What does Ferdinand believe "even against an oracle" in act 4 of The Tempest?

In act 2 of Shakespeare's The Tempest, Ferdinand falls in love at first sight with Prospero's daughter, Miranda.

In order to test Ferdinand's love for Miranda, Prospero charges Ferdinand with falsely claiming to be the Prince of Naples and with being a spy and traitor who intends to take his island from him. Prospero enslaves him with his magic and leads him away.

The next time we see Ferdinand in act 3, scene 1, Prospero has put him to hard physical labor stacking logs. Miranda comes to see Ferdinand, and they profess their love for one another as Prospero observes them from a distance.

In act 4, Prospero apologizes to Ferdinand for enslaving him and making him undergo such a hard test of his love for Miranda, gives him permission to marry Miranda, and praises Miranda to him.

PROSPERO: [to Ferdinand] If I have too austerely punished you,
Your compensation makes amends, for I
Have given you here a third of mine own life—
Or that for which I live—who once again
I tender to thy hand. All thy vexations(5)
Were but my trials of thy love, and thou
Hast strangely stood the test. Here, afore Heaven,
I ratify this my rich gift. O Ferdinand,
Do not smile at me that I boast of her,
For thou shalt find she will outstrip all praise,(10)
And make it halt behind her.

FERDINAND: I do believe it
Against an oracle.

PROSPERO: Then, as my gift and thine own acquisition
Worthily purchased take my daughter . . . [4.1.1-15]

In ancient Greece, an oracle was most often a priest or priestess through whom the gods were believed to speak directly, and who gave advice and made prophecies based on the will of the gods. Oracles were believed to tell the truth, although their prophecies were sometimes cryptic and difficult to understand.

Ferdinand is comparing Prospero to an oracle, and saying that he truly believes what Prospero is telling him about Miranda.

What is an oracle and what does Ferdinand disbelieve against an oracle in The Tempest?

In ancient Greece, an oracle was a gateway to the will of the gods. It was a place that, for a fee, people could consult with a priest or priestess, through whom the gods spoke, to receive prophecies and advice from the gods. The most famous (and most expensive) oracle was the Oracle of Apollo at Delphi, which was established in the eighth century BC.

Unfortunately, the information that the oracles provided was often cryptic and confusing—and sometimes even contradictory—and it was up to the individual to figure out exactly what the oracle meant.

A side business grew out of this for "prophets" and "seers" (like Teiresias in Oedipus Rex), who would interpret the oracle's information for a fee.

As far as Ferdinand in Shakespeare's The Tempest is concerned, the oracles were considered to be absolutely truthful and infallible.

In act 4 of The Tempest, Prospero gives Fernando permission to marry his daughter, Miranda, and Prospero praises Miranda to him:

PROSPERO: . . . Here, afore Heaven,
I ratify this my rich gift. O Ferdinand,
Do not smile at me that I boast of her,
For thou shalt find she will outstrip all praise,
And make it halt behind her.

FERDINAND: I do believe it
Against an oracle.

PROSPERO: Then, as my gift and thine own acquisition
Worthily purchased take my daughter (4.1.7–15)

Prospero wasn't telling Ferdinand anything he didn't already know and believe. Ferdinand had already met Miranda, fallen in love with her, and seen for himself the remarkable person she was.