On 3/31/2013 11:20 PM, david petry wrote: > On Saturday, March 30, 2013 5:33:12 AM UTC-7, Jesse F. Hughes wrote: > >> david petry <email@example.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. >
Well, I do not know if that conclusion necessarily follows. But, it would seem that you are advocating a "utility criterion" for deciding what may and what may not constitute mathematics.
The question becomes, then, how can one know what constitutes mathematics in advance of the needs of those who would apply that criterion? How shall we understand truth-directed epistemic utility under the assumption that truth is a principal goal of empirical science?
And, in the article on scientific progress cited below, you will find comment:
"... truth cannot be the only relevant epistemic utility of inquiry"