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thomblake comments on (Subjective Bayesianism vs. Frequentism) VS. Formalism - Less Wrong
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Comments (106)
Probably better put in terms of being a formal system, rather than "a set of mathematical discoveries". But I fear that tends towards begging the question!
This treatment (notably the use of terms like "conceding ground") suggests that you are engaging in a "political"/"debate" mode rather than a "truth-seeking" mode. This leads me to believe that we have more to lose by accepting the "Bayesian/Frequentist" duality than by dissolving it entirely and changing our terminology to match. This matches my impression of previous forays into the "Bayesian/Frequentist" 'holy wars'.
If politics is mind-killing, then it must certainly be avoided even at great cost with respect to our most basic tools of rationality.
Indeed, though in that case you've spent far more time on this than most who exercised the default 'ignore' option.
A good point.
I understood what you meant - I just did not see any inarticulateness on the part of User:potato.
I normally see this being explicitly the subject on Bayesian/Frequentist debates, and many long conversations with philosophers have revolved around whether "equating probability with subjective belief" is an "ontological confusion".
Duly noted. I'll try not to give this impression in future.
I may have simply failed to notice these arguments taking place. In order to dissolve any such ostensible ontological question, I'd recommend pointing out that to say probability is one or other thing is merely a statement to the effect that one interpretation is preferred for some reason by the writer - since both interpretations satisfy the Cox postulates or Kolmogorov axioms, we could define probability to be either subjective degrees of belief or long-run frequency, and make sound and rational inferences in either case (albeit perhaps not with the same efficiency). This should be enough to persuade an otherwise sensible person that he's engaged in a futile argument about definitions.
Formalism attempts to solve the problem by effectively tabooing the concept of probability such that it no longer has a definition. Although we might be able to get around the problem that I mentioned by answering the question ""what is this thing that I am computing using Bayes's theorem?" by saying "the posterior subjective degree of belief" or "the posterior frequency", it's easy to see how the same kind of philosophers would end up arguing over whether, in the case of a coin flip for example, we are really talking about prior and posterior subjective degrees of belief, or about prior and posterior long-run frequencies. And we would have lost the use of the word "probability", which makes our messages shorter than they would otherwise be.
To the extent that there is such a thing as the proper use of words, to delete useful words from our vocabulary in order to (probably unsuccessfully) prevent people from having a definitional argument that could best be dispelled by introducing them to such notions as "dissolving the question" and reductionism isn't it. On the other hand I'll give user:potato credit for exposing an issue that may be more problematic than I at first believed.
I expect that we are substantially in agreement at this point.