On Thu, Mar 27, 2008 at 03:22:54PM -0700, nichomachus wrote:
>
> I have been following this discussion and I wanted to respond to this
> point because I fail to see why this is such a damning criticism of
> the MUH. How is in inconsistent to affirm the existence and reality of
> mututally exclusive axiom sets? I realize how that sounds so I would
> like to amplify this point with the example that a mathematical
> platonist may believe in the independent existence of both Euclidean
> and non-Euclidean geometries. Each system is defined by its own set of
> axioms and though any two may be mutually inconsistent, any one alone
> may be entirely self-consistent. In other words, we don't merge the
> axiom sets. Rather, each set defines one mathematical object or entity
> that exists independently and in its own right. This is the way that I
> read Tegmark's work anyway. I am interested to get other takes on this
> point.
>

##
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Tegmark is unfortunately ambiguous on this point. I read Tegmark as
you do, that the ensemble is the union of all finite axiom systems,
which is of course enumerable (over a given alphabet). This
formulation then connects with the dovetailer approaches of both
Marchal and Schmidhuber.
However, there is an alternative interpretation that Tegmark's
ensemble contains all of mathematics, and then Russell's paradox does
present a problem, which Brian is attempting to find a solution.
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Mathematics
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