Ken,
> proven as true in a formal axiomatic system. Thus, "truth" is an
> underdetermined state when it comes to the application of enumerable
It is always important to say here that "truth" in respect to Gödel is a
mathematical notion (relationship structure/model and formal system), it
is often wrongly invoked in philosophical discussion ("Gödel said there
can be no truth .. therefor crazy idea etc")
> Gödel's second theorem states that a formal axiomatic system is complete if
> and only if it is inconsistent.
There are perfectly complete and and consistent axiomatic systems.
(propositional calculus); heck, even the mega-expressive first order
logic (see the completeness theorem).
http://en.wikipedia.org/wiki/Completeness_theorem
Incompleteness arises when you introduce arithmetic (robinson arithmetic
suffices, presburger arithmetic not; in short: you need addition and
multiplication in your arithmetic -> with this you can construct gödel
numbers, define recursion, and get your (first) incompleteness theorem,
from which second follows easily.
Cheers,
Günther
--
Günther Greindl
Department of Philosophy of Science
University of Vienna
[EMAIL PROTECTED]
Blog: http://www.complexitystudies.org/
Thesis: http://www.complexitystudies.org/proposal/
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