Not all were convinced by the earlier posts about symmetrical pragmatic encroachment and closure concerns, so I thought I’d add a bit about the context–together with a really unrealistic example.
My thinking about this occurred in the context of thinking about Pascal’s wager argument. Not the actual argument but a modification of it. So change the case where there is slightly more evidence for God’s existence than against. And change the costs of disbelief to 0. (Pascal thought the costs were infinitely negative, but suppose you are just a conditional immortalist, so that the cost of disbelief is the same whether God exists or not.) And let the benefits/costs of belief if God doesn’t exist be roughly the same (he claimed that believers would “lose some vices” so would benefit slightly; but let’s disagree and claim its a wash).
So, now the benefits of belief are supposed to be infinite, with no risks of error at all. And if one imagines a position where the extent to which the benefits lower the threshold needed for knowledge is measured by how expansive the benefits are, then even the slightest tilt of the evidence in favor of the claim could be enough to put one in a position to know. So, given the right theology (and abstracting from the plethora of other problems with the wager argument), it would be really quite easy to be in a position to know, on the basis of the evidence, that God exists.
(Depending on how the symmetry is characterized, maybe even the slightest epistemic probability away from certainty of falsehood would also put one in a position to know, but I imagined the position being one where knowledge requires some epistemic underpinning favoring a claim over its denial.)
Then consider inference cases where all is known by the inferrer: both the underlying epistemic measure and the way in which pragmatic factors undermine knowledge of the premises. The inferrer isn’t deterred since the motive concerns figuring out the underlying epistemic measure to which the believer proportions strength of belief. Imagine the degree of belief is above the threshold for belief, and that the risks of the premise prevent knowledge of it but benefits of belief in the conclusion don’t, then we get an unpalatable conclusion. So some other device, other than pragmatic encroachment and shifting thresholds, is needed to explain why one isn’t in a position to know the conclusion of the inference.
The need for an additional codicil ought to count as additional theoretical complexity, detracting from the overall simplicity and beauty of the fundamental idea. Not an objection, but in some sense a theoretical cost. And, to repeat a point made in the earlier posts, this is not meant to count as a cost for any actual pragmatic encroachment position; its about a theoretically well-motivated, symmetrical approach to the idea that comes to some grief.