William Watson Goodwin, Syntax of the Moods and Tenses of the Greek Verb

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[*] 684. The infinitive is said to stand in indirect discourse and its tenses correspond to those of the indicative or optative, when it depends on a verb implying thought or the expression of thought (one of the class of verba sentiendi et declarandi), and when also the thought, as originally conceived, would have been expressed by some tense of the indicative (with or without ἄν) or optative (with ἄν), so that it can be transferred without change of tense to the infinitive. Thus in βούλεται ἐλθεῖν, he wishes to go, ἐλθεῖν represents no form of either aorist indicative or aorist optative, and is therefore said to be not in indirect discourse. But in φησὶν ἐλθεῖν, he says that he went, ἐλθεῖν represents ἦλθον of the direct discourse. The distinction in the time of the infinitive (especially of the aorist infinitive) in these two uses is obvious.

It may be asked why the infinitive after certain other verbs should not be said to stand in indirect discourse; for example, why in κελεύει σε ἐλθεῖν or μὴ ἐλθεῖν we should not say that ἐλθεῖν represents ἐλθέ or μὴ ἔλθῃς of direct discourse. This might perhaps be done; and we might possibly make ἐλθεῖν in βούλομαι ἐλθεῖν represent ἔλθοιμι, may I go. But with other verbs of the same class, as those of advising, teaching, striving, choosing, no form of direct discourse can even be imagined. It is much harder to draw a line between these last verbs and verbs like κελεύω and βούλομαι, or even between these two, than where it is drawn above. It is impossible to say where a Greek would have drawn the line, or to be sure that he would have drawn any line at all; for our own use, the usual definition of the infinitive in oratio obliqua (as given above) is certainly the most convenient.