In physics we call some results “laws” and some “theories.” The difference has absolutely nothing to do with our certainty in the validity of the results.
Newton’s Laws of motion are called that because they can be written as concise mathematical equations, and allof the content is there. Einstein’s Theory of special relativity is just as valid, and even contains Newton’s Laws as a special case, but the content of the theory can’t be written in simple, concise equations. There are several equations included in special relativity, but they do not represent the entire content. For example, the most important statement of the theory cannot be written in equation form at all: “The measured speed of light in a vacuum will be the same for all observers in inertial reference frames, regardless of the relative speed of their reference frame.”
Darwin’s Theory of Evolution likewise cannot be written in concise statements (mathematical or otherwise), but our certainty in its validity is no less than in Newton’s Laws.
Another important subtlety: I was careful to say that we are certain of the validity. People who don’t know better are fond of saying that Newton’s Laws are wrong. This is a fallacy. Scientific laws and theories can only be valid or not, they can never be true.
In physics we call some results “laws” and some “theories.” The difference has absolutely nothing to do with our certainty in the validity of the results.
Newton’s Laws of motion are called that because they can be written as concise mathematical equations, and allof the content is there. Einstein’s Theory of special relativity is just as valid, and even contains Newton’s Laws as a special case, but the content of the theory can’t be written in simple, concise equations. There are several equations included in special relativity, but they do not represent the entire content. For example, the most important statement of the theory cannot be written in equation form at all: “The measured speed of light in a vacuum will be the same for all observers in inertial reference frames, regardless of the relative speed of their reference frame.”
Darwin’s Theory of Evolution likewise cannot be written in concise statements (mathematical or otherwise), but our certainty in its validity is no less than in Newton’s Laws.
Another important subtlety: I was careful to say that we are certain of the validity. People who don’t know better are fond of saying that Newton’s Laws are wrong. This is a fallacy. Scientific laws and theories can only be valid or not, they can never be true.
Now do theorem
You mean, as opposed to lemma? I’ve never been confident that I understand the difference between those. :(