I used to admire aphorisms and their authors. My admiration faded when I read the Math Review of my book (MR2510150) by A.I. Dale. Let me start with a legal disclaimer - I do not blame Dale himself for all the problems with aphorisms that I complain about below, just like an atheist should not blame a single religious person for all the alleged problems with religion.
After reading of Dale's review I came to the conclusion that aphorisms are as good as "sound bites" used by politicians. They appear to be significant while in fact they are unjustified generalizations. I will illustrate my disillusionment with aphorisms with the discussion of those that were used in Dale's review.
The first aphorism quoted by Dale is Karl Pearson's: "To draw a distinction between the scientific and philosophical fields is obscurantism." I do not see any significant message in this sentence. Obviously, everything is related to everything else, so, in particular, science and philosophy are related to each other and nobody can ever separate them completely. The "distinction between the scientific and philosophical" should be made whenever such distinction can clarify the subject matter under consideration, to the extent that it is possible. I consider it absolutely necessary to mix science and philosophy in my book. On the other hand, I think that it is very useful to disentangle philosophical theories and statistical methods in various chapters of my book to elucidate their meaning and ascertain their value.
The second aphorism used by Dale is Thomas Huxley's: "Science is, I believe, nothing but trained and organised common sense." This sentiment was expressed long before the creation of quantum physics. I argue myself, on page 231 of my book, that ultimately quantum physics starts and ends with observations that are direct and intuitive. But I do not see what useful or interesting idea may be contained in the claim that quantum physics is "trained and organised common sense."
The dubious value of Huxley's aphorism is even more apparent in the context of my book. Philosophers proposed several interpretations of probability, roughly classified as logical, frequency, subjective and propensity. As far as I can tell, all philosophers writing about probability tried to "organize common sense" into fully developed and detailed theories. So Huxley is right in this narrow sense but his idea completely fails to indicate which of the philosophical theories of probability that have the ambition to "organize common sense" are either true or useful. More specifically, I do not see how Huxley's aphorism can give a slightest hint on how to resolve the dispute between frequency and Bayesian statistics.
Next comes Pearson's: "science is description rather than explanation." Once again, I will start with general comments. Some roses are red. The details of this natural phenomenon involve quantum physics because colors are determined by electrons jumping between possible orbits. To say that quantum physics "describes" rather than "explains" the color of roses does not inspire any significant thoughts in my mind.
More significantly, Pearson's idea has quite radical logical consequences. If science does not provide explanation then what does? It is possible that nothing can provide an explanation. I do not find any depth in such conclusion. Alternatively, philosophy and religion are the only sources of explanations. This may be true, depending on the definition of "explanation". Given the extreme lack of consensus on any subject among philosophers and theologians, suggesting that only philosophy and religion can supply explanations is as good as saying that there are no explanations at all.
In the context of my book, Pearson's idea that "science is description rather than explanation" has the same problem as Huxley's. I do not see how this aphorism can give a slightest hint on how to resolve the dispute between frequency and Bayesian statistics.
This quote of Pearson relates to the broader comment (or aphorism) of Nietzsche that "physics is only an interpretation of the world (...) and not an explanation".
ReplyDeleteMy reaction to Nietzche's aphorism is the same as to Huxley's: I do not see how Nietzche's aphorism can give a slightest hint on how to resolve the dispute between frequency and Bayesian statistics.
ReplyDeleteIt does not. And cannot. There simply is no way to resolve the dispute. Both approaches are mostly consistent (a frequentist argument) and are tautologically optimal for the criteria associated with them. In this sense, this reflects Nietzsche's and Pearson's quotes, namely that decision theoretical average losses, including Type I and Type II errors, are interpretations of the worth of statistical procedures, not an explanation... In my vision of the field, it somehow ends up as a matter of taste and practicality in implementing the methods.
ReplyDelete"Taste" is an illusion. If a statistician works on her own project and never publishes her findings, she can use "taste" as much as she wants. But when her research is presented in public, fellow statisticians and other scientists will tolerate only certain Bayesian priors and only certain frequentist and Bayesian models. The philosophical challenge is to describe the limitations imposed by the community and to try to justify them (or criticize them).
ReplyDelete"Practicality in implementing the methods" sounds like a good idea but it suffers from the same problem as other aphorisms - it gives no clue as to what to do. Most, perhaps all, statisticians believe that their methods are practical. So every single statistician, no matter what kind of statistics he does, believes that he applies the principle of "practicality". If everybody is right, nobody is right. If quality standards are not explicitly specified then the best and the worst methods are on equal footing.