by Bayesianism — the new positivism No matter how atheoretical their inclination, scientists are interested in relations between properties of phenomena, not in lists of readings from dials of instruments that detect those properties … Here as elsewhere, Bayesian philosophy of science obscures a difference between scientists’ problems of hypothesis choice and the problems of prediction that are the standard illustrations and applications of probability theory. In the latter situations, such as the standard guessing games about coins and urns, investigators know an enormous amount about the reality they are examining, including the effects of different values of the unknown factor. Scientists can rarely take that much knowledge for granted. It should not be
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Lars Pålsson Syll considers the following as important: Theory of Science & Methodology
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Bayesianism — the new positivism
No matter how atheoretical their inclination, scientists are interested in relations between properties of phenomena, not in lists of readings from dials of instruments that detect those properties …
Here as elsewhere, Bayesian philosophy of science obscures a difference between scientists’ problems of hypothesis choice and the problems of prediction that are the standard illustrations and applications of probability theory. In the latter situations, such as the standard guessing games about coins and urns, investigators know an enormous amount about the reality they are examining, including the effects of different values of the unknown factor. Scientists can rarely take that much knowledge for granted. It should not be surprising if an apparatus developed to measure degrees of belief in situations of isolated and precisely regimented uncertainty turns out to be inaccurate, irrelevant or incoherent in the face of the latter, much more radical uncertainty.
For all scholars seriously interested in questions on what makes up a good scientific explanation, Richard Miller’s Fact and Method is a must read. His incisive critique of Bayesianism is still unsurpassed.
Given that we study processes that are adequately captured by our statistical models (think of urns, cards, coins, etc), Bayesian reasoning works. The problem, however, is that when we choose among scientific hypotheses, we standardly lack that kind of knowledge. As a consequence — as Miller puts it — “Bayesian inference to the preferred alternative has not resolved, even temporarily, a single fundamental scientific dispute.”
Assume you’re a Bayesian turkey/chicken and hold a nonzero probability belief in the hypothesis H that “people are nice vegetarians that do not eat turkeys/chickens and that every day I see the sun rise confirms my belief.” For every day you survive, you update your belief according to Bayes’ Rule
P(H|e) = [P(e|H)P(H)]/P(e),
where evidence e stands for “not being eaten” and P(e|H) = 1. Given that there do exist other hypotheses than H, P(e) is less than 1 and a fortiori P(H|e) is greater than P(H). Every day you survive increases your probability belief that you will not be eaten. This is totally rational according to the Bayesian definition of rationality. Unfortunately — as Bertrand Russell famously noticed — for every day that goes by, the traditional Christmas dinner also gets closer and closer …