On 27 Jul 2011, at 15:36, benjayk wrote:
Bruno Marchal wrote:
On 24 Jul 2011, at 22:08, benjayk wrote:
Yes. A tiny part of arithmetic is already sufficiently rich to
implement (in the original mathematical sense) very complex
emulation
bearing entities much powerfull than that tiny arithmetical
entities,
and those can become lucid on the web of arithmetical dream, which
will be, as seen from inside (the points of view), terribly
complex,
so that paradoxically, the whole of mathematics can only scratch
the
arithmetical truth. Analytical truth and physical truth are
simplification of the arithmetical truth by arithmetical creatures.
I think you confuse arithmetical truth with TRUTH.
That is a consequence of comp. If "we" are machine at some level,
then
it is absolutely undecidable if there is anything more than
arithmetical truth.
The analytical truth and the physical truth and the theological truth
can be seen as internal "epistemological views". In arithmetic there
are defined by Bp, or variants, or by by scheme B_n x & x (x
arithmetical formula, B_n being some other Löbian machine, for
example)
My point is that this truth has little to do with arithmetic in
particular.
Indeed, any first order specification of a universal system will do.
They are "ontologically" equivalent: with the combinators you have the
numbers, and with the numbers, you have the combinators. So
combinatoric truth and arithmetical truth, and Conway-game-of-life
truth are all the same truth, with different shape or implementations.
Arithmetic just happens to be powerful enough to point towards it.
All other
universal systems accomplish the same. So to say just number
relations exist
and all else is an "epistemological view" on that is a very narrow
interpretation.
Arithmetical truth contains fortranic truth, lispic truth,
combinatoric truth, etc.
It does not contains theological truth, nor physical truth, except in
the 'epistemological' points of view of the creature they have all.
So, arithmetic is made into a theory of everything, and arithmetical
truth does play the role of the big unameable things. If you take
fortran programs as ontology, exactly the same can be said. Once you
search a theory of everything, comp does confuse truth and
arithmetical truth, or Truth and fortranic truth, etc. When number
relation exist, all other universal system exist in a similar
ontological sense. In arithmetical truth the fortranic truth is
automatically given, you don't need to introduce points of view,
unlike the analytical and the physical, for which you need the
epistemology (to interview the fortran program or the numbers).
Bruno
--
View this message in context:
http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p32148047.html
Sent from the Everything List mailing list archive at Nabble.com.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com
.
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
