In a recent paper, Seyed Ali Kalantari and Michael Luntley propose the following prohibitive norm of belief, as superior to other extant formulations of truth norms governing belief.
(1) For any S, p: it is not the case that S ought not to believe that p only if p is true. [Their (11).]
As they note, the formula looks cumbersome, but a more intuitive re-formulation is readily available:
(2) For any S, p: it is permitted for S to believe that p only if p is true. [Their (12).] (Kalantari and Luntley, 2013: 422)
If one leaves aside considerations about the temporal profile of believing and about beliefs apparently made true by being believed—and, of course, if one assumes that beliefs are subject to permissive and prohibitive norms—then the proposal has plausibility. However, puzzles arise when we bring to bear considerations of time and constitution.
Consider the following case. At t1, exactly one person, A, believes that (p and at least two people believe that p), for true p not about persons or beliefs. A has a false conjunctive belief, since it is false that at least two people believe that p. Since it is false, at t1, that (p and at least two people believe that p), according to (2), and plausibly enough, A is not permitted to hold the belief, since they would be so permitted only if it were true that (p and at least two people believe that p). So far, so good. Trouble arises when we consider a second person, B, distinct from A, and ask about what they are permitted to believe.
Is B permitted to believe that (p and at least two people believe that p)?
Suppose the question were raised at t1. In that case, it appears that B is not permitted so to believe, since the belief would then be false and so not true. However, suppose that, at t2, B forms the belief anyway, and comes to believe that (p and at least two people believe that p). Since, on natural assumptions, A and B are distinct both now believe p, it is true, at t2, that (p and at least two people believe that p). So, as far as (2) advises, it is at t2 permissible for B (and indeed A) to believe that (p and at least two people believe that p).
What should we say about this situation? Is it a situation in which B should be permitted to form the target belief? Or is it right to say, instead that, even though B is in a position to see that were they to form the belief, it would then be true, they are not permitted to form the required belief and must run a dog-leg through, e.g., first forming the belief that (p and exactly one person believes that p)?
For present purposes, I leave the question open. It may be, however, that further reflection on the role of temporal considerations might figure in refining the alleged prohibition.
Kalantari, S. A. and Luntley, M. (2013). ‘On the logic of aiming at truth.’ Analysis 73(3): 419–422.