On Apr 1, 8:36 pm, david petry <david_lawrence_pe...@yahoo.com> wrote: > On Monday, April 1, 2013 2:25:31 AM UTC-7, Dan wrote: > > On Apr 1, 7:20 am, david petry <david_lawrence_pe...@yahoo.com> wrote: > > > 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 > > Are you suggesting that applied mathematicians are not real mathematicians? > > > Scientists take the mathematics given to > > them [...] and use it to build theories > > Revisionist history? A huge amount of mathematics was developed by scientists simply because they needed it, and then the mathematicians took it and added their own bells and whistles.
Our "limited model" of Real Numbers, Geometry , or Peano Arithmetic has always worked flawlessly , never needing revision ,(the epitome of falsifiability) , at most needing completion with new axioms , trough reflection (not unlike the transfinite sequence of ordinals) . Falsifiability only comes into consideration when you have something apparently 'external' against which to test your mathematical models . Your mathematical models are proven wrong only because Reality, by definition , is right . Mathematics, in and of itself ,has no 'external elements' , is self-consistent, therefore not falsifiable . What's so hard to understand?
Upon perceiving the World, by contrast, we always must return to Mathematics to build our models, lest it remain , to us , unstructured chaos .
I see no further way in which I could contribute to this discussion . So , by all means, go ahead .Develop your models and concepts of 'falsifiable mathematics' .
"If the fool would persist in his folly he would become wise." - William Blake