david petry <email@example.com> writes:
> On Saturday, March 30, 2013 5:33:12 AM UTC-7, Jesse F. Hughes wrote: > >> david petry <firstname.lastname@example.org> 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.
I still don't understand.
Can you give an example of some piece of mathematics that an applied mathematician would choose to avoid, because it's not "falsifiable"?
And can you tell me whether the axioms of, say, the theory of real numbers are falsifiable? If so, can you please give me an argument to that effect?
Of course, if the theory of real numbers is not falsifiable, it would seem you have a problem, right? Don't applied mathematicians (and scientists!) use that theory regularly?
-- Jesse F. Hughes
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