Bayesians have suggested that belief is not an all-or-nothing notion, but rather one that comes in degrees from 0 to 1 (which happen to obey the Kolmogorov axioms of probability, at least for rational agents). I’ve lately been wondering whether we can do the same with knowledge – on something like a justified true belief account, we can obviously grade knowledge based on the strength of the belief involved, but it could also be graded based on the level of justification. If instead we can figure out a way to grade knowledge directly, maybe we can get a more sophisticated account of knowledge out of this, rather than seeking the “fourth condition”. The most natural attempts would probably involve something like the tracking account given by Sherri Roush in Tracking Truth (which I embarrassingly still haven’t read yet).
Anyway, thinking about this, I was struck by this account of knowledge given by Roger Shuy, over at Language Log:
1. One believes it to be true.
2. One has good reason to believe it to be true.
3. There is a substantial probability that it is true.
It seems quite parallel to the JTB account (or, BJT in this ordering), except that he seems to have weakened the truth condition quite a bit! I’ve sometimes thought that slightly relaxing the factivity condition on knowledge could make it fit much better with ordinary linguistic usage, but everyone tells me I’m crazy when I suggest this.
If we consider the correctness of knowledge attributions, rather than the obtaining of the actual state of having knowledge, then maybe this makes more sense – an agent A can judge an assertion that S knows P to be correct to degree D, where D=J*T*B, and J is S’s degree of justification for P, T is A’s subjective probability that P is true, and B is S’s subjective probability that P is true. Perhaps J and B should actually be modified to be A’s estimate of S’s degree of justification and subjective probability, rather than being the actual degree of justification and subjective probability.
Of course, this still doesn’t account for Gettier cases unless we understand “degree of justification” in some very strong way, and this might be totally crazy, but it’s just something I’m playing around with.