Hi Stephen,
SPK:
>What I would very much
like to understand is why your modelizations only
>seem to include the
natural numbers.
BM:
Because I use the
computationalist hypothesis in the cognitive
science.
It means that relatively to
my most probable neighborhood I am determined
by a number: my program or
godel number if you want. It is the number which
make it possible to survive
with a digital brain/body, or to survive a
reconstitution.
SPK:
>Why do you not seem to
allow for the
>entire Cantorian hierarchy of ordinals and cardinals?
>entire Cantorian hierarchy of ordinals and cardinals?
I allow them. Since Godel we
know that even to study properties of
natural numbers we need the
whole Cantor Paradise.
(Like complex number are
indispensable in pure number theory).
Note that in set theory
cardinality notion are relative. A set can be
uncountable as seen in a
model, and countable as seen in another model.
SPK:
>This, of course, neglects
the fundamental problem that some people have,
>such as myself, with the
use of Platonia to "explain away"
quantities
>such as mass, charge and
angular momentum.
BM:
I do not explain them away. I
explain them and similar terms.
It is the *whole* purpose of
the UDA and AUDA.
SPK:
>What I would like to
know, in addition to the above
>question, is how do you
answer Stephen Hawking's (?) question: "What
breaths
>fire into the
equations"? or my version: How are the solutions to all
>possible mathematical equations computed?
>possible mathematical equations computed?
BM:
I don't need the hypothesis
of "breath". I guess you believe in the
need
of a material-causal universe
computing the solutions of the mathematical
equations. But, once you
accept a minimal amount of arithmetical realism,
all the relevant computations
exist arithmetically. Look at Maudlin 1989
paper to understand that this
is enough, and, even, cannot be ameliorated,
once you assume the comp.
hyp.
Regards,
Bruno
