Re: The Relativity of Existence

[meekerdb]

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

The Relativity of Existence

Authors: Stuart Heinrich

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 everyth...@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

[Richard Ruquist]

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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[acw]

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

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).

[meekerdb]

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

Brent

[Bruno Marchal]

Provable depends on the theory. If the theory is unsound, what it
proves might well be false.

And if you trust the theory, then you know that "the theory is
consistent" is true, yet the theory itself cannot prove it, so reality
is larger that what you can prove in that theory.

So in any case truth is larger than the theory. Even when truth is
restricted to arithmetical propositions. Notably because the statement
"the theory is consistent" can be translated into an arithmetical
proposition.

Bruno


http://iridia.ulb.ac.be/~marchal/

[meekerdb]

Does arithmetic have 'finite information content'? Is the axiom of succession just one or
is it a schema of infinitely many axioms?

Brent

[Bruno Marchal]

Arithmetical truth has infinite information content.

Peano Arithmetic has about 5K of information content, even with the
infinitely many induction axioms, for they are simple to generate.
There are two succession axioms (0 ≠ s(x), and s(x) = s(y) .-> x = y.
Those are not scheme of axioms.

Bruno



http://iridia.ulb.ac.be/~marchal/

[meekerdb]

That's what I thought. So the above Excerpt does not contradict Godel's incompleteness
because it refers to "systems with finite information content".

>
> Peano Arithmetic has about 5K of information content,

Which is just the information in the axioms (actually that number seems high to me).

Brent

[Bruno Marchal]

Gödel's theorem applies also to many systems with infinite information
content. Even arithmetical truth itself is undecided on many second
order arithmetical propositions, and some occurs naturally like in the
G* (first order) modal logic.

Arithmetic has few information content, but "arithmetic seen from
inside" as an infinite (and beyond!) information content. This should
be the case for any proposed TOE.

>
>>
>> Peano Arithmetic has about 5K of information content,
>
> Which is just the information in the axioms (actually that number
> seems high to me).

OK. (I said 5K to imply it is very little, but 5K is much too much
indeed). Note that my computer already uses 4K for an empty document,
but that kind of thing is very contingent.

Bruno

>
> Brent
>
>> even with the infinitely many induction axioms, for they are simple
>> to generate. There are two succession axioms (0 ≠ s(x), and s(x) =
>> s(y) .-> x = y. Those are not scheme of axioms.
>>
>> Bruno
>>
>>
>>
>> http://iridia.ulb.ac.be/~marchal/
>>
>>
>>
>

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http://iridia.ulb.ac.be/~marchal/