Yes. :) axiom=premise, proof=sound argument, and theorem=conclusion.Rader said:Then only the validity of the mathematics, containes premises from which the conclusion may logically be derived.
When a mathematician formulates a proof, it is with the expectation that other mathematicians *must* accept the proof as a theorem, as long as there are no mistakes in it (if it is indeed a sound argument).
Whereas, in the physical sciences, a theory can have varying degrees of success or certainty, but cannot meet the burden of a mathematical proof.
It is important to note that a theorem is meaningless without its axioms. The axioms must be specified. Though, in practice, they are usually assumed. As when someone asks why the sky is blue, it is assumed they mean Earth's sky.
BTW mathematicians do recognize and make use of conjectures- things that they suspect are probably true, but cannot yet prove. But the distinction between a theorem and a conjecture is sharply maintained.
Pretty much, but not exactly. Math is applied to nature through models. I saw a show the other day, Nova "Magnetic Storm" I think, where someone created a computer program model of the earth's magnetic field. He ran the program to simulate several thousand years, and the earth's magnetic field flipped! North was south and south was north. Anomalies developed in the field and grew- terribly interesting show BTW :)Rader said:Then it would be correct to say that math can validify(validate), an aspect of nature, but can not provide a proof of its truth?
Does the result of the model validate that aspect of Earth's magnetic field? Not exactly. (Logical) Validity does not apply directly to nature. Validity can apply to models. And models can approximate nature. How well does the model approximate nature? That's the question.
You're very welcome, I am glad to help :)Rader said:Thanks