david petry <firstname.lastname@example.org> writes:
> 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? >
Okay, so then Fermat's last theorem is a proper mathematical statement (i.e., is falsfiable) and its negation isn't.
And Goldbach's conjecture is a proper mathematical statement and its negation isn't.
And, given a certain plausible set of assumptions regarding observations of the universe, "the universe is infinite" is a proper scientific hypothesis, but "the universe is finite" is non-scientific (because the former is falsifiable in principle and the latter is not).
Very well. If you're happy claiming that it's good mathematics to investigate Goldbach's conjecture, but bad mathematics to investigate its negation, well, more power to you. Courage of your oddball convictions, and all that.
-- Jesse F. Hughes "[Lancelot] sighed, defeated. 'It is as practical to hurry an acorn toward treeness as to urge a damsel when her mind is set.'" -- John Steinbeck, /The Acts of King Arthur and His Noble Knights/