Friday, July 14, 2017

No, I Don't Believe Probability Judgments Are "Subjective"

Tom was, I think, worried that this is what I was suggesting. Then he got what my claim is. But in case others misapprehend it...

1) There are no judgments whatsoever that are "purely subjective." Any judgment is an attempt to assert something about the world. Although Oakeshott's arguments on this point (in Experience and Its Modes, chiefly) are more robust, I think M. Polanyi's arguments in Personal Knowledge are still very good but also more accessible. If I claim that "The odds of that coin coming up hands are one in two," I am saying something about the world "out there," rather than commenting upon some "purely personal" state of my own.

2) As such, there are better and worse judgments about what the probability of some event is. If all I know is, "Tom is flipping a fair coin," then the correct probability to assign to "The coin will come up heads" is .50. One way to defend my claim here is to note that anyone else having only the same knowledge as me about the situation can assuredly win money from me in the long run if I choose any other probability while they choose .50.

3) But that perfectly correct probability judgment, given my state of ignorance about the flipping, will become decidedly mistaken should my knowledge of what is going on change: for instance, suppose I suddenly gain the superpower of instantaneously being able to assess all the forces acting on a coin at the moment it is flipped so as to "see" whether any particular flip will come up heads or tails. If I gain that superpower, my correct assignment of probability to "The coin will come up heads" is either zero or one, depending on what I "see."

4) And finally, even if I have that superpower, should the casino in which I am betting become suspicious, and only allow me to bet on coin flips from another room (so that I can't gauge the forces at play in the flip), my correct probability judgment reverts to .50.

So, the objectively correct judgment of the probability of some event occurring depends on how much knowledge we have when making that judgment: if all we know is that Joe is a 50-year-old American male, we might be correct in judging that the probability he will live to 80 is .50. (I just picked .50 as a plausible number: I'm not looking this up in the mortality tables at the moment!) But if we then learn he is planning on committing suicide tonight, we would be correct in revising our estimate to, "Well, his probability of living to 80 is pretty close to 0."

1 comment:

  1. "Tom was, I think, worried that this is what I was suggesting."

    No, that's not what bothered me. You were talking about probability at an epistemological level and pointing out that it only exists AS SUCH at that level, while I was (incorrectly) attributing a metaphysical quality to it.

    ReplyDelete

Open Source Software and Skin In the Game

I have been tinkering in the Haskell programming language recently. Trying to up my game, I have begun reviewing and working on issues in th...