 A fundamental result describes the conditions under which a method can reliably find the correct hypothesis among a countably infinite or finite number \(\mathbf{H}\) of mutually exclusive hypotheses that jointly cover all possibilities consistent with the inquirer’s background assumptions. A learner for \(\mathbf{H}\) maps a finite sequence of observations to a hypothesis in \(\mathbf{H}\). For example in the New Riddle of Induction, the natural projection is a learner for the hypothesis set \(\mathbf{H}\) that comprises “all emeralds are green”, \(H_1 =\) “all emeralds are grue(1)”, \(H_2 =\) “all emeralds are grue(2)”, etc. for all critical times \(t\). A learner reliably identifies, or simply identifies, a correct hypothesis from \(\mathbf{H}\) if for every complete data sequence the following holds: if \(H\) from \(\mathbf{H}\) is correct hypothesis for the data sequence, then there is a finite number of observations such that the learner conjectures the correct hypothesis \(H\) for any further observations consistent with the data sequence. The generalizing method and the natural projection rule are examples of reliable learners for their hypothesis sets.