So, the scientist in me asks: what areas of knowledge are out of the scope of science and the scientific method?
Well, now your are doing Philosophy of Science.
I'm not the smartest guy around, but I see myself still reading philosophy while still very close to laying on my death-bed, while I know I wouldn't care that much then about whether worm-holes exist or if the physical Universe is finite or infinite. In that respect philosophy will still be relevant, at least for me. I find the human species one of the most interesting things that I've read or heard about, and I think philosophy does a good job of talking about us.
This comic shows the limits of empiricism nicely: http://existentialcomics.com/comic/132
Axioms that can be empirically shown to be likely true or likely false.
Also it treasures smaller set of axioms rather than larger ones.
Modern scientists don't usually like philosophy and don't write about this stuff from a philosophical point of view. It's more necessary than ever that philosophers get with the program. Pretending that science hasn't taken the lead in explaining the natural world won't help. People like Nick Bostrom who think about what science reveals do, even though he's probably hated in philosophy circles, like Daniel Dennett or Lawrence Krauss are.
Science as an empirical practice of truth-seeking is reliant on philosophy for its foundations. Of course it is possible to "do science" without having any interest in epistemology, just as it is possible to program computers without having any interest in computer science, or to do mathematics without having any interest in mathematical foundations.
Theorization of multiverses...
Please keep in mind that multiverses haven't actually been discovered. They are a very real possibility if the model of inflation of the early universe (and thus eternal inflation) is correct. But since the Planck satellite hasn't found conclusive b-mode polarisation patterns, inflationary models should be viewed with a bit of scepticism. On the other hand: inflation can explain a lot of problems in the early universe that would arise without it: magnetic monopoles, the large-scale homogenity and isotropy and geometric flatness. So, it remains a valid model, and the best explanation of the very early universe.
We should be aware of the things we don't know, and not just assume multiverses, when there is no conclusive evidence.
I mean, you wouldn't say that "Large areas of science are routinely demolished" by newer science, even though strictly speaking it's true, and you'd therefore give up on science as a whole?
(And if I'd really want to be mean, I'd ask you if science has ever even proven the "real world" exists or that science is true, but I think you got my point.)
I know philosophy is extremely rigorous. Science is fiddly, it works in approximations. Philosophers hate ad hocs postulates like dark matter or cosmological constants. They hate not knowing how certain things work. That's part of the problem. They need to apply their rigor to theories that have the chance of being false.
You also have to remember that science operates within it's own framework, and assumes concepts of truth that are accepted within this community, such as the scientific method to gain knowledge. But these are presumed to be true, without anyone having had proven them.
Philosophy on the other hand, as a more general subject, even questions these frameworks and has to operate without any pre-given framework. A Platonist won't be shunned by a scientific discovery, since it isn't a threat to it's epistemological framework.
Therefore I say that science is part of philosophy, but this doesn't mean it's wrong or bad. Everyday life proves it's helpfulness. One just has to keep in mind, that there is no proof it's ultimately true, and that all objections are "appeals to emotion". Followers of Scientism, even though they wouldn't say it themselves, do this, dogmatically believing that they are the true way and that's the problem everyone has with them. (I'm not saying it's better when Platonists or anyone else does it, but the others are more common nowadays)
If Philosophy is going to argue that the scientific method doesn't work, or that the world doesn't exist, we can't trust our senses or stuff like that, go ahead. Has there been any practical advancement on this line of thinking in the last 50 years? do you envision that the scientific method will be revised by anything discovered in philosophy?
Could you explain what you mean with this?
>If Philosophy is going to argue that the scientific method doesn't work
The critique isn't as blunt as you make it out to be. Philosophers argue that the scientific method isn't the ultimate epistemological tool to find out everything and to understand all there is to know.
>that the world doesn't exist >we can't trust our senses or stuff like that
Just as a side note, this hasn't been disproven, since it's beyond the reach of science. Science, as a materialist/physicalist philosophy presumes itself to be true, while at they same time limiting itself.
>Has there been any practical advancement on this line of thinking in the last 50 years?
What do you mean with "practical advancement"? For one to ask or answer this question seriously, one has to take a lot of things for granted and such as concepts of "practical" or "advancement". And what's so special about the last 50 years?
>do you envision that the scientific method will be revised by anything discovered in philosophy?
Philosophy as a discipline isn't science, you don't "discover" things, since that presumes these truths to be out there, ready to be found, which doesn't mean that people don't search for them.
But besides that, what do you mean with "revised"? The critique isn't as already mentioned, that the scientific method isn't right (it most certainly is a very good tool regarding science itself), but that it can't be the only one, used to find out everything. That's just naive positivism.
What I mean is that every time this debate happens it's the same a lot of "what do you mean by that?" And "define achievement". My thesis is that as a tool to gain knowledge about the natural world philosophy is not helpful anymore because the parts that are useful, logic and argumental rigor, are integrated in science already. Philosophy is still useful in ethics and morals but not useful in epistemology and metaphysics unless they follow modern science, which very few do.
If you are talking about idealist philosophy, and are asking yourself how much their theories on the true substance of the world has contributed to the general wellbeing of the average human being, then I already said, that most people would agree that the products of science, as a materialist philosophy, are more helpful.
I might remembering it wrong, but I think one of the main questions asked by Socrates was "how can we be good persons?". And "what does 'good' mean?". That question absolutely does inform my every-day choices about the real world, because me not being a religious person and not believing in the after-life and such I base most of my every-day thingies on thinking if what I'm actually doing is "good" or not. Asking yourself that is a philosophical question. That and a little bit of Kant, and his "people should never be means to an end".