Wednesday, March 25, 2009

Hájek: Whether You Like It or Know It or Not, You Have a Reference Class Problem

Alan Hájek is an extraordinarily perceptive commentator on (the) reference class problem(s). See "The Reference Class Problem is Your Problem Too", Synthese 156: 185-215. 2007. He maintains that conditional probability should be a "primitive" for axiomatization of probability theory and that taking this view dissolves the "metaphysical" form of (the) reference class problem(s). However, he candidly admits this approach does not dissolve the epistemological version of the problem(s) [footnotes omitted]:
Now, the bad news. Giving primacy to conditional probabilities does not so much rid us the epistemological reference class problem as give us another way of stating it. Which of the many conditional probabilities should guide us, should underpin our inductive reasonings and decisions? Our friend John Smith is still pondering his prospects of living at least eleven more years as he contemplates buying life insurance. It will not help him much to tell him of the many conditional probabilities that apply to him, each relativized to a different reference class: “conditional on your being an Englishman, your probability of living to 60 is x; conditional on your being consumptive, it is y; …”. (By analogy, when John Smith is pondering how far away is London, it will not help him much to tell him of the many distances that there are, each relative to a different reference frame.) If probability is to serve as a guide to life, it should in principle be possible to designate one of these conditional probabilities as the right one. To be sure, we could single out one conditional probability among them, and insist that that is the one that should guide him. But that is tantamount to singling out one reference class of the many to which he belongs, and claiming that we have solved the original reference class problem. Life, unfortunately, is not that easy—and neither is our guide to life.

Still, it’s better to have one problem than two. I will leave it to others to judge the extent to which I have succeeded in ridding us of the metaphysical reference class problem. But I am aware that I have not solved the epistemological problem. I invite you to join me in the search for a solution for the interpretations of probability that have a genuine claim to being guides to life. After all, whichever interpretation you favor, the epistemological version of the reference class problem is your problem too.

  • One man's metaphysics is another man's physics?
    Folk physics?
    Folk physics has its uses -- and in an important sense it may be even "true."
  • P.S. I suspect that a successful "solution" to the epistemological version of the reference class problem(s) requires a bit of metaphysics (i.e., some basic assumptions about [wo]man and the world [s]he inhabits).
    N.B. By putting solution in quotation marks I do not mean to assert that a satisfactory solution of some kind is impossible. (Of course, there are solutions and there are solutions: one solution will not necessarily solve -- thank goodness! -- every possible problem about the choice and use of reference classes.)

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    coming soon: the law of evidence on Spindle Law

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