Assuming both use accepted rules of logic, which of the two theories would be accepted and on what basis, for example: simplicity etc.
closed as primarily opinion-based by tfb, John Rennie, user191954, Jon Custer, glS Oct 1 '18 at 16:04
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It is rare that two completely different models account equally well for observations. What is more common is that one of them maintains its accuracy over a broader range of experimental conditions, or that one successfully predicts new phenomena that the other does not.
For example, when dealing with things like the earth orbiting the sun or how to do corrective burns to guide a space probe to Pluto, Newtonian gravity works just as well as general relativity does. But when dealing with extremely massive objects like collapsing stars, GR predicts black holes, time dilation, and gravitational waves that travel at the speed of light, and Newtonian gravity does not. As such it is a closer representation of nature than Newtonian gravity.
Note that in this context, physicists already know that there lies a domain in which general relativity will inevitably fail: it cannot furnish a mathematical description of the singularity at the center of a black hole. GR will itself be superceded by another model in that realm, which no one yet knows how to formulate. In any case, for that new model to be considered valid or correct, it must accurately account for everything that Newtonian gravity and GR now account for (and furnish testable predictions).