Date: Mar 25, 2013 10:37 AM
Subject: Re: Mathematics and the Roots of Postmodern Thought
On Mar 25, 7:28 am, david petry <david_lawrence_pe...@yahoo.com>
> Mathematics and the Roots of Postmodern Thought
> Author: Vladimir Tasi?
> Oxford University Press, 2001
> "[this book] traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century" -- from a blurb appearing in Google Books
> I've always thought there was a connection:
> Theorem: Truth, reality and logic are mere social constructs.
> Proof: By Godel's theorem, yada, yada, yada
> I actually believe that postmodernism is driving western civilization into a dark ages. And I think that's a good reason for getting mystical metaphysical nonsense out of mathematics. But no one seems to care.
Rather ironic that you're attempting to use Godel's theorem to
undermine meaning in mathematics . Godel himself was a platonist .
His theorem is intended to show the limitations and incompleteness of
formal systems , in CONTRAST with the mathematical reality to which
they point to . The whole thing is based upon constructing a statement
that is unprovable (within the formal system) , but nonetheless true
(as far as 'mathematical reality' is concerned) .
The only thing that's seriously undermined by Godel's theorem is the
position known as mathematical formalism : the idea that mathematics
is a mere game of symbols , and we should limit our procedures of
proof and mathematics to mere algorithms ,and a finite unextendable
formalism (Principia Mathematica for example ) . Thus formalists
hoped to eliminate any 'metaphysical elements' : the meaning of the
symbols doesn't matter , just follow the rules of the game. As we
should know , meaning , to the extent that it cannot be captured in
its entirety by formalism ,is intimately related to 'metaphysics' and
inseparable from it . We should be wiser in our days , we know that
there are many things algorithms are incapable of solving (the Halting
problem for example ) , nonetheless , any well defined program either
halts of does not halt , always . Thus we should expect that the mind
can , eventually , solve any problem of the sort , regardless of the
limitations of of formalism .