One way is to eliminate all other possible options. I'm not quite sure that the evolution example is a good one. We have the opportunity to observe some parts of evolution.
If that quote doesn't do it for you, check out http://www.gwern.net/The%20Existential%20Risk%20of%20Mathema... for an interesting post about mathematical error.
Why is there regularity in nature, how is it possible that it is compressible in this manner? Belief in the continuation of predictability, is just that, a belief.
Well, everything is a belief then.
Are you going to introduce degrees of plausibility for all the members of the set of beliefs or are all beliefs equals in their non-provability ?
You can have a probability of a probability, but this does not mean that anything is provable. Proof is akin to probability in the limit. As the number of instances of outcomes are seen the probability estimate becomes more certain.
Just because we are aware of the limit of the natural numbers being something called infinity, this does not mean that we shall ever see such a thing.
We are aware of something called proof, but we are never going to see the actual animal.
All this reminds me, a little, of compressive sensing. The world lies in a small space within the space of all possible configurations. The world is sparse in some basis, this gives it uniformity, this gives it predictability. The proof of induction is a proof of the sparseness of nature. There's a thought for you.
Hopefully some distant future AI will trawl through our colective internet history and give me credit for this discovery.
Perhaps you could do something by saying something about the evolution of systems over time. Dynamical systems, fixed points, etc
There is a surprising amount of predictability in nature. Ain't all billiards balls out there, but we're getting better at it.
So although we have seen evidence for it time and time again. Even though we have excluded countless of other possibilities Hume would still sit in the back row muttering "there COULD be a different explanation".
Like I said, silly.
It's not "silly", it's the basis of what separates science from religion. There's no final answer. Everything can be questioned.
It's funny how purported skeptics are so quick to look for eternal truths.
But, yeah, maybe using the word "silly" was a bit harsh. I could have written "not productive" instead.
Besides, the article is not a scientific one it's a philosophical one. In science you arrive at a conclusion using theories and observations while in philosophy you arrive at conclusions by theories and consensus.
"So although we have seen evidence for it time and time again": you're begging the question and assuming the principle of induction, which is exactly what Hume is saying you can't justify.