One might think that having a less extreme (i.e., further from 0 and 1, and closer to 1/2) credence than is justified by the evidence is pretty safe epistemically. So, if one wants to be safe, one should move one’s credences closer to 1/2: moderation is safer than extremism.
But if one is to be consistent, this doesn’t work. For instance, suppose that the evidence points to clearly independent hypotheses A and B each having probability 0.6, but in the name of safety one assigns them 0.5. Then consistency requires one to assign their conjunction 0.5 × 0.5 = 0.25, whereas the evidence pointed to their conjunction having probability 0.6 × 0.6 = 0.36. In other words, by being more moderate about A and B, one is more extreme about their conjunction.
In other words, once we have done our best in evaluating all the avilable evidence, we should go with the credence the evidence points to, rather than adding fudge factors to make our credences more moderate. (Of course, in particular cases, the existence of some kind of a fudge factor may be a part of the available evidence.)
I'm still not sure what it means to assign percentages to credence (unless there are actual probabilities at play, as with rolling a fair die or something), but I have to say that the result of 50% credences on two separate matters meaning that I have a 25% credence on the conjunction is very counter-intuitive. I mean, mathematically it makes perfect sense; but it doesn't fit my intuition about my own credence. For example, if I had decent reason to think that Pluto has some gold on it, such that I set my credence to 50%, and I had decent reason to think that my wife would choose Chinese food for our lunch (again, 50%; especially in this town where Chinese and Mexican are almost all there is for us to eat!), I don't see why I should have only a 25% credence that both of those are true. Perhaps it goes back to my not understanding what it means to have 50% credence on something that isn't overtly probabilistic.... Certainly it can't be a frequentist sort of probability (in which I'm expected respond one way half the time and the other way the other half). I dunno....
ReplyDeleteLeaving aside conjunctions, wouldn't consistency also require that, as I move my credence in P closer to .5 than the evidence justifies, I also move my credence in ~P closer to 0 or 1 than the evidence justifies?
ReplyDeleteMichael:
ReplyDeleteIt could actually be frequentist, though it's not my preferred embodiment for the story. One could say that to have 57% credence in Q given evidence E is to estimate at 57% the frequency of a proposition being true given sufficiently analogous evidence.
For instance, if my credence that a distant figure is Alice on the basis of the figure vaguely looking like her is 57%, that could just be my estimate of the frequency of times that a figure at that distance that vaguely seems like x is in fact x.
The difficulty with this is the reference class problem.
Clifton:
ReplyDeleteI think you made a slip. If the evidence justifies 0.57 for P and I move my credence to 0.54, then my credence for ~P moves from 0.43 to 0.46, and hence it also gets closer to 0.5. No?
Right. Not sure what I was thinking. Or at least not sure why I was thinking it.
ReplyDelete