firstname.lastname@example.org (Jim Carr) writes: | |A counter-example can overturn a theory as well, but the main |difference is that mathematical consistency of a physical theory |is only part of what we mean by a good theory, whereas it is |all that we demand of a good theorem.
Torkel Franzen <email@example.com> writes: > > What should a good theorem be consistent with?
Maybe it was a poorly formed sentence. A good theorem must be consistent with the axioms and definitions that establish the mathematical system it lives in; that is, it must be proved true. Hence, a single counter-example can prove it wrong.
A good theory must be all of that, and be consistent with data. Since data have experimental uncertainties, a single datum is seldom sufficient to cause the collapse of a theory.
-- James A. Carr <firstname.lastname@example.org> | "They invented band!" http://www.scri.fsu.edu/~jac/ | Spectator at 1997 inaugural parade Supercomputer Computations Res. Inst. | commenting on the Macarena done by Florida State, Tallahassee FL 32306 | the Florida A&M Marching 100