"T.H. Ray" wrote: > > ... > > In the conventional sense of "experiment," in empirical > term, falsifiability implies the failure of theory. Not > so in mathematics, where theories are only falsifiable > in the context of their theoretical self-consistency.
I may have missed your point, but it is the same in mathematics as well. Suppose one wonders if ab = ba; no experiment that shows for particular a's and b's that ab = ba will prove commutativity, but one experiment that shows that ab =/= ba will disprove it.
> Thus -- the canon of experimental science is constantly > being revised to subtract falsified theories. Not so > with mathematics, in which a theorem once proved is always > true (though not always useful). That makes mathematics > a liberal art, not an empirical science. > > Tom
-- The world will little note, nor long remember, what we say here.