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?
Im reading Truesdell's (America's greatest 20th century physicist?) book now where he goes through the history of fluid mechanics and the paucity of experiments. If I remember ill send you the reference
"The computer: ruin of science and threat to mankind”
https://people.maths.ox.ac.uk/~ball/Miscelleaneous%20Article...
Bloody brilliant. 70 years ago he foresaw the problems of modern science.
Interestingly enough I just realized in Italian there is an old word, "dotto" that literally would mean "someone who has been taught" but concretely is used in the sense of well educated, knowledgeable, wise, cultured.
Bologna, the home of the first university, has the nickname "la Dotta", i.e. the educated one.
the very definition of a "theory" in the scientific sense of the word (e.g. "theory of evolution") includes the ability to test it using the scientific method.
the wikipedia page goes into great detail: https://en.wikipedia.org/wiki/Scientific_theory
and this is a good brief explanation: https://web.archive.org/web/20170709065046/http://science.ke...
Jumping to specifics, Evolution Theory is relatively easy to demonstrate on short time scales of under a year with fruit flies, and can also be demonstrated on longer timescales of five, ten, thirty years given patience .. with ongoing field observations of some two centuries now in various locations.
https://www.the-scientist.com/news-opinion/fruit-flies-evolv...
And yes, I know about little bugs changing color and bacteria becoming resistant to antibiotics.
But, strictly speaking, that isnt what we're taught is "science" in 10th grade, is it? That's really an observation of what we cannot control fitting nicely into our theories.
The embarrassing thing about evolution is that biologists keep having to tweek it in ways that are bewildering if evolution is (I think better) understood as information theory. For example, why did biologists reject horizontal gene transfer?
Anyway the whole field is sitting atop of an ignored quantity-quality emergent behavior which is also the most interesting question.
PhD is the degree you usually get at that level for English, Classics, Economics, Histrory etc..
Some Universities use DPhil (Oxford) for all these but I know of no other degree at that level except for those two (MD is effectively lower and DSc is usually some form of honourary degree and I am not certain what LLD is)
https://oge.mit.edu/graduate-admissions/programs/doctoral-de...
Most early physic had surprisingly little explanatory or experimental connection to the actual physical world.
But it often made up for that with a solid grounding in popular mythology and the produce of some extraordinary imaginations.
You know, like philosophy!
Anyway, those crazies came up with atomistic theory to explain silly myths.... and ended up explaining phase change as an emergent phenomenon.
The ancients were not just the famous Greek, Roman, Babylonian, Indian and Chinese philosophers, who made progress in reasoning.
Human's across every culture have spun creative explanations for natural phenomena, going back as far as we have any records.
- Why does it rain? How can we make it rain?
- What are the planets? What do their cycles and alignments mean?
- What is an illness? How do we avoid it? Cure it?
Even those philosophers were not immune to this kind of thinking.
Non/Pre-scientific answers to unanswerable questions gave satisfied people’s need for order and gave them hope.
Today, many people still take such answers seriously where there is no science (afterlife, cosmic justice, ...), and even where there is (astrology, crystals, etc.)