On 18 Jan 2014, at 10:09, LizR wrote:
On 18 January 2014 19:51, meekerdb <meeke...@verizon.net> wrote:
On 1/17/2014 10:18 PM, LizR wrote:
On 18 January 2014 19:12, meekerdb <meeke...@verizon.net> wrote:
But where does it exist? X has to be conscious of a location, a
physics, etc. If all this is the same as where I exist, then it is
just a translation of this world into arithmetic. It's the flip
side of "A perfect description of X is the same as X", i.e. "X is
the perfect description of X". If every perfect description is
realized somewhere in arithmetic (and I think it probably is)
nothing is gained by saying we may be in arithmetic.
Don't we gain less entities, making Occam a bit happier? If we can
get the appearance of a universe without having to actually have
one, can't we "retire the universe" and just stick with the
"appearance-of-one-with-equal-explanatory-value" ? (Not an original
idea, of course, I'm fairly sure Max Tegmark said something along
those lines regarding his mathematical universe hypothesis -- that
if the maths was isomorphic to the universe, why bother to assume
the universe was physically there?).
I'm asking why have the maths?
Well (putting on my AR hat) we have it because the maths is
necessarily existent, while the universe isn't.
You cannot prove Ex(x = 0) in pure logic. So "necessity" is an
indexical depending on the their you build on.
Axioms become necessary (in consistent theories), like their
consequences. But math is not necessary per se.
Now, you might share with me and others, the mysterious feeling that
17 is prime is close to a logicall necessity, but this comes from the
fact that we do have the intuition making us believe in RA or PA.
In that sense, arithmetical truth is "necessary", and indeed few
people doubt it.
But above arithmetic, it is less clear, and I prefer not to assume too
much strong axioms, in the ontology. Then the whole math will makes
sense in the epistemology of each particular universal numbers.
Logicians have succeed in making a term like "arithmetic" rather
precise, but they have also provided evidences that this is not the
case for "mathematics" in general. The notion of mathematical universe
is inconsistent, despite a set theory like NF might seem to be able to
give sense to it. Anyway, with comp, we don't need, and cannot use
more than arithmetic, without doing some treachery, even for the math.
Of course there's an answer - we can manipulate the maths - but then
doesn't that proves that the maths aren't the universe. They
wouldn't be any use as predictive and descriptive tools if they WERE
the things described. They are only useful because they are
abstractions, i.e. they leave stuff out (like existence?).
Well .... the maths does have that "unreasonable
effectiveness" (that you're probably bored to death hearing about).
And one reason for that could be because it is - in the guise of
some yet-to-be-discovered TOE - isomorphic to the universe.
An infinity of TOE have been discovered. All first order logical
specifications of any Turing complete structure will do.
The laws of physics are invariant for the choice of TOE among them. So
RA is already a TOE.
RA is not comp. RA does not assume things like "yes doctor" or even
consciousness.
But the statement "RA is a TOE" is a theorem in the theory, or
metatheory, COMP.
In a sense, AUDA eliminates logically the use of comp in the TOE, but
this, to be honest, makes only sense thanks to keeping comp at the
meta-level.
Bruno
http://iridia.ulb.ac.be/~marchal/
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