Something of the essence of Karl Popper
In the works by the more mature Karl Popper, entitled The Open Society and Its Enemies,--which I think is worthwhile reading for anyone interested in science--especially in the footnotes--he suggests that some people writes so that no matter what happens, it can be explained by their writing. His favourite examples are S. Freud and K. Marx. But perhaps more importantly, he suggests, implicitly, that any statement at all that can be checked can be called 'a theory'. So if somebody says, "It is sunny outside", that's a theory because one can go outside and check it. Of course normally a theory is in a larger framework of assumptions etc, but he is deliciously informal about it. One doesn't have to be a professor to come with a theory.
If somebody comes with a series of statements of this sort: "A is the case, and B is the case, and anybody who don't see that, hasn't got the proper faith", then that person has not come forth with a theory because the statement doesn't invite any form of checking.
As Popper often stated, and here he agreed with R. Carnap and many others, we cannot really prove theories--at least not the more complex of theories. If Einstein's equations of gravitation predicts that a star should seem to be a little closer than it is to another star when seen through a telescope, then if it's not seen, that's an instance of disconfirmation, and if it's seen, that's an instance of confirmation. But the disconfirmation may be because the telescope was wrongly set, and the confirmation may also be because the telescope was wrongly set but in some other way. So we gather disconfirmation and confirmation and this affects the credibility of a theory.
In the prolongation of this, it is clear also that for any set of data, there can be very many theories. Others have suggested that the simplest theory should be selected. But in complex situations, it may be far from simple to select the "simplest" theory. That depends on priorities and world view and background assumptions.
The most interesting statement, in my opinion, in the Open Society volumes by Popper is--given that it comes from him--in a footnote, where he says that he do believe that intuition can be part of what it takes to prove something; he speaks then in a context of mathematics. Indeed, there are schools of thought in mathematics, eg in the wake of the works of "The Intuitionists", which hold that much of mathematics is founded on logical inferences that intuitively can be doubted.
