The Fundamental Axiom of Science

I was checking my list of unpublished drafts (it is reasonably large, I must say) and found an interesting thing. It refers to an old article by now, but as the theme is recurrent, I think it's worth to write about it anyway. 

The article is here and is about the role of faith in science. After some introductory material, the author says that there is something called "the fundamental axiom of science", which I quote here:

Patterns observed in the past enable us to predict what will happen in the future. 

It's also said that Hume argued that there is no rational basis to believe in that and that Kant tried to solve this problem, but failed. Therefore, according to the article, this must be taken as an act of "faith" and that science only works if the axiom is true.

To be fair with the article, I have to say that the author argues correctly that the usual meanings of the word faith have no place in science, but at the end he really confuses me by saying that the above "axiom" of science has to be simply believed if you want to do science. It doesn't. And I will explain why. In the last paragraph, the author gets close to the answer, but he blows it up in the same way as Mt Saint Helens in his example.

So, as always, things boil down to Bayes and I will try to be as brief as possible. The example of Mt Saint Helens given by the author above is a wrong critique to Bayesian inference. It talks about a guy who refused to leave the place after being warned that it would blow up because it had never blown up before, so it would continue like that. The guy died.

In fact, if no one has ever warned the guy, that was the most sensible decision he could take. A sensible decision is not something that leads to a successful result, but one that is the best given the information you have. When the guy refused to listen to the warning, he ignored extra information.

Bayes inference is carried out by taking into account ALL available information, not only what you choose to take according to your personal taste. Here enters the reason why we DO believe in the so-called fundamental "axiom" written above. That's because ALL the information we have today (and I truly mean ALL) points to the fact that we actually can use models to (within limits) make predictions. It's not a question of faith, it's a question of inference. Bayesian inference. Now, if you want to call Bayesian probabilities by the word "beliefs", as it is sometimes done in technical jargon, and if you want to associate this with faith, well, that's up to you, as long as you understand that this IS NOT an arbitrary kind of belief AND CHANGES as more information comes about.

In any case, as all other things in science, if we could never find models that would work, or if suddenly our models stop working, we have to abandon that idea. That is how true science is made. Nothing is a dogma. Everything is subject to change and revision. If you don't like uncertainty, I'm sorry, but that's how science is.

About the "fundamental axiom", I prefer a less pompous name, like "basic working hypothesis", but I don't think that's very catchy.