In article <firstname.lastname@example.org>, david petry <email@example.com> wrote:
> On Friday, March 15, 2013 6:18:08 AM UTC-7, Jesse F. Hughes wrote: > > > I assumed that this relationship between "falsifiability" and > > mathematics allowed one to distinguish non-mathematical claims from > > mathematical claims. If not, what role does falsifiability play? In > > science, it distinguishes scientific hypotheses from non-scientific. > > Yes, exactly, I'm suggesting it would be reasonable to have falsifiability > play the same role in mathematics that it plays in science. Why do I need to > keep repeating that for you?
The reason that falsifiability is useful in science is because scientific conjectures are about how the physical world works and such conjectures can be compared to the was the world is observed to work.
But the theorems of mathematics are not about how the world works.
A mathematical model of how the world works can be shown to be a false representation, but it may still be mathematically perfectly consistent and "true" as a model, just not a good model of that aspect of reality.
Pure mathematicians are, by and large, not so much interested in how well a mathematical structure models some aspect of physical reality, where as applied mathematicians are, by and large, not so much interested in anything else. --