It's also worth adding that the scientific method is fundamentally based on unprovable axiomatic assumptions. In other words it's still philosophy all the way down. To be clear, I don't think all philosophical ideas are equally valid and this particular set of axioms has proven quite useful in practice, but at best all we can really say is that it provides a user window for examining reality. We don't know how wide that window happens to be and how much of reality we can see through it.
We don't even know if the scientific method is the best it could be in what we use it for. After all, it was only expanded with the idea of falsification in the 20th century yet we were still doing useful science before than.
In practice, science is, and has been, rather flexible about its assumptions, and, ironically, has been criticized for that by philosophers - and yet it has been remarkably successful, arguably because it gives a lot of weight to empiricism and not so much to debating axioms.
> We don't know how wide that window happens to be and how much of reality we can see through it... We don't even know if the scientific method is the best it could be in what we use it for.
It is telling that these sentiments are not followed by something beginning "analytical philosophy, in contrast..."
> [Science] was only expanded with the idea of falsification in the 20th century yet we were still doing useful science before than.
It was doing de facto, though somewhat ad hoc, falsification long before Popper focused his attention it. The philosophy of science is much more descriptive than prescriptive.
Having said this, you may be surprised to learn that I spend a some of my free time reading and thinking about various aspects of philosophy. I must say, however, that I feel that western metaphysics lost its way in its attempt to address fundamental questions through the analysis of language.
> It's also worth adding that the scientific method is fundamentally based on unprovable axiomatic assumptions.
No, it isn't. This is a very common myth, but it is in fact a myth. Science has no axioms.
> We don't even know if the scientific method is the best it could be in what we use it for.
That's true. But what we do know is that the scientific method is vastly more effective than anything else humans have come up with in helping us navigate our existence and exercise some degree of control over our destiny.
> After all, it was only expanded with the idea of falsification in the 20th century yet we were still doing useful science before than.
That is also true, and that is one of the reasons to believe that the scientific method is special and unlikely to be improved upon. It's not just an arbitrary choice. It is privileged, and there is actually reason to believe that this privileged status is a reflection of some underlying reality. But this is not an axiom, it's a result.
We don't even know if the scientific method is the best it could be in what we use it for. After all, it was only expanded with the idea of falsification in the 20th century yet we were still doing useful science before than.