I’ve been thinking about Adam Elga’s recent version of the equal weight view of disagreement. This view endorses “giving ground in the face of disagreement about many matters, but not about disagreement itself”. I think this leads to some odd results when the disagreement about disagreement is sufficiently similar to the underlying first-order disagreement.
Suzy and Billy are doing there arithmetic homework. One of the questions is: What is the average of 0.87 and 0.59? Suzy says that she is quite confident that the answer is 0.73. In fact she is 87% confident that is the correct answer. Billy says that he is not that confident, he is only 59% confident that the correct answer is 0.73. Suzy regards (or at least prior to this question regarded) Billy as an epistemic peer when it comes to this kind of question.
Question: On the equal weight view of disagreement, what credence should Suzy have that the correct answer is 0.73?
The defenders of the equal weight view face a small puzzle here. On the one hand, if they say that Suzy’s credence in p should be the average of the credences of her peers, then the credence she should have is 0.73. After all, that is the average of the credences of her peers. On the other hand, if her credences should be directly responsive in this way to the fact that the average of 0.87 and 0.59 is 0.73, then plausibly she should simply believe, with full credence, that the average of 0.87 and 0.59 is 0.73. That is, her credence that the correct answer is 0.73 should be 1.
This example is a little hackneyed, but I think there’s a general lesson here. Anyone who, like Adam, posits any mathematically defined rule for credences says that at some stage in evaluation, we simply have to say that credences must be sensitive to mathematical facts. But once we’ve said that, we have to wonder just which stage that is. I think, contra the equal weight view, that it’s typically very early in evaluation. One’s credences should be sensitive to mathematical facts directly (i.e., to the fact that the correct answer is 0.73), and not just to mathematical facts about credences of epistemic peers (e.g., the fact that the average of Suzy’s peers’ credences is 0.73). At risk of overlooking the obvious, I can’t see any reason to think otherwise, once the issue is stated in this form.
Related question: At which stage in the Achilles and the Tortoise dialogue should Achilles have refused the Tortoise’s recasting of his argument? I say – the very first time the Tortoise attempts to cast a rule of inference as a premise. Sometimes I think Adam’s version of the equal weight view is like a theory that accepts the Tortoise’s first alteration to Achilles’ argument, and rejects the second. There’s a regress that needs to be blocked, and he blocks it, but I can’t see why we would want to block it just there.