Abstract
Two challenges to the method of reflective equilibrium have been developed in a dispute between Michael D. Resnik and Stewart Shapiro: because the method itself involves logical notions, it can neither be specified in a logic-neutral way nor can it allow logical pluralism. To analyse and answer these claims, an explicit distinction is introduced between judgements held prior to the process of mutual adjustments and judgements in agreement with the systematic principles, which result from the process. It is then argued that from the presystematic perspective, the method of reflective equilibrium permits developing and justifying rival logics, and hence it allows reasonable disagreement about logics; but such pluralism is no longer available from the perspective of fully developed logical systems.