A friend from Elba surprised me by sending the interesting paper and discussion of Dennis Lindley (2000), “The Philosophy of Statistics,” which I hadn’t seen in years. She suggested, as especially apt, J. Nelder’s remarks; I recommend the full article and discussion:
(from) Comments by J. Nelder:
Recently (Nelder,1999) I have argued that statistics should be called statistical science, and that probability theory should be called statistical mathematics (not mathematical statistics). I think that Professor Lindley’s paper should be called the philosophy of statistical mathematics, and within it there is little that I disagree with. However, my interest is in the philosophy of statistical science, which I regard as different. Statistical science is not just about the study of uncertainty but rather deals with inferences about scientific theories from uncertain data. Continue reading
Error Statistics Philosophy 