On 3/1/2012 7:37 PM, Richard Ruquist wrote:


On Thu, Mar 1, 2012 at 7:14 PM, meekerdb <meeke...@verizon.net <mailto: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
    
<http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHALAbstract.html>  
If
    you join the everything-list@googlegroups.com
    <mailto: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

Presumably those true things would not be 'real'. Only provable things would be true of reality.

Brent

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