Thursday, January 26, 2023

A cure for some cases of TMI

Sometimes we know things we wish we didn’t. In some cases, without any brainwashing, forgetting or other irrational processes, there is a fairly reliable way to make that wish come true.

Suppose that a necessary condition for knowing is that my evidence yields a credence of 0.9900, and that I know p with evidence yielding a credence of 0.9910. Then here is how I can rid myself of the knowledge fairly reliably. I find someone completely trustworthy who would know for sure whether p is true, and I pay them to do the following:

  1. Toss three fair coins.

  2. Inform me whether the following conjunction is true: all coins landed heads and p is true.

Then at least 7/8 of the time, they will inform me that the conjunction is false. That’s a little bit of evidence against p. I do a Bayesian update on this evidence, and my posterior credence will be 0.9897, which is not enough for knowledge. Thus, with at least 7/8 reliability, I can lose my knowledge.

This method only works if my credence is slightly above what’s needed for knowledge. If what’s needed for knowledge is 0.990, then as soon as my credence rises to 0.995, there is no rational method with reliability better than 1/2 for making me lose the credence needed for knowledge (this follows from Proposition 1 here). So if you find yourself coming to know something that you don’t want to know, you should act fast, or you’ll have so much credence you will be beyond rational help. :-)

More seriously, we think of knowledge as something stable. But since evidence comes in degrees, there have got to be cases of knowledge that are quite unstable—cases where one “just barely knows”. It makes sense to think that if knowledge has some special value, these cases have rather less of it. Maybe it’s because knowledge comes in degrees, and these cases have less knowledge.

Or maybe we should just get rid of the concept of knowledge and theorize in terms of credence, justification and truth.


SMatthewStolte said...

In the Meno, when Socrates talks about knowledge as something that is tied down (like the statues of Daedalus), the thing that does the tying down doesn’t seem to be 20th century ‘justification’ or anything about reaching a certain credence but “an account of the reason why”:

“True opinions . . . are not willing to remain long, and they escape from a man’s mind, so that they are not worth much until one ties them down by (giving) an account of the reason why [τις αὐτὰς δήσῃ αἰτίας λογισμῷ]. . . . After they are tied down, in the first place they become knowledge, and then they remain in place” (97e–98a).

I wonder if we get more stability when we do this route than the justification/credence route.

Alexander R Pruss said...

Maybe Socrates is more talking about understanding than knowledge, something like medieval scientia or Aristotle's derivation from essence.

If you see someone doing a bizarre thing, you have no idea why they are doing it, but you can see and hence know that they are doing it. Conversely, one can give an account of why something is so without knowing the thing: for instance, suppose the police have a strong suspicion that Alice killed Bob, and they know exactly what motive Alice had to kill Bob, but they don't have much evidence to back up the suspicion. In that case, they can give an account of the reason why, but they don't have knowledge of why Alice killed Bob, even if in fact she did.

SMatthewStolte said...

I expect that is what Socrates is getting at. My thought is that this might be the reason we think that knowledge is something that is tied down—because scientia or derivation from essence or something like that is stable, even if ‘having passed the evidential threshold’ isn’t.