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 
> Heinrich<http://arxiv.org/find/physics/1/au:+Heinrich_S/0/1/0/all/0/1>
> 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.
>
>
>
> http://arxiv.org/pdf/1202.4545.pdf
>
>
>
> "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
> consistent."
>     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
> true,"
>     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.
> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
> If you join the everything-list@googlegroups.com , he will explain it to
> you.
>
> "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.
>
>
> Brent
>

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

>
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