Date: Apr 1, 2013 5:25 AM
Subject: Re: Mathematics and the Roots of Postmodern Thought
On Apr 1, 7:20 am, david petry <david_lawrence_pe...@yahoo.com> wrote:
> On Saturday, March 30, 2013 5:33:12 AM UTC-7, Jesse F. Hughes wrote:
> > david petry <david_lawrence_pe...@yahoo.com> writes:
> > > Here's what I actually believe: Falsifiability, which is the
> > > cornerstone of scientific reasoning, can be formalized in such a way
> > > that it can serve as the cornerstone of mathematical reasoning. And
> > > in fact, it's already part of the reasoning used by applied
> > > mathematicians; ZFC, which is not compatible with falsifiability, is
> > > not a formalization of the mathematical reasoning used in applied
> > > mathematics. Also, Godel's proof is not compatible with
> > > falsifiability.
> > You say that falsifiability is "already part of the reasoning used by
> > applied mathematicians."
> > What do you mean?
> Applied mathematicians know they have to produce something that is of use to the scientists, which does imply that they are taking falsifiability into consideration.
Real mathematicians do their own thing ... no physicist thought
Hilbert spaces or Riemannian geometry would have any real application
when they first appeared . Scientists take the mathematics given to
them (which , I repeat , relative to itself is not falsifiable , but
simply true (2+2 = 4 , or the Fermat's theorem for that matter, is not
falsifiable) , and use it to build theories in a (mostly) falsifiable
(yet still horrid ,adhoc , and inconsistent , if you consider
ultraviolet divergence for example) manner . If scientists ever
happen to come about a true theory,that predicts that event A will not
happen, then that theory is not falsifiable , even if scientists
believe it so . Event A simply will not happen . Or , you could have a
definition of a 'falsifiable but never falsified theory' , that would
seem awkward .
The point relating to mathematics is :
Suppose I give you , the scientist, a proof that Fermat's theorem has
no counterexamples .Then you , nonetheless , proceed to build a
machine , that runs continually ,cheeking for counterexamples (until
it runs out of memory) . What you're implying in this situation is
that one of us is an idiot .