Jerry Dworkin pointed out to me that Mike Leigh’s film “All or Nothing” contains a scene that seems to support interest-relative-invariantism. The script is “here”:http://www.script-o-rama.com/movie_scripts/a/all-or-nothing-script-transcript.html, though be warned that link contains pop-ups.

bq. Husband: Give us a clue, then.
Wife: ‘Biblical son of Isaac, five letters.’ Starting with a ‘J.’
H: Jonah.
W: Oh, yeah.
H: No, it ain’t. It’s what’s-his-name. Jacob.
W: Are you sure?
H: Yeah.
W: It’s a thousand pound prize.
H: Is it? No, I ain’t sure, then.

Well, maybe it is only interest-relative-invariantism about ‘sure’, rather than ‘knows’, but it seemed like a good way to celebrate the “publishing of Jason Stanley’s book on IRI”:http://bengal-ng.missouri.edu/~kvanvigj/certain_doubts/?p=480. More on IRI after the fold.

My version of IRI was based on the following two idea. S has a justified belief in _p_ if her degree of belief in _p_ is justified, and that degree is high enough to amount to a belief. Since what degree of belief S must have in _p_ to count as believing that _p_ is sensitive to S’s context (or interests or whatever) this is something like a form of IRI about justified belief.

Now it would be nice if that ‘if’ in the theory could be strengthened to an ‘iff’, but I don’t think that’s so, because of the following two cases.

Confident Carla and Sceptical Suzy each have the same evidence _e_, and each are in the same practical situation with respect to _p_. In that situation, degree of belief 0.8 suffices for belief in _p_. That is, they don’t face any choices that amount to bets on _p_ at odds greater than 4 to 1 against.

* The evidence _e_ justifies a degree of belief in _p_ of 0.9.
* Confident Carla is too confident about the strength of the evidence; her degree of belief in _p_ is 0.95.
* Sceptical Suzy is too sceptical about the strength of the evidence; her degree of belief in _p_ is 0.85.

Question: Which of the two of them justifiably believe that _p_? I’m inclined to say that they both do, though I’m more confident about Suzy than about Carla. But the little theory above, if strengthened to a biconditional, would say that neither justifiably believe that _p_. That seems to be a problem.

I think the thing to say is that S justifiably believes that _p_ iff S believes that _p_, and S is justified in having a high enough degree of belief in _p_ to count, in her context, as believing that _p_. That makes both Suzy and Carla justified believers, though it is a more complicated theory than the one I hoped would be true.