This article introduces and clarifies a neglected sense of the word ἤ (‘or’) employed by Aristotle and other authors. In this sense, called ‘indifferent’, ἤ signifies ‘one or the other, regardless of which’. It is shown how attention to this use makes it possible to explain the source of the ambiguity of certain sentences, most obviously, though not exclusively, sentences that make a necessity claim about an embedded disjunction, for example ‘It is necessary that A or B’. Why this sense cannot be explained, as some scholars have suggested, by the distinction between exclusive and inclusive ἤ is also discussed. Finally, it is shown how awareness of this sense might rescue Aristotle from a gross inconsistency.