Here’s the shorter version of Tim Williamson’s argument against scepticism.

1. All (extant, prima facie plausible) arguments for radical scepticism require, as a premise, that we have the same evidence as a brain-in-a-vat (or whatever equivalent goes in the story).
2. The only argument for that premise is that the brain-in-a-vat does not know it has different evidence to what we have, and that if it had different evidence to us it would know that it had different evidence to us.
3. But it is not in general true that when two people have different evidence, both of them are in a position to know that they have different evidence.
C. All (extant, prima facie plausible) arguments for radical scepticism rely on a false premise.

There’s a lot of loose ends in that, all of which are tidied up in Williamson’s book, but that’s the general picture. And it’s a pretty interesting argument. I’m persuaded by the argumnts that premises 1 and 3 (or to be precise their tidied up versions) are correct. But I think there’s a different kind of justification for the claim that we have the same evidence as some brains-in-vats, one that does not appeal to the ‘transparency’ as Williamson puts it, of evidence. Or at least it doesn’t appeal to it directly. I’ll leave it up to you to judge whether it appeals to it indirectly.

Consider Stewart Cohen’s “New Evil Demon” argument against reliabilism. Cohen says that a BIV has no reliable belief forming mechanisms, but intuitively it has many justified beliefs. Indeed, intuitively my BIV twin is justified in having just the same beliefs that I am justified in having. It’s worth getting clear about the argument at this stage, because it turns out to be crucial to my case that this isn’t a demonstrative argument. (The demonstrative argument would I think have to appeal to something like transparency of evidence, and that’s false.) Rather, it’s an inductive argument … for a premise in a sceptical argument!

The evidence I’m appealing to consists of simply running through the cases where you might think I have a justified belief and my BIV twin does not, and intuiting that really we are alike in justificatory status with respect to every such belief. Induction takes us from those cases to the general claim.

Now two people can be alike in whether they are justified in believing p for all p without having the same evidence. At least in principle. But the best explanation, certainly the simplest explanation, for why each and every one of us is justified in believing the very same things our BIV twins are justified in believing is that we have the same evidence. This is a straight abductive inference, but none the worse for that. After all, what other explanation could there be for this striking coincidence.

So there’s an argument that I have the same evidence as my BIV twin that doesn’t appeal (directly) to transparency of knowledge, or anything like it. I don’t think it works, but only because I don’t think Cohen’s new evil demon argument works. If I did think that, and lots of philosophers do, even ones who don’t believe principles like the transparency of evidence, I would take this to be a different kind of argument for scepticism than the kind Williamson quite powerfully attacks.