Sunday, July 19, 2015

External Factors and Evidential Symmetry

I'm thinking about the relationship between factive reasons and internalism.

A certain gumball machine has two possible modes. In mode A, it delivers blue gumballs with 90% probability, and red gumballs with 10% probability; in mode B, those proportions are reversed. (The probability for each gumball is independent.) Every morning, a fair coin is flipped to determine in which mode it will remain for the duration of the day. Vibhuti knows all of this. She begins our story with an epistemic probability of .5 for proposition h.
h: the machine is in mode A.
Now two of Vibhuti's friends who have been to the gumball machine today come along. Tunc tells her that he bought a gumball, and it was blue. (This is evidence in favour of h.) Eric tells her that he bought a gumball, and it was red. (This is evidence against h.) Tunc and Eric are equally (and highly) honest and reliable (and Vibhuti knows this). The evidential situation looks entirely symmetric, so Vibhuti's evidential probability for h looks still to be .5.

But certain approaches to evidence might disrupt this apparent symmetry. Suppose it turns out that Eric is lying, but Tunc is telling the truth, and indeed, reporting something he knows. (We've stipulated that this is unlikely, but not that it's impossible.) The lie is skillful, and Vibhuti isn't suspicious; she very reasonably takes both of their assertions at face value. Let's also take on board the following epistemic assumptions (if only to see where they lead):

  1. Testimony almost always puts one in possession of knowledge of the fact that the testimony occurred.
  2. Testimony at least sometimes puts one in possession of knowledge of the fact testified.
  3. E=K.
(Note that I am not assuming a reductivist approach to testimony; there's no claim that the knowledge from 2 typically or ever is based on the knowledge from 1.)

Given these assumptions, it looks like we may not get Vibhuti's case as symmetrical after all. Although she has some evidence in favour of h and some against it, it isn't all symmetrical. For it looks like her relevant evidence is the following:
  • Tunc says he got a red one.
  • Tunc got a red one.
  • Eric says he got a blue one.
The first and third on this list look to be symmetrical for and against h. But the strongest item here counts unambiguously in favour of it. You might think that the second swamps the first in evidential relevance—that sort of seems right—if so, then we could just look at this list:

  • Tunc got a red one.
  • Eric says he got a blue one.
Here we have one piece of evidence in each direction, but the first item, which counts in favour of h, looks stronger than the second. So it looks like there's going to be some pressure against the idea that Vibhuti's evidential probability in h is .5; it seems like it should be higher than .5.

So how, if at all, could E=K (and really, the challenge applies to a broader range of views: anyone strict enough to demand true evidence, but lax enough to allow testimonial contents sometimes to be evidence) accommodate the apparent evidential symmetry in cases like this? I see four options.
  1. Deny that one can ever get the contents of testimony as evidence, because we don't really know the things we're told, even when we're told by people who know. (Skepticism about testimony.) This might be more palatable than it seems if accompanied with some kind of contextualism about both 'knows' and 'evidence'.
  2. Deny that one can ever get the contents of testimony as evidence, because not all knowledge is evidence—maybe only direct or basic knowledge counts as evidence. (E=BK)
  3. Deny that in particular cases like this one can get knowledge via testimony. If one friend is lying to you, then you're in a skeptical situation where testimony is unreliable. (But will this solution be general enough?)
  4. Admit everything I've said about what evidence Vibhuti has, but argue that, for purposes of evidential probability, the situation is symmetrical after all. (The relationship between evidence and evidential probability is complex; I'm really working with something of a 'black box' for the latter—must we suppose that the black box delivers the assymetrical verdict in a case like this?)
Maybe there are more, I'm not sure.


  1. Interesting!

    Did I miss something, or did blue gumballs accidentally become black gumballs midway?