Two detectives, D1 and D2, are investigating a murder. In fact, the butler did it. But all the evidence suggests the gardener did it. D1 believes that the butler did it; D2 believes that the gardener did it.

It’s easy enough to describe and evaluate these cognitive states. D1 and D2 have both made judgments. Both of those judgments are about the identity of the murderer. D1’s judgment tracks the truth, but not the evidence. D2’s judgment tracks the evidence, but not the truth.

We can expand this story without many complications. Assume that the evidence about the evidence is not at all misleading. The evidence supports the proposition that the evidence supports the proposition that the gardener did it. D1, as you may expect, believes the evidence supports the proposition that the butler did it, and D2 believes the evidence supports the proposition that the gardener did it.

It’s easy enough to say something about these judgments as well. D1’s judgment tracks neither the evidence nor the facts. D2’s judgment tracks both the evidence and the facts. These judgments are not, in the first instance, about the identity of the murderer. Rather, they are about the epistemic significance of the evidence. So we have a few different arguments, by Leibniz’s Law, that D1’s belief that the butler did it is distinct from his belief that the evidence supports the proposition that the butler did it. And D2’s belief that the gardener did it is distinct from her belief that evidence supports the proposition that the gardener did it.

Things get trickier when the evidence is less one-sided, as the following example shows.

D3 and D4 are investigating whether the chef was an accomplice to the murder. The evidence supports this to degree 0.7. That is, the evidential probability that the chef was an accomplice given the available evidence is 0.7. But the evidence D3 and D4 have suggests that the evidence supports the chef being an accomplice to degree 0.95.

Now some people will say that what I’ve supposed in the previous paragraph is incoherent. That shouldn’t stop us treating it as a supposition. The supposition that there’s a largest prime entails all propositions, but we can sensibly suppose it. More directly, I think there are plenty of examples where something like the previous paragraph could be true. Assume, for example, that D3 and D4 had a rather bad statistics professor in detective school, and this professor told them that a certain statistical method was usable in cases like this, when in fact it was not. Using the method would increase the apparent probability that the chef is the accomplice from 0.7 to 0.95. D3 and D4 aren’t statistics experts, so their evidence suggests that this method works. But in fact, since the professor was wrong, the method doesn’t really increase the likelihood that the chef was the accomplice.

Let p be the proposition that the chef was the accomplice, and E the evidence D3 and D4 have. Let’s assume, for simplicity, that D3 and D4 have correctly identified E. Then consider the following four attitudes:

1. D3’s credence of 0.95 in p.
2. D4’s credence of 0.7 in p.
3. D3’s belief that E supports p to degree 0.95.
4. D4’s belief that E supports p to degree 0.7.

State 1 does not track the evidence; state 3 does. So by Leibniz’s Law, states 1 and 3 must be different states. Similarly, states 2 and 4 must be different states.

I’ve been doing quite a bit of work on the evidential significance of cognitive states like states 1 through 4. (Short answer: whatever significance there is will generally be screened by the evidence the state is based on.) I’ve usually called this work on the evidential significance of judgments. I think this is an OK bit of terminology, though it’s a bit tricky to call states 1 and 2 judgments. After all, we normally think of judgments as having propositional content, and the content of the judgment characterising the state. But there’s no way to do that with both 1 and 2. If we say that the content of the judgment is p, then we can’t distinguish a state like 1 from a state like 2. (I think that’s not a terrible result, but it is odd.) If we say the content of the judgment is that p is supported by E to a certain degree, then we have no way to distinguish a state like 1 from a state like 3. And we proved in the previous paragraph that they were distinct. If we say the content of the judgment is p, we have to say that judgments come in degrees. If we say that the content of the judgment is a proposition about the force of E, we violate Leibniz’s Law. It’s bad to be illogical, so I adopt the first of these options.

There’s another argument for 1 and 3 being separate states, namely that they have separate contents. But I don’t think that’s overly compelling on its own. After all, it isn’t quite clear what the content of 1 is. In the previous paragraph I argued that it’s p, but that argument rests on the Leibniz’s Law argument. So I think the Leibniz’s Law argument does all the work here.

If D3 says, “Almost certainly, p”, is she expressing state 1 or state 3? I think she could be expressing either of them. That’s to say, “Almost certainly, p” is a reasonable enough way of expressing 1, and a reasonable enough way of expressing 3. In the past I’ve gone on at some length defending broadly cognitive accounts of statements like “Almost certainly, p”, arguing that they must be interpreted as expressions of state 3. But I no longer think there are good arguments for that position.

The main argument for such a position is a variant on the general Frege-Geach argument against expressivism. If we thought that expressions like “Almost certainly, p” only ever expressed states like 1, then we wouldn’t be able to give them truth-conditions (apart from p) and hence we’d have a hard time embedding them in more complex sentences. But if we think that whenever such an expression is, say, the antecedent of a conditional it gets interpreted as having the same meaning as the content of the belief in state 3, we don’t have any problem with explaning embedding. So I now think the force of an utterance like “Almost certainly, p” just varies. Sometimes it expresses a belief about evidential probabilities, and sometimes it expresses a credence.