Higher-order evidence is evidence about what you should think. It's nontrivial just if it allows higher-order uncertainty—uncertainty about what you should think. Mundane cases abound. I'm very confident the plane is safe, but I wonder whether I should be more (less) so—statistics is hard, after all. Theoretically interesting cases do too. Disagreement: I thought Kim was the best candidate, but my colleagues thought otherwise—I'm probably more confident than I should be. Impairment: The answer to question 17 seems obvious, but I'm running on 5 hours of sleep—I'm probably missing something. Tendencies: My argument seems convincing, but I always think my arguments are convincing—I might be overconfident. And so on.
The Question: What does higher-order evidence teach us? The Claim: A lot.
Part One ("Building Bridges") sets the stage. I argue that higher-order evidence is nontrivial and important—undergirding epistemic practices like focusing, checking our work, combatting bias, and working together. But our current theories don't do it justice: those that posit connections between first- and higher-order attitudes are beset with triviality results; those that deny them are beset with paradox. All of these problems can be seen only once we use models of probabilistic epistemic logic to investigate higher-order evidence. The way forward, then, is to apply them systematically in developing our theories.
Part Two ("Evidence: A Guide for the Uncertain") does so. I extract several precise puzzles of higher-order evidence—cases where you should expect your (total) evidence to be misleading. I then propose a new principle, Trust, to capture the idea that "What the evidence supports is likely to be true." Trust (provably) banishes our puzzles, allows nontrivial higher-order evidence, and characterizes an elegant class of models with a natural interpretation. More: Our puzzles can be unified as failures of the value of evidence in the sense made famous by I.J. Good (1967). Trust is (provably) necessary and sufficient for the value of information—for a non-paradoxical, nontrivial theory of higher-order evidence.
Part Three will explore applications and consequences in an interpersonal setting. How should multiple agents—each satisfying Trust—react to disagreement? Can they agree to disagree? To what extent (and in what circumstances) should they "conciliate"? What does this tell us about proposed theories of peer disagreement? Etc.
Can the Knowledge Norm Co-Opt the Opt-Out? (2014). Thought: A Journal of Philosophy (3) 4: 273-282.