As an introduction, Alan F. Chalmers' What Is This Thing Called Science? is good. It covers Popper in chapters 5 to 7 (Introduction & Naive Falsificationism, Sophisticated Falsificationism, Limitations). Then it moves on (as it were) to Thomas Kuhn's The Structure of Scientific Revolutions, Imre Lakatos' Falsification and the Methodology of Scientific Research Programmes (great short read, btw, applying those ideas to maths: Lakatos' Proofs and Refutations), and Feyerabend's Against Method. Chalmers then covers Bayesianism, new experimentalism, the nature of scientific laws, and scientific realism.

They've all pointed out problems with Popper's demarcation criterion. Not sure there's really a good catchy replacement, though. It seems to amount to "it's complicated".

One of the problems with Popper's account is the following: an observation is never about only one hypothesis, but about it and a whole set of auxiliary hypotheses. So, if your observation does not line up with the prediction, do you throw out the theory, or some auxiliary hypothesis? (Eg, Uranus didn't move as predicted, so Newton's physics was wrong. But wait, it was not a problem with Newton's physics, but there was another planet, Neptune.) Quine's notion of a "web of belief" captures that quite nicely - you don't just take one hypothesis, test it, and drop it if falsified, but you adjust the whole edifice such that it becomes coherent again. See [1].

[1] https://en.wikipedia.org/wiki/Duhem–Quine_thesis

Not to contradict anything you've said, but my original message above was in response to something very different than I think you're talking about. I see a lot of comments where people seem to treat Science as some unquestionable list of facts and treat Scientists reverently. It's like they've made a religion out of it and don't dare question the priests - which is ironic/silly when they're refuting conventional religions.

Anyways, maybe my current view is a little too hard line on good science relying on falsification, but I still reject the notion that any scientific belief is verifiable / provable. A given theory may be the best we have, but a new piece of information could change it radically.

All I wanted to add is that things are more complicated than just that one demarcation line, and philosophy of science has not stood still over the last half century.

What I mean is, people don't find an experiment about nanostructures that doesn't work and start going "hey I think I have disproved quantum mechanics!". Even when the OPERA faster-than-light neutrino debacle was going on, physicists were largely saying "We are pretty sure that there is some mistake in either the model or the experiment such that these neutrinos are not moving faster than the speed of light." In fact the objection goes a little further than that: according to Newtonian mechanics, geocentrism is perfectly admissible. There is absolutely nothing wrong with constructing a geocentric frame of reference and doing Fourier expansions of the motions of planetary bodies. No experiment has disproven it because it's just a mathematical choice of accelerated reference frame to analyze the motion of the planets. According to unmodified Popper, each of the first two should have led to a rejection of the scientific principles which led to them, while the latter would mean that geocentrism and heliocentrism are pseudoscience and there was never any scientific switch between them -- all of that sounds wrong.

So Kuhn introduced the idea that there is a separation of science into two parts, "theory" and "model". A scientific theory like quantum mechanics or heliocentrism is a platform for building models and deciding what questions are worth asking and how one goes about asking them. They are a "platform for computation" in a sense, and most of them are "Turing complete," there is nothing that they can't model somehow. So classical mechanics turns out to be able to do something with quantum mechanics if we use something like Bohm's pilot wave theory. And Couder and Fort's droplets on a vibrating oil bath show an experimental realization of particles which nevertheless diffract in a classically explicable way, underscoring this point. Kuhn said that theories need to be abandoned during some sort of "scientific revolution" but was very hazy on how exactly that happened. But he was a huge fan of Popper and wanted to say that Popper was fundamentally right about the way that we model systems, discarding models immediately when they do not fit experiment and coming up with better models.

Kuhn picked up a lot of flak because one of the things Popper's works were trying to do was to discredit things like psychiatry and astrology as being "pseudoscience" rather than real science because they could explain everything and thus never stuck their neck out -- thus Kuhn's work seemed to need some extra structure about the manner that we actually conduct such a revolution, otherwise astrology might not be a pseudoscience but an "eventual science" or so: if theories are just some sort of aesthetic agreement on behalf of the existing scientists then what stops us all from deciding that we rather like reading our weekly horoscopes?

This challenge was to my mind best resolved by the "research programmes" idea of Imre Lakatos. He philosophizes that theory choice -- fundamental progress in science -- is best seen as motivated by lazy grad students. Like, laziness is a virtue on this account: grad students have to make a contribution to the published literature that excites their peers and makes a name for themselves, and they do not have much time to do it.

So, why do people use the Copenhagen interpretation for everything if very few people philosophically accept its ontology? Because it is mathematically equivalent to all of the other interpretations but is astonishingly easy to use, just "yeah the wavefunction collapsed so now this is reality, I don't strictly have to care about that collapse happening across spacetime instantaneously because that's not observable anyways, so here are my experimental results." Lazy grad students will choose that ten times out of ten over coming up with the correct pilot-wave mechanics and simulating it. Why did heliocentrism win if Newtonian mechanics says that geocentrism is 100% experimentally valid? Because the heliocentric models are easier to build and reason about with straight mechanics, and lazy grad students will take Newton's law of gravity any day over those epicycles.

You can in some respects view this as Occam's razor but Occam's razor is painfully ill-specified. A better view of it is that it's a survival-of-the-fittest, a theory of scientific evolution. So, theories are "genes" which make it easier or harder to publish interesting discoveries that are modeled with those theories in scientific journals. Based on others reading those papers and extending those results in various ways, theories "reproduce" and the ones that reproduce most effectively are the ones that best adapt to their (ever-changing) environment.