The Rational Inquirer offers an original account of the rational response to peer disagreement in terms of a duty to double-check one's initial conclusions and a permission to retain an inquiry-directing attitude of hypothesis toward those conclusions. This allows for a vindication of the competing rational pressures to revise and retain one's original views that give rise to the distinctive puzzle of peer disagreement.Michele Palmira conceives of peer disagreement as higher-order evidence that generates a genuine epistemic duty to double-check one's initial conclusions. His inquiry-theoretic approach contrasts with existing approaches that characterise the rational response to higher-order evidence in terms of doxastic duties to revise or retain one's beliefs. He develops a pluralist view of the aims of inquiry, offers a definition of double-checking, and defends the genuine epistemic nature of the duty to double-check. Palmira shows that while the duty to double-check is incompatible with rational belief retention, it is compatible with the retention of an attitude of hypothesis whereby two peers retain their cognitive leanings toward conflicting answers to the question at hand. He also contends that hypothesis is a sui generis doxastic attitude that does not reduce to suspended judgement or credences, develops a non-evidentialist and consequentialist view of the central epistemic norm governing rational hypothesis, and argues that the account on offer compares favourably with recent views that also appeal to doxastic attitudes other than belief and suspended judgement.