Date: Mar 25, 2013 10:37 AM
Author: dan.ms.chaos@gmail.com
Subject: Re: Mathematics and the Roots of Postmodern Thought
On Mar 25, 7:28 am, david petry <david_lawrence_pe...@yahoo.com>

wrote:

> 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 .