Date: Mar 26, 2013 3:51 PM
Subject: Re: Mathematics and the Roots of Postmodern Thought
On Mar 26, 9:18 pm, david petry <david_lawrence_pe...@yahoo.com>
> On Tuesday, March 26, 2013 4:05:38 AM UTC-7, Dan wrote:
> > Gödel's theorem is here to stay .
> As I have argued previously, if we treat mathematics as a science and accept falsifiability as the cornerstone of mathematical reasoning, then Godel's theorem is utterly utterly trivial, while at the same time, his proof of the theorem is not a valid proof.
I've had a look at that post . Certainly an interesting viewpoint .
Let he who shows an inconsistency in PA cast the first stone . Godel
never intended his proof to be just a 'hollow formalism' .
In it there appears a complex interplay of 'numbers as symbols' and
'numbers as meaning' . There must always be a certain 'metaphysical
element' that eludes formalism in discussing consistency . I would
wager my life on PA being consistent. Would you do the same for the
inverse? By eliminating this element you create a false dichotomy
between two meaningless views of mathematics .
Of A and 'not A' , only one must be true . If scientists don't believe
us because they can't see the foundation upon which our method rests ,
then so be it . They certainly won't manage to disprove us .
If you ever manage to falsify Godel's theorem or PA , then we have
something to talk about .
Until then ,they remain true . You know what can't be falsified? The
truth . The final theory . If it is in concordance with Reality,
falsification equates to falsifying Reality itself . Mathematics is
reality . Reality is infinite , as is the mind . Our formal systems
are finite .Thus , the dichotomy that is Godel's theorem . The first
principle that is to be falsified when doing mathematics is the
principle of falsifiability .