One of the things that’s confusing about truth norms for belief is how exactly they apply to real people—people with incomplete information.

Even if we work with “one should: believe p only if p is true”. After all, I guess we can each be pretty confident that we fail to satisfy the truth-norm. I’m confident that at least one of my current beliefs is untrue. I’m in preface-paradox-land, and there doesn’t seem any escape. It doesn’t feel like I’m criticizable in any serious way for being in this situation. What is the better option (OK, you could say: switch to describing your doxastic state in terms of credences rather than all-or-nothing beliefs, but for now I’m playing the all-or-nothing-belief game).

So I’m not critizable just for having beliefs which are untrue. And I’m not criticizable for knowing that I have beliefs which are untrue. Here’s how I’d like to put it. There are lots of very specific norms, which can be schmatized as “one should: believe that p if p is true”. It’s when I know, of one particular instance, that I’m violating this “external” norm, that I seem to be criticizable.

Let’s turn to the indeterminate case. Suppose that it’s indeterminate whether p, and I know this. And consider three options.

- Determinately, I believe p.
- Determinately, I believe ~p.
- It’s indeterminate whether I believe p.

I’m going to ignore the “suspension of belief case”. I’ll assume in (3) we’re considering a case where the indeterminacy in my belief is such that, determinately, I believe p iff p is true.

In case (1) and (2), for the specific q in question, I can know that it’s indeterminate whether I’m violating the external norm. But for (3), it’s determinate that I’m not violating this norm.

It’s very natural to think that I’m pro tanto criticizable if I get into situation (1) or (2) here, when (3) is open to me (that is, I better have some overriding reason for going this way if I’m to avoid criticism). If this is one way in which criticism gets extracted out of external truth-norms, then it looks like indeterminate belief is the appropriate response to known indeterminacy.

But that isn’t by any means the only option here. We might reason as follows. What’s common ground by this point is that it’s indeterminate whether (1) or (2) violates the norm. So it’s not determinate that (1) or (2) do violate the norm. So it’s not determinate that a necessary condition for my beliefs being criticizable is met. So it’s at worst indeterminate whether I’m criticizable in this situation.

I can’t immediately see anything wrong with this suggestion. But I think that nevertheless, (2) (3) is the better state to be in than (1) (1) or (2). So here’s a different way of getting at this.

I’m going to now switch to talking in terms of credences *as well as* beliefs. Suppose that I believe, and am credence 1, that p is indeterminate. And suppose that I believe that p—but I’m not credence 1 in it. Suppose I’m credence 0.9 in p instead (this’d fit nicely, for example, with a “high threshold” account of the relationship between credence and all-out belief, but all I need is the idea that this sort of thing can happen, rather than any sort of general theory about what goes on here. It couldn’t happen if e.g. to believe p was to have credence 1 in p).

In this situation, I have 0.1 credence in ~p, and so 0.1 credence in p not being true (in the situation we’re envisaging, I’m credence 1 in the T-scheme that allows this semantic ascent).

I’m also going to assume that not only do I believe p, but I’m perfectly confident of this—credence 1 that I believe p. So I’m credence 0.1 in “I believe p & p is not true”—so credence 0.1 in the negation of “I believe p only if p is true”. So I’m at least credence 0.1 that I’ve violated the norm.

Contrast this with the situation where it’s indeterminate whether I believe p, and p is indeterminate, in such a way that “p is true iff I believe p” comes out determinately true. If I’m fully confident of all the facts here, I will have zero credence that I’ve violated the norm.

That is, if we go for option (1) or (2) above, when you’re certain that p is indeterminate, and are less than absolutely certain of p, then it looks to me that you’ll thereby give some credence to your having violated the aleithic norm (with respect to the particular p in question). If you go for (3), on the other hand, you can be certain that you haven’t violated the alethic norm.

It seems to me that faced with the choice between states which, by their own lights, may violate alethic norms, and states which, by their own lights, definitely don’t violate alethic norms, we’d be criticizable unless we opt for the second rather than the first *so long as all else is equal*. So I do think this line of thought supports the (anyway plausible) thought that it’s (3), rather than (1) or (2), which is the appropriate response to known indeterminate cases, given a truth-norm for belief.

(As noted in the previous post, this is all much quicker if the truth-norm were: one should, determinately( believe p only if p is true). But I do think the case for (3) would be much more powerful if we can argue for it on the basis of the pure truth-norm rather than this decorated version).