@Cognostic,

"Proof" is the word that applies to mathematics or other systems of pure logic (such as chess) that are defined by a set of given postulates. A theorem is proven when the tools of deductive reasoning can derive it from the postulates and/or other proven theorems. Any logical loophole is fatal to such a proof.

In the world of atoms and energy (and anything that can affect that world) we use inductive reasoning to arrive at new discoveries. (Deductive reasoning has the important role of testing what we think is right.) Inductive reasoning begins with the accepted evidence (those "facts" that we are highly confident of) and hopefully ends up with a cause that is heads and shoulders above any other conclusion. The acid test is for that explanation to make non-trivial predictions that can be checked out. The "checking" might involve a laboratory experiment or a geological trip. If an idea leads to numerous good predictions and deep insights, generating a whole fruitful area of exploration, and fits in with other conclusions that have earned their stripes, being a good explanation for a wide range of related observations, then it becomes a scientific "theory." (Scientific theories are not half-baked! That's the vulgar, common definition of "theory.") Think of "atomic theory."

Since an infinite number of explanations can be attached to any set of facts, there will always be loopholes. Thus, certainty seems to be impossible in the world of atoms and energy. (If you have consciousness, that might be the only thing you can be 100% certain of.) "Proof," then, is not the criteria for the world of atoms and energy. The currency is credibility. Every time an idea predicts something unexpected or survives a rigorous test it becomes more credible. When our confidence in an idea becomes so strong that we consider it perverse to seriously debate it as though it might be wrong, then we might call it a "fact." The fact of biological evolution and the fact that the sun will rise tomorrow are examples. However, even these facts are not written in stone since we must allow the logical possibility that some startling new evidence might change everything. (Ever watch the "Matrix"?) We accept them but we don't write them in stone. Thus, a good scientist will often tell you that certainty is not what science is about, but that doesn't make one idea as good as another. We are very confident in some ideas while considering others far-fetched.

So, evidence is vital for defining the degree of confidence we have in an idea. Every scientific theory rests on a mountain of evidence. If an hypothesis is strongly confirmed we sometimes loosely say that it has been "proven," but that is really a word for deductive systems of logic. In that sense evidence doesn't prove anything, but it does add degrees of credibility to a claim, sometimes leading all the way to successful theories. Or, it may shoot a claim down!