IT is said, therefore, that Ancaus who dwelt in Samos in Cephallenia, was begot by Jupiter, whether he derived the fame of such an honorable descent through virtue, or through a certain greatness of soul.
The author (Iamblichus) does not present himself as the omniscient narrator but informs his readers that he is limited by his sources: "it is said".
The sources or "traditions" allow for various interpretations and Iamblichus, presenting himself as not having any reason to presume one over the other, cites both.
In consequence, however, of this nobility of birth being celebrated by the citizens, a certain Samian poet says, that Pythagoras was the son of Apollo. For thus he sings, . . .
It is worth while, however, to relate how this report became so prevalent.
Iamblichus expresses his reliance upon sources. Further, he seeks to understand the background to his sources; e.g. how did they come to express what they did?
Indeed, no one can doubt that the soul of Pythagoras was sent to mankind from the empire of Apollo, either being an attendant on the God, or co-arranged with him in some other more familiar way: for this may be inferred both from his birth, and the all-various wisdom of his soul. And thus much concerning the nativity of Pythagoras.
Again Iamblichus sets himself apart from his subject by relating what he knows of Pythagoras to what we could call today his (I's) "religious beliefs".
I further expresses his arms-length distance from his subject by informing the reader that he has completed the first detail of the life of Pythagoras, and implies he is now about to relate the next.
We are not immersed in a story from which the narrator hides his presence. We share Iamblichus's distance from the subject, and are constantly reminded that we are being told information that our author has drawn from various sources and various "traditions" or accounts, and that we are studying the life in some sort of objective order.
I do not suggest that we therefore can conclude that what Iamblichus says is "historically true". Obviously that is not always the case. For example, he writes in the next section:
But, when Mnesarchus considered with himself, that the God, without being interrogated concerning his son, had informed him by an oracle, that he would possess an illustrious perogative, and a gift truly divine, he immediately named his wife Pythais . . . .
This is the rhetoric of fiction. Here Iamblichus switches to the omniscient narrator conveying to readers even the inner thoughts and motivation for an immediate response to those thoughts of Mnesarchus.
I am commenting on what I see as the "rhetoric of historical" narrative and not on the historical reliability of the content itself. That's another story and discussion. The point, I think, is that readers/hearers of Iamblichus's bio of Pythagoras are being informed that they are hearing the results of the author's investigations into the details of P's life. That is, they are listening to/reading what we might call a "historical biography".