On 3/2/2012 03:37, Richard Ruquist wrote:
On Thu, Mar 1, 2012 at 7:14 PM, meekerdb<meeke...@verizon.net>  wrote:

  On 3/1/2012 9:27 AM, Bob Zannelli wrote:

  The Relativity of Existence
Authors: Stuart 
Subjects: History and Philosophy of Physics (physics.hist-ph); General
Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)

Despite the success of physics in formulating mathematical theories that
can predict the outcome of experiments, we have made remarkably little
progress towards answering some of the most basic questions about our
existence, such as: why does the universe exist? Why is the universe
apparently fine-tuned to be able to support life? Why are the laws of
physics so elegant? Why do we have three dimensions of space and one of
time? How is it that the universe can be non-local and non-causal at the
quantum scale, and why is there quantum randomness? In this paper, it is
shown that all of these questions are answered if existence is relative,
and moreover, it seems that we are logically bound to accept it.


"To be clear, the idea that our universe is really just a computer
simulation is highly controversial and not supported by this paper."
     Of course there's no sense in which reality can be a computer
simulation EXCEPT if there is a Great Programmer who can fiddle with the
program.  Otherwise the simulation and the reality are the same thing.

"By the principle of explosion, in any system that contains a single
contradiction, it becomes possible to prove the truth of any
other statement no matter how nonsensical[34, p.18]. There is
clearly a distinction between truth and falsehood in our reality,
which means that the principle of explosion does not apply to
our reality. In other words, we can be certain that our reality is
     Hmm? I'd never heard ex falso quodlibet referred to as "the principle
of explosion" before.  But in any case there are ways for preventing a
contradiction from implying everything, c.f. Graham Priest's "In
Contradiction".  Contradictions are between propositions. Heinrich is
saying that the lack of contradictions in our propositions describing the
world implies the world is consistent.  But at the same time he adopts a
MWI which implies that contrary events happen all the time.

"In fact, there are an infinite number of ways to modify an axiomatic
system while keeping any particular theorem intact."
     This is true if the axioms *and rules of inference* are strong enough
to satisfy Godel's incompleteness theorem, something with a rule of finite
induction (isn't that technically a schema for an infinite set of
axioms?).  Then you are guaranteed infinitely many true propositions which
are not provable from your axioms, and each of those can be added as an
axiom.  Otherwise I think you only get to add infinitely many axioms by
creating arbitrary names, like "aaaaaa" and "aaaaab"...

"From the perspective of any self-aware being, something is real if it is
     A very Platonic and dubious proposition. "True" applies to
propositions not things.  2+2=4 is true, but that doesn't imply anything is
real.  "Holmes friend was Watson" is true too.

"Recognizing this, the ultimate answer to the question of why our reality
exists becomes trivial: because self-awareness can be represented
axiomatically, any axiomatic system that can derive self-awareness will be
perceived as being real without the need for an objective manifestation."
     This is what Bruno Marchal refers to a Lobianity, the provability
within a system that there are unprovable true propositions. Marchal
formulated this idea before Tegmark and has filled it out and made it more
precise (and perhaps testable) by confining it to computation by a univeral
dovetailer - not just any mathematics.
If you join the everything-list@googlegroups.com , he will explain it to

"Not many things can be proven objectively true, because
any proof relying on axioms is not objective without proving
that the axioms are also objectively true."
     This is confusion bordering on sophistry.  He has introduced a new,
undefined concept "objective" and stated that any objectively true
statement has an objective proof.  Proof is well defined since it means
"following from the axioms by the rules of inference".  Proving something
from no axioms just requires more powerful rules of inference.  There's no
principled distinction between rules of inference and axioms.

"If the ROE is correct, then reality is defined by the things that
are provably true, and any additional undecidable statements
simply have no bearing on that reality."
     But does he mean provably true from zero axioms plus the usual rules
of first (or second) order logic?  Earlier he argued that the world must be
an axiomatic system because you could just define it by one axiom for each
fact.  Which would make the 'axiomatic system' useless.  It's equivalent to
"The universe just is."

The argument boils down to:

1. The world (mulitverse/universe) must be an axiomatic system because
it's consistent and every consistent system can be described by an
axiomatic system.  A description in terms of an axiomatic system is an
explanation and a true explanation is one that exists (he really needs that
the thing explained exists).

2. There can be no way to pick out one axiomatic system over another
because if there were that would constitute a lower level axiomatic system
in which would reduce the selected system to a theorem. So all axiomatic
systems must exist, really really exist.


Excerpt: "Any system with finite information content that is consistent can
be formalized into an axiomatic system, for example by using one axiom to
assert the truth of each independent piece of information. Thus, assuming
that our reality has finite information content, there must be an axiomatic
system that is
isomorphic to our reality, where every true thing about reality can be
proved as a theorem from the axioms of that system"

Doesn't this thinking contradict Goedel's Incompleteness theorem for
consistent systems because there are true things about consistent systems
that cannot be derived from its axioms?  Richard

I wonder if the author means that there must be a model of an axiomatic system which happens to be a reality, because otherwise, all an axiomatic system does is limit the models, more and more (with more axioms added, as long as not inconsistent).

Overall, his idea seemed rather interesting, although the measure problem with it seems even more troublesome than in COMP. He also seems to be limiting the systems to some COMP-like requirements (finite information), but if you're doing that, you should either postulate: some system capable of universal computation (UDA then applies) or a system capable of less than that (some unjustified ultrafinitist version) or some infinitary ontology (concrete infinities in the mind and more, hard to justify for beings with supposedly finite minds).

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