Belief, testimony and trust

Suppose that to believe a proposition is to have a credence in that proposition above some (perhaps contextual) threshold p_b where p_b is bigger than 1/2 (I think it’s somewhere around 0.95 to 0.98). Then by the results of my previous post, because of the very fast decay of the normal distribution, most propositions with credence above the threshold p_b have a credence extremely close to p_b.

Now suppose I assert precisely when my credence is above the threshold p_b. If you trusted my rationality and honesty perfectly and had no further relevant evidence, it would make sense to set your credences to mine when I tell you something. But normally, we don’t tell each other our credences. We just assert. From the fact that I assert, given perfect trust, you could conclude that my credence is probably very slightly above p_b. Thus you would set your credence to slightly above p_b, and in particular you would believe the proposition I asserted.

But in practice, we don’t trust each other perfectly. Thus, you might think something like this about my assertion:

If Alex was honest and a good measurer of own credences, his credence was probably a tiny bit above p_b, and if I was certain of that, I’d make that be my credence. but he might not have been honest or he might have been self-deceived, in which case his credence could very well be significantly below p_b, especially given the fast decay in the distribution of credences, which yields high priors for the credence being significantly below p_b.

Since the chance of dishonesty or self-deceit is normally not all that tiny, your overall credence would be below p_b. Note that this is the case even for people we take to be decent and careful interlocutors. Thus, in typical circumstances, if we assert at the threshold for belief, even interlocutors who think of us as ordinarily rational and honest shouldn’t believe us.

This seems to me to be an unacceptable consequence. It seems to me that if someone we take to be at least ordinarily rational and honest tells us something, we should believe it, absent defeaters. Given the above argument, it seems that the credential threshold for assertion has to be significantly higher than the credential threshold for belief. In particular, it seems, the belief norm of assertion is insufficiently strong.

Intuitively, the knowledge norm of assertion is strong enough (maybe it’s too strong). If this is right, then it follows that knowledge has a credential threshold significantly above that for belief. Then, if someone asserts, we will think that their credence is just slightly above the threshold for knowledge, and even if we discount that because of worries that even an ordinarily decent person might not be reporting their credence correctly, we will likely stay above the threshold for belief. The conclusion will be that in ordinary circumstances if someone asserts something, we will be able to believe it—but not know it.

I am not happy with this. I would like to be able to say that we can go from another’s assertion to our knowledge, in cases of ordinary degrees of trust. I could just be wrong about that. Maybe I am too credulous.

Here is a way of going beyond this. Perhaps the norms of assertion should be seen not as all-or-nothing, but as more complex:

1. When the credence is at or below p_b, we are forbidden to assert.

2. When the credence is above p_b, but close to p_b, we have permission to assert, but we also have a strong defeasible reason not to assert, with the strength of that reason increasing to infinity as we get closer we are to p_b.

If someone abides by these, they will be unlikely to assert a proposition whose credence is only slightly above p_b, because they will have a strong reason not to. Thus, their asserting in accordance with the norms will give us evidence that their credence is not insignificantly above p_b. And hence we will be able to believe, given a decent degree of trust.

Note, however, that the second norm will not apply if there is a qualifier like “I think” or “I believe”. In that case, the earlier argument will still work. Thus, we have this interesting consequence: If someone trustworthy merely says that they believe something, that testimony is still insufficient for our belief. But if they assert it outright, that is sufficient for our belief.

This line of thought arose out of conversations I had with Trent Dougherty a number of years ago and my wife more recently. I don’t know if either would endorse my conclusions, though.