On 2/9/2012 3:40 PM, acw wrote:
Another way to think of it would be in the terms of the Church Turing
Thesis, where you expect that a computation (in the Turing sense) to
have result and that result is independent of all your
implementations, such a result not being changeable in any way or by
anything - that's usually what I imagine by Platonia. It is a bit
mystical, but I find it less mystical than requiring a magical
physical substrate (even more after MGA) - to me the platonic
implementation seems to be the simplest possible explanation. If you
think it's a bad explanation that introduces some magic, I'll respond
that the primitively physical version introduces even more magic.
Making truth changeable or temporal seems to me to be a much stronger,
much more "magical" than what I'm considering: that arithmetical
sentences do have a truth value, regardless if we know it or not.
[SPK]
I am only asking that we put the abstract world of mathematics on an
even footing with the physical world, I am _not_ asking for a
"primitive" physical world. I will say again, just because a computation
is independent for any particular implementation that I, you or any one
else is capable of creating does not eliminate the necessity that
somehow it must be implemented physically. Universality of computation
is NOT the severing of computation from its physical implementability.
This is not the same kind of claim as we see of the ultrafinitist and/or
constructivist; it is just a realistic demand that ideas cannot be free
floating entities. We cannot believe in free floating numbers any more
than we can believe in disembodies spirits and ghosts.
What is a non-primitive physical world, what is it based on?
'Existence'? What is that, sounds primitive to me. If we accept
'existence' as primitive, how does math and physical arise out of it?
It seems so general to me that I can't imagine anything at all about
it, to the point of being a God-like non-theory (although I can
sympathize with it, just that it cannot be used as a theory because
it's too general. We'll probably have to settle with something which
we can discuss, such as a part of math.)
Why is 'physical' implementation so important? Those "free floating"
numbers could very well represent the structures that we and our
universe happen to be and their truths may very well sometimes be this
thing we call 'consciousness'. As for 'spirits' - how does this
'consciousness' thing know which body to follow and observe? How does
it correlate that it must correlate to the physical states present in
the brain? How does it know to appear in a robotic body or VR
environment if someone decides to "upload" their mind (sometime in the
far future)? What's this continuity of consciousness thing?
Granted that some particular mathematical structure could represent
the physical, I'm not sure it makes sense gran the physical any more
meaning than "that which we(our bodies) observe as being part of".
Hi ACW,
A "non-primitive world" would be a world that is defined by a set
of communications between observers, however the observers are defined.
The notion of a "cyclical gossiping" as used in graph theory gives a
nice model of how this would work and it even shows a nice toy model of
thermodynamic entropy. See #58 here
<http://books.google.com/books?id=SbZKSZ-1qrwC&pg=PA32&lpg=PA32&dq=cyclical+gossiping+graph+theory&source=bl&ots=NAvDjdj7u-&sig=kk03XrGRBzdVWI09bh_-yrACM64&hl=en&sa=X&ei=jCI1T8TpM4O4tweVgMG_Ag&sqi=2&ved=0CC8Q6AEwAg#v=onepage&q&f=false>
for a statement of this idea. Also see
http://mathworld.wolfram.com/Gossiping.html
Onward!
Stephen
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