I think you're being partially blinded by a complex definition of science. A more intuitive notion of science is that the strength of an idea is based on evide

I think you're being partially blinded by a complex definition of science. A more intuitive notion of science is that the strength of an idea is based on evidence alone. The philosophers will hate you but science will make more sense. > There's no particular reason that you've got to be able to build an isomorphism between a class of evidence and a numeric type in order for that evidence to be valuable and scientific. As you hinted at, the experiment has been unofficially done many times and the evidence suggests the quantitative approach is better. That is the particular reason as far as I can tell. (Numbers may not be technically essential, but measurement and comparison are. That leads to things like everybody agreeing that a piece of metal in Europe is exactly one kilogram and everybody talks about mass in reference to that one object. It was a qualitative decision to choose which kilogram became the standard, but from then on measuring mass was quantitative and easily communicable. Fields that can't establish conventions for their observables in this way are generally not very scientific.) My argument was that when holding the field constant puts qualitative and quantitative science on the same footing, it's a bad sign for that field. Take chemistry: when qualitative arguments were equal to quantitative it was called Alchemy. When quantitative approaches took over it changed the world.