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 .