Failing to reject an hypothesis is a different intellectual exercise than demonstrating that elliptic curves are modular, from which it follows that Diophantine equations of order greater than two have no solutions in integers.

The Heartland Institute's Rich Trzupek hasn't yet grasped that point.  He starts with an assertion by Penn State climatologist Michael Mann that ought not to be controversial.
“Proof is for mathematical theorems and alcoholic beverages. It’s not for science,” Mann says. “Science works in evidence through best explanations, most credible theories, and so in a sense we’re at a disadvantage because we have to play by the rules, the other side doesn’t… They’re not offering up credible alternatives or explanations. In most cases they’re trying to pick holes. Not real holes, just things that the public will think are holes, in the science. We are at a disadvantage.”

Bound by honesty, the scientific consensus is going to struggle to overcome this problem, appearing unable to actually back up its results with tangible events, offering, Cassandra-like, warnings of a future that will go unheeded until it is too late.
Mr Trzupek is either suggesting that the case for consensus isn't strong enough, or is demonstrating the failure of his chemistry professors to explain methodology.  (That may be a common failing: q.v.)
Now it seems pretty obvious that Mann’s attempt to separate proof from science stems from increasing public awareness that the warming predicted by the high-sensitivity models that Mann and others have championed just hasn’t occurred over the last fifteen years. No matter. You don’t need “proof” when you have “credible theories.”

That comes as something of a shock to me. When I was going to school to earn my degree in chemistry, we were taught that science was indeed all about absolute truths and proofs at the end of the day. “Credible theories” is how you got to those truths, not an alternative to them.
Where you have anomalies, you have to reexamine the premises of your models. Where the evidence is refractory, you have to be particularly sensitive to the possibility that complex adaptive systems do what they darn well please, as well as to the premises of your model.  Here's where the academic stance (no final say) conflicts with Political Principle.  Mr Trzupek responds to some of his critics.
Anyway, the point of my particular screed was not to reaffirm the difference between Chesterson’s (rather obvious) point that two plus two equals four because there can be no other result, and the scientific need for proof in our discipline’s eternal search for truth. It was to re-emphasize the fact that offering evidence that your particular hypothesis approaches reality is even more important in the scientific sphere. Such evidence is not to be despised, but rather to be embraced.
Well, 2 + 2 = 11(3). We generally don't work in base 3 in intellectual endeavours. But when intellectual endeavours take on political colouration, then the fun begins.
In my case, as a chemist, I see the intricacies of my discipline misrepresented by the “environmental movement” on a regular basis. And the reasons I use my skill as a communicator (however poor those skills may be) to push back against those misrepresentations are my love for science in general, and for chemistry in particular.
Those misrepresentations might be political. To make sense of the evidence, though, it takes a theory to beat a theory.
You can have an idea that seems right, and is supported by some observations, but may eventually be shown wrong (or incomplete) by better tests. Ideas are tentative. Provisional.

Of course, some ideas are better than others. It turns out some do an excellent job describing reality, and some not so much. And even the ones that are good can be better.
The problem isn't necessarily with the theories, or even with the evidence. It's more often with the policy implications.
From climate science we know the Earth is warming; the evidence for that is overwhelming. We know humans are at least partially if not mostly to blame for these increasing temperatures; the evidence for that is overwhelming. We know the ramifications are costly at best and catastrophic at worst; the evidence for that is overwhelming.
Yes, and what to do about the evidence, and how to choose to respond to that evidence and at the same time to all the other troubles confronting people, is outside the realm of settled science.  The best social scientists can do is often to teach the controversies.

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