SneerClub

I had a long reply which i think made some errors of interpretation as to what you’re saying. I find this “cancels” language confusing, but I don’t have the energy to do any more in-depth clarification on this thing!

I suppose your use of this term “cancel each other out” confuses me, since as far as I can tell it isn’t the premises which cancel each other. I get that in your schematism Davis has got to the right conclusion by luck, through faulty reasoning, but I can’t see any way to make sense of this by pointing at the interaction between his faulty premises.

The way I see your working:

1). Davis thought that the NYT didn’t HAVE any justification for calling Alexander racist (F)

2). Davis thought that the NYT didn’t NEED any justification for calling Alexander racist (F)

C). Davis thought that the NYT had all the justification they needed for calling Alexander racist (T)

Now he would be “epistemically lucky” to have reached that conclusion regardless of how he got there (as long as it was the wrong way). In fact writing it out like that it’s clear that the the argument, as you’ve presented it anyway, is poorly constructed: one of the premises is completely irrelevant, because whether or not the NYT has justification is irrelevant if they don’t need any. The valid premise is (2), which is what would make his conclusion correct by his own lights, except that it’s an untrue premise.

(The role that premise (1) plays in Davis’s actual argument is different: it disputes the claim that the NYT had justification. But this is only good for what it’s intended to do: refutation of a counter-argument. But the refutation of a counter-argument is a separate component in the broader conclusion “The NYT is right AND for the wrong reasons AND the NYT’s supporters are wrong, insofar as they think the NYT is justified”)

Where premise (1) comes back in is that the NYT did have justification, or better, they “didn’t not” have justification. That they didn’t have justification is false. But the falsehood of this doesn’t GET Davis anywhere, what gets him to the conclusion is premise (2) (which is still false). Rather, had he believed the correct opposite of premise (1) (“the NYT did not fail to have justification”) he would have got to the true conclusion. But the “cancel[ing]” here doesn’t enhance Davis’s good luck, it enhances his epistemic misfortune: his premise would have been relevant had he believed its opposite.

Notably, premise (2) doesn’t play any functional role in the truth or falsity of premise (1), and it doesn’t play any functional role in the narrative of how we get to premise (1) (or the opposite of premise 1). So it cannot be due to any cancelling effect that the opposite of premise (1) turns out to be true. Rather, what it does do is deepen the intuitive sense that Davis got especially lucky to get to the right conclusion, given that his premises pointed so far in the opposite direction when the truth was so close by.

But with things laid out like that it seems that Davis didn’t really have much epistemic luck at all, and the intuitive sense is a misleading artefact of your reconstruction of his argument as involving some procedure by which his faulty premises cancelled one another out. The deepened intuition I just mentioned is false, because in fact the odds of Davis getting it right or wrong are not especially interesting - he just thinks, for completely independent reasons, that Scott Alexander is in fact a racist, and indeed, contra Davis, Davis is using much of the same evidentiary/rational base as the rest of us, including (his version of) the NYT. Moreover, since Davis is just getting to that conclusion by premises which turn out to be faulty (AND independent premises which are true), and there is no “cancelling” procedure, he’s epistemically lucky in an extremely ordinary way, and at the very least not in the way you’re describing (whereby some mathematically interesting procedure gets him to that true conclusion).

If I had to pick a mathematical model, it'd be a drunken walk.