Ancient holy men, whatever their motives, and whatever their methods, held forth on matters of hidden causes and predictions. Therefore, they were their ages closest thing to a philosopher or a scientist.
Of course the favorite epistemology of the priesthood is that of divine revelation. In Theory and History Chapter 3, Mises discusses revelation:
Revealed religion derives its authority and authenticity from the communication to man of the Supreme Being's will. It gives the faithful indisputable certainty.
This revelation can be through direct meetings with a deity (Moses on the Mountain), a message sent by a deity via a portent (the manifestation of a cross before Constantine). It is usually the task of the high priest to participate in direct meetings, usually behind curtains in an inner sanctum. And it is usually the task of a diviner, augur, or reader of dreams to perform the latter.
There is yet another, quite remarkable form of divine revelation is the kind which Homer himself, as a poet, proclaimed to have been privy to: divine inspiration
One of the most evocative expositions of inspiration can be found in the Theogony of the other great archaic Greek poet. Hesiod vividly tells the story of his divine inspiration, which can be paraphrased as follows.
One ancient day, at the foot of Mount Helicon in Boeotia, a lowly shepherd named Hesiod tended his flock. Upon entering a clearing, he found to his astonishment nine unspeakably beautiful goddesses standing before him. These were the Muses, the divine patronesses of the rhythmical arts (that which we call "music" in derivation from their name). It is by the grace of the Muses that the choir sings, the flutist trills, and the dancer twirls. One might call them the stage moms of the universe.
These benificient goddesses impart their own divine abilities upon the mortals they favor. And on that day, they chose to favor a mere shepherd. The Muses gave Hesiod a staff of laurel to signify his new status, and literally inspired him by exhaling their "divine voice" directly into the shepherd's lungs (the word "inspire" is derived from the Latin word for "to breathe in"). With the divine voice came not only the ability to sing, but the knowledge of songs themselves. And these were not short songs of love or worship. These were songs that told stories: true stories. Nor were these just brutish tales of kings and wars, but of origins: the genesis of man, the births of the gods, and the dawn of existence itself. Thus did Hesiod the shepherd become Hesiod the poet.
Divine inspiration is also the purported source of authority for many prophets (see the inspiration by Apollo of Cassandra and the Delphic Oracle, as well as the inspirations of Mohammed of the authors of the Holy Bible).
Inspiration might be thought of as a form of divine empowerment, or as Socrates has it in Plato's Ion a form of possession.
In all its varieties, divine revelations presents an insurmountable problem for the scientist. As Mises continues in Theory and History:
However, people disagree widely about the content of revealed truth as well as about its correct—orthodox —interpretation. For all the grandeur, majesty, and sublimity of religious feeling, irreconcilable conflict exists among various faiths and creeds. Even if unanimity could be attained in matters of the historical authenticity and reliability of revelation, the problem of the ve- racity of various exegetic interpretations would still remain.