vinux, are you on the TS dropbox share yet? I have something there you might like to read.
Anyway, people talk about PoS they usually spit out positivism, Popper, and Kuhn. I agree that Kuhn is highly misinterpreted. I think he had a brilliant perspective on PoS, but his work was largely best exemplified by the historical synopses he did. People who criticize him tend to focus on wacky ideas like incommensurability (to which Feyerabend seemed to focus more on, to me). Kuhn's real contribution as I see it is identifying the historical role of institutional changes in the scientific culture like the inclusion of measurement and quantification in experimental design. Lakatos sort of did the same thing from a more abstract view in the development of theoretical ideas (especially in mathematics).
In any case, the issues with positivism, etc., aren't really important in modern philosophy of science. The idea that we could rigorously lay out science in some formal terms is clearly ridiculous. The more interesting subject is trying to identify the place of subjectivism in science--what role does interpretation play in the conclusions we draw from scientific experiments?
Noetsi is right that knowledge is an important part of PoS. However, that sort of sweeps a grand amount of detail under the rug and dispatches the interplay between ontology and epistemology: e.g., does having a justifiable methodology that allows us to trust the conclusions of experiments as relaying knowledge about the phenomena under investigation also entail that we're making ontological assertions? Again, interpretation plays a big role here because both in terms of method, theory, and pragmatics, the results of any experiment can be interpreted in numerous ways and the very theoretical foundation that supports a methodology presumes certain things about the way the world is (we don't want to draw circular conclusions here!). The whole issue of paradigms and revolution is neither here nor there. Frankly, most philosophers in this area I've read agree that whatever dramatic shifts we've seen were in part due to large changes in scientific methodology. Of course you can talk about dramatic changes when you move from non-measurement to measurement scientific methods or you can talk about incommensurable interpretations when comparing Greek theorizing to modern scientific theories. But I'd rather stay away from getting into the details of that.
I don't know what would be considered a philosophy of statistics, largely because statistics is not necessarily a theoretical science. It is a methodology. It's theory is mathematical. It's practice can be taken as an art, in some regards. When we talk about the philosophy of biology or physics, we're talking squarely about the theories on which they are founded. Now, I am happy to jump on the philosophy of mathematics bandwagon. It's still something I'm interested in majoring in. But let's be clear, there are some distinct differences between philosophy of science as a study of the practice of science and the philosophy of statistics as a study of the practice of, say, data inquiry. I say data inquiry because if we look at statistics mathematically, we're really just going to sit here talking about mathematical/probability theory. That's not to say there aren't interesting questions, but I think there are distinct topics. I don't think that the topics that are of interest to the philosopher of science or of mathematics are really pertinent to those of statistics, because where PoSt comes in, we're really talking about PoS with statistical/inductive methodology. Difference.
With that said, the interests we have of statistics as a methodology with its relationship to the philosophy of science are squarely found in the philosophy of science. Already mentioned was the great Ian Hacking. He's done great work on inductive methods in science. Wesley Salmon has also explored methodology, but with an emphasis on causality (see
Causality and Explanation). Then it goes without saying that Nancy Cartwright is especially lucid in explaining the way methods, especially statistical and econometric, play a role in science (take your pick, I haven't been let down by any of her books! But a good start is
How the Laws of Physics Lie, and an advanced read is
Hunting Causes and Using Them. We can also get pretty specific, like the philosopher of biology, Elliott Sober, does a good review of statistics role in interpreting facts in the first chapter of
Evidence and Evolution. I also found Hausman's anthology on
The Philosophy of Economics useful in exploring related topics with an economic emphasis.
The point of this listing is that if we're going to talk about PoSt, then we might want to do so in terms of methodology as has been the focus in all these areas of the philosophy of science. This doesn't diminish its importance or the interesting topics that can be covered, as the books above detail. We just have to respect what role statistics plays in scientific inquiry and how that can be explored in the philosophy of science. We can certain get abstract and talk about inductive reasoning (Hacking is good at this, among others both classic and contemporary) or we can get specific and focus on statistics as a mathematical inquiry. That realm of inquiry, though, should be made explicit when we talk about the various topics to follow, whatever those may be.
Addendum: There are a few particularly statistical questions that arise regarding statistical methodology and (inductive) inference. I'm reminded of this by Sober's work. The most important being the role of evidence in our inferences. But this isn't necessarily statistical, per se. It's brought up in pretty much every book I listed above. Where it's particularly statistical as in Sober's book is that evidence (data) plays a role through our methodology to give us a certain basis for drawing conclusions (e.g., confidence intervals). The more obvious one is the philosophical position we take regarding our interpretation of method, which in statistics is usually summed up as the frequentist vs Bayesian positions (I like Sober's focus on likelihoods). This doesn't deviate from my premise that PoSt is a look at method, but it does reveal there are important philosophical issues involving knowledge and interpretation
about that method qua method. I don't think we can take these issues as philosophical questions of theory, per se, because there is no theoretical basis that the method is Bayes or about frequency. You can take one method, one conclusion, and simply interpret it from both positions sometimes. Neither position provide a theory that draws that interpretation for us. This, however, requires a bit of depth regarding what a
theory means in a technical and philosophical sense.
