[Will]

Hunpecked and Renegade: alarikf is right here. You do not throw out an entire theory as invalid just because some data does not fit the model, but other data fits perfectly well. If you are going to throw out a theory that works in some cases, you need to present another theory that explains the data that fits the existing theory, and also explains some of the data that does not fit the existing theory. Until then, you only add on constraints to the existing model stating under what conditions the model is reasonably accurate, and under what conditions the model fails.

Renegade, your mathematical example is contrived. That is a simple equation, with two unknowns, that can trivially be shown false for values of y not equal to 1. I would propose that this "theorem" remains perfectly valid as long as we are restricting y in this way. It will even predict results with reasonable accuracy as long as y is very close to 1. What alarikf is saying is that it would be preposterous to use the example of x=0.6 and y=2.5 to throw out the entire statement when it works perfectly well with y=1.0. This is the same reasoning behind the Copernican->Newtonian->Einsteinian models for how the planets move the way they do. Children are still started off with a model like the one of Copernicus (minus the ether part) for the solar system. I know I believed that the orbits of the planets (except for Pluto) was perfectly circular. And that's alright for the basic rote learning of small children, who aren't expected to know the dynamics of motion yet. The theory is later supplanted in school by the Newtonian model for physics, where I learned that Pluto wasn't the only odd one, and all the planets had elliptical orbits, and for 99+% of situations, Newton is perfectly adequate. Einstein added more that explained difficult bits like how Mercury's orbit acted the way it did without the influence of another planet, and how things change around black holes, etc. Each iteration of the model came about because we got more data, and the data was more accurate, and the model changed based on this. But if we use Einstein's model of gravity, we will still get results that look a lot like what we would get with Copernicus' model. And if I only use y=1, the equation (2x)/(xy) = 2 will still hold. You can complain all you want about some anomalies, but if a lot of the data still fits, and you don't have a better model, any good scientist MUST use the best existing model, or supplant it with an improved version.