<firstname.lastname@example.org> wrote in message news:email@example.com... > Karl Malbrain wrote: >> Patricia Shanahan wrote:
> Let theory A be geometry using Euclid's rules, including the parallel > postulate; i.e., loosely speaking, that parallel lines don't intersect. > > > Let theory B be Euclid's postulates, excluding the parallel postulate, > and instead including the postulate that every pair of distinct > parallel lines intersect at two points. > > Theory A is useful in certain cases; theory B is useful in other cases. > Why must one be "true" and the other "false", simply because the two > theories contradict each other?
If we are to believe the physicists, theory B describes the "real" world and theory A is an idealization that only works "locally".
I don't think a physicist would ever say something is "true", but one might say Euclidian geometry is "false". A pair of parallel lines do intersect at two points.