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
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