This is a quote from Popper in Logic of Scientific Discovery, Section 10:
This view, according to which methodology is an empirical science in its turn—a study of the actual behaviour of scientists, or of the actual procedure of ‘science’—may be described as ‘naturalistic’. A naturalistic methodology (sometimes called an ‘inductive theory of science’ has its value, no doubt. A student of the logic of science may well take an interest in it, and learn from it. But what I call ‘methodology’ should not be taken for an empirical science. I do not believe that it is possible to decide, by using the methods of an empirical science, such controversial questions as whether science actually uses a principle of induction or not. And my doubts increase when I remember that what is to be called a ‘science’ and who is to be called a ‘scientist’ must always remain a matter of convention or decision.
I believe that questions of this kind should be treated in a different way. For example, we may consider and compare two different systems of methodological rules; one with, and one without, a principle of induction. And we may then examine whether such a principle, once introduced, can be applied without giving rise to inconsistencies; whether it helps us; and whether we really need it. It is this type of inquiry which leads me to dispense with the principle of induction: not because such a principle is as a matter of fact never used in science, but because I think that it is not needed; that it does not help us; and that it even gives rise to inconsistencies.
Thus I reject the naturalistic view. It is uncritical. Its upholders fail to notice that whenever they believe themselves to have discovered a fact, they have only proposed a convention. Hence the convention is liable to turn into a dogma. This criticism of the naturalistic view applies not only to its criterion of meaning, but also to its idea of science, and consequently to its idea of empirical method.
Naturalism, sadly, is not yet dead. Possibly the most popular modern form of naturalism is Bayesian epistemology, which claims that some kind of probabilistic form of induction with personal probabilities is how science “really works”. Is this supposed to mean that science can make a theory more likely by observation? Or is it supposed to imply that it is a fact of psychology that people attribute more probability to well-tested theories? Either claim would be false. Observations do not imply the truth of theories that correctly predict those observations, nor do they make such theories more probable since a theory is either true or false. Neither science nor the human brain has the miraculous ability to break the laws of logic.
See also my earlier post on Six Varieties of Inductivism.
On Bayesian subjectivism, in my thesis on the Duhem problem I had a look at the Bayesian contribution and the result was not encouraging. When you had to choose between a major theory and a minor discrepancy you got a nice result but that was not the case when you had two serious rivals in competition, which is the more interesting situation. To achieve credibility the Bayesians need to find examples where serious scientists are using their approach and findinbg it helpful in their daily activities. The same applies to all forms of inductive inference and inductive support.
http://www.the-rathouse.com/Theses/Duhem-QuineInBayesNewExperimentalism.html