On 3/15/2013 7:16 PM, Virgil wrote: > 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. >
Oddly, the two converge with what is "true" in set theory to the extent that foundational claims are given credence.