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PhD is a license to teach (i.e. doctor) philosophy. Specifically, in "science" fields, natural philosophy. Natural philosophy was the original (and i think better) name for science, especially physics. It was understood to be an important subbranch of philosophy. I think its better name because it elucidates an important epistemological difference: science is a method, not knowledge. I learn science when I learn about experimental design. Im not learning science when I learn about evolution; rather Im learning a theory, very likely to be true, that is almost impossible to put under scrutiny using the scientific method. The Pythagorean theorem has no science and is 100% true. In fluids, Bernoulli devised experiments to demonstrate to his calculus illiterate colleagues what he had already mathematically proven. Science is a bad term. |
Maybe I misunderstood you, but I have the feeling you're downplaying the importance of experiments in Physics. Once you mathematically prove something, you proved that a statement is true when given a certain set of axioms. This is enough in Mathematics, like your example of the Pythagorean theorem, but it isn't in Physics. The reason being that proving something Mathematically consistent isn't enough to prove that it reflects what happens in the real world. A famous example in pop science of this is string theory.
I also have some doubts about what you say regarding evolution theory, but I'm not familiar whit how biologists verified it. Maybe every time a new fossil is found we can consider it as an experiment that can add a data point in favor or against the theory?