimate reality?

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