Originally posted by adam warlock
I was only talking about the word principle in the context of Physics.
The thing is that I like to use coherent language and the incoherent usage of Law and Principle in Physics rubs the wrong way.
I look at it this way:
An Uncertainty Theorem would apply to a given situation, and can be proved.
From your original link I take these two quotes:
"A recurring theme in mathematics is that of duality:"
"....thanks to various mathematical manifestations of the uncertainty principle."
One could almost call 'duality' a principle, but it is not a general rule, hence the weaker 'theme'.
A principle is not a single instance of a law, but a more general rule that seems to apply to more than one situation - but can't necessarily be stated exactly.
Lets think about the principle "opposites attract". It can be applied to magnetism, electricity, and even boys and girls. It is not a Theorem.
So you may find the 'uncertainty principle' manifesting itself in different situations, and for each situation, you could have an 'uncertainty Theorem'.
"In quantum mechanics, the Heisenberg uncertainty principle states by precise inequalities that certain pairs of physical properties, like position and momentum, cannot simultaneously be known to arbitrary precision."
Notice the generality of the statement. "Certain pairs of physical properties".
If you go down the page you will find various 'uncertainty principles' in maths and physics, and finally some 'uncertainty theorems'.
Is it just tradition, or a subtle difference in the meanings of 'principle', 'law' and 'Theorem'?