There is a logically and linguistically peculiar sense of ἤ (‘or’) not noted in the LSJ (s.v.), but sufficiently distinct to deserve comment. The sense is most easily apprehended when a claim is made about some state of affairs signified by a disjunction, for instance that it is necessary. A particularly clear example is given by Aristotle at Metaph. 6.2.1027a32–b6, where he argues that, given certain conditions, a future event (in his example, someone dying) either will result of necessity or will not result of necessity. However, the way in which Aristotle expresses this is problematic (Metaph. 6.2.1027b4–6):

In its familiar or common use, ἤ may have an ‘inclusive’ sense (A ἤ B ἤ both) or an ‘exclusive’ sense (A ἤ B, but not both), though it has the latter sense more frequently than the former. Certainly, in this context, Aristotle intends the exclusive sense. Unfortunately, this does not fully disambiguate the clause, for it can be read as affirming either the necessary truth of the disjunction—that either she will die or she will not (but not both)—or that of necessity she will die or of necessity she will not die (but not both). This second ambiguity, which the context resolves in favour of the latter reading, results from the possibility of two different interpretations:

1. 1. The ‘wide scope’ interpretation, according to which the disjunction as a whole is necessary but neither disjunct need be.

2. 2. The ‘narrow scope’ interpretation, according to which each disjunct is necessary.

This ‘scope ambiguity’ is familiar and has been noted by scholars.Footnote ¹ Aristotle's work is particularly rich in examples, though it is only occasionally problematic, since context usually clarifies his meaning.Footnote ² But his usage is not unique. We can find examples of the ambiguity in, among others, Plato, Xenophon, Demosthenes, Theophrastus and Epictetus.Footnote ³ As with Aristotle, context typically allows us to disambiguate the scope in each of these cases.

On the assumption that the ‘wide scope’ interpretation is a result of exclusive ἤ, it has been concluded that inclusive ἤ might explain the ‘narrow scope’ interpretation.Footnote ⁴ Neither the assumption nor the conclusion is supported by the evidence. Not only may the ‘narrow scope’ interpretation apply in cases where ἤ is exclusive, but the ‘wide scope’ interpretation can apply when ἤ is inclusive.Footnote ⁵ The distinction between the ‘narrow scope’ and the ‘wide scope’ interpretations cannot be explained merely by the distinction between inclusive and exclusive ἤ. How, then, can we explain it?

It is difficult to see how context alone might explain the distinction, at least where the context in question is syntactic, since the same syntactic context can be present in both interpretations; indeed, this is precisely what is responsible for the ambiguity. Instead, I suggest that the ‘narrow scope’ interpretation is to be explained by an unfamiliar sense of ἤ.

The cases where ‘narrow scope’ readings are intended are distinguished by a sense of ἤ to which I will refer as the ‘indifferent’ sense. In this sense, ἤ has the force of ‘one or the other, regardless of which’ and implies that it is a matter of indifference, with respect to claims made about the state of affairs it signifies, whether one rather than another of the disjuncts holds, since the claim applies to each equally. The above example from Aristotle confirms this, for there his point is that all future events are necessary, so that, whether she dies or does not, necessity applies. Similarly, at Pl. Tht. 190c2–3, Socrates is emphasizing the impossibility of any judgement of the form ‘A is necessarily B’, where A and B are non-identical; the disjuncts merely signify specific examples of such judgements. In both of these cases, the disjuncts signify examples or instances of what the necessity claim applies to. Closely related are cases where the disjuncts signify possibilities and the force of the indifferent ἤ is that the necessity applies to each and every such possibility. These possibilities may be mutually exclusive or not, but their relations to each other are less significant than their relations to the necessity claim governing them.

However, indifferent ἤ is not restricted to necessity claims; indeed, occurrences of it may be embedded in any larger clause that makes a claim about some disjunctive state of affairs. At Eth. Eud. 2.10.1226b10,Footnote ⁶ for instance, Aristotle remarks that people deliberate about whether ‘this or that’ (τόδε ἢ τόδε) contributes to their end. It is clear from the context Aristotle means that, regardless of whether this or that is the object of deliberation, deliberation is directed towards something that contributes to the end. Once more, Aristotle's usage is not unique. Plato clearly invokes a similar use when he writes that ‘If Simmias here or someone else has something to say, he should not remain silent’.Footnote ⁷

In the indifferent sense, ἤ is similar in meaning to εἴτε … εἴτε, which, as Smyth notes,Footnote ⁸ ascribes ‘equal value’ to each disjunct. εἴτε … εἴτε has the sense of ‘whether … or’ or ‘if … or’ and each εἴτε introduces a subordinate clause that qualifies a claim made in a main clause. εἴτε … εἴτε is most similar in use to indifferent ἤ when both of its subordinate clauses qualify the same claim. In such cases, the main clause asserts some state of affairs that obtains regardless of whether one or the other (or all, in some cases) of the possibilities signified by the εἴτε clauses obtain: ‘The good man is happy whether he is large and strong or small and weak.’Footnote ⁹ However, unlike εἴτε … εἴτε, ἤ can signify a disjunction that is the subject or object in a claim (for instance a claim of necessity) rather than merely qualify it.

A final point to signal the importance of indifferent ἤ. At Int. 9.19a36–9, Aristotle denies the necessity of all assertions being true or false. Some scholars have felt that, for reasons of syntax and usage, it is impossible to read this claim as narrow scope.Footnote ¹⁰ Moreover, context does not seem to decide the issue one way or the other. If it is intended as ‘wide scope’, then Aristotle appears to be guilty of a flagrant inconsistency, since he repeatedly affirms the necessity of all assertions being true or false.Footnote ¹¹ However, if the ἤ in this circumstance is the indifferent ἤ, then the same syntax that legitimates the ‘wide scope’ reading would legitimate the ‘narrow scope’ reading. Together with the evidence of his commitment to all assertions being true or false, the ‘narrow scope’ reading becomes the more plausible alternative and Aristotle is thereby rescued from a gross blunder.