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 .