For whatever reason, I was reading David Enoch’s draft of “Not Just A Truthometer: Taking Oneself Seriously (but not Too Seriously) in Cases of Peer Disagreement”, when I noticed something that surprised me:
Fifth, and again following the literature here, I will focus on cases where the disagreeing peers share all the relevant evidence, and indeed where this very fact is a matter of common knowledge between them. Typical examples include a simple arithmetical calculation (what evidence could anyone possibly lack here?), philosophical debates where all concerned know of all the relevant arguments, and perhaps also moral debates of a similar nature.
This is probably pretty obvious, but the stipulation that the two parties to a dispute share all relevant evidence has very strange consequences for anyone who accepts Williamson’s thesis (E=K) that our evidence just consists of all and only those propositions that we know.
Two parties to a disagreement might share all relevant information prior to thinking about the issue, but once they begin thinking about the issue, they’ll make various inferences, and given that they end up disagreeing, they’ll probably infer different things. If any of those things they inferred count as knowledge, then they no longer share the same evidence.
And so, with a casual stipulation at the beginning of their papers, Enoch and most other writers about disagreement have been brushing aside one of the more prominent theses in contemporary epistemology.
Postscript: I say “brushing aside” because this isn’t strictly an incompatibility. You can maintain E=K, discuss the topic of disagreement with the stipulation of identical evidence, and then just admit that peer disagreement is not only a little bit uncommon, but incredibly unlikely. This is not how the discussion proceeds, and there would be reason to carefully scrutinize any paper that did proceed that way.