Date: Apr 1, 2013 2:31 AM
Author: fom
Subject: Re: Mathematics and the Roots of Postmodern Thought

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 <david_lawrence_petry@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.
>


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.

http://en.wikipedia.org/wiki/Utility#Discussion_and_criticism

http://en.wikipedia.org/wiki/Applied_mathematics#Utility

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?

plato.stanford.edu/entries/epistemic-utility/

And, in the article on scientific progress cited below,
you will find comment:

"... truth cannot be the only relevant epistemic
utility of inquiry"

http://plato.stanford.edu/entries/scientific-progress/#TruInf

They conveniently note that the most notable proponent
of falsifiability had been aware of this.