Bruno Marchal wrote:
Tegmark argues that reality is a mathematical structure and states that an
open problem is finding a mathematical structure which is isomorphic to
reality. This might or might not be clear: the mathematical structure with
the property that all mathematical structures can be embedded within it is
precisely the mathematical structure we are looking for.

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The problem is in defining "embedded". I am not sure it makes set
theoretical sense, unless you believe in Quine's New foundation (NF). I am
neutral on the consistency of NF. With a large sense of "embedded" I may
argue that the mathematical structure you are looking for is just the
(mathematical) universal machine. In which case Robinson arithmetic (a tiny
fragment of arithmetical truth, on which both platonist and non platonist
(intuitionist) is enough. Indeed, I argue with comp that Robinson
arithmetic, or any first order specification of a (Turing) universal theory
is enough to derive the appearance of quanta and qualia.
Actually, I'm using what's called NF with urelements (NFU) which according
to what I've read is consistent.
http://plato.stanford.edu/archives/sum2009/entries/quine-nf/ (section 7.
Coda).
Where would I go about finding out a survey of concepts including "universal
machine"? Are they known to exist? How are they defined? It would be much
easier if I didn't have to reinvent the wheel.
The last sentence in the quote excites me: The leap from mathematics to
things such as quanta and qualia is something I haven't really understood.
Digital mechanism (the tiny arithmetic TOE) entails already a large part of
Quantum Mechanics, and then group or category theoretic considerations (and
knot theory) might explain the 'illusions' of time, space, particle, and
(symmetrical) hamiltonians, and why indeed physical reality should appear as
an indeterminate state of a physical vacuum. But the logic-math problems
remaining are not easy to solve. That is normal in a such top down,
mind-body problem driven, approach to physics (and
psychology/theology/biology).
Interesting!
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