On Mar 26, 9:18 pm, david petry <david_lawrence_pe...@yahoo.com> wrote: > 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. > > https://groups.google.com/group/sci.math/msg/25be708362cb7e?
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 .