An advantage provided by the Greek myths and legends, not present in the Bible, is that these can easily be transferred into the contemporary world without too many problems around the supernatural. A great many people balk at Christianity—have done for centuries now—because many incidents described in the Bible seem ridiculous. Famously, Jefferson shredded his Bible so that it only retained ethical precepts and no supernatural elements whatsoever; but if you do this then you remove all the narrative support, all the depth, that carries the ethical injunctions along and makes them memorable. You might as well settle for the time-travelling slackers Bill and Ted’s commandment: “Be excellent to each other.” Although, of course, this very commandment is more in keeping in its concern for excellence with Ancient Greece than anything in the Bible.
By contrast, you can take a lot of what is in the Odyssey and the Iliad and read it in a way that is consistent with psychology, albeit in an analogical way. There are very few “miracles” in either text; there are few events that strike a modern person as incredulous. Now, the gods make constant appearances throughout both stories and intervene in the action; surely that is too much for moderns? I can see the atheists sneering that they have yet to see Athena walk up Bond Street or Ares outside a pub about to be charged with incitement to riot.
Fair enough, yet the very extensive pantheons found in Greek and Roman mythology pretty much map onto the whole of human psychology. Christianity really offers a dualistic God—in the Old Testament harsh and in the New Testament soft—combined with a good son (Jesus), and an all-embracing mother (Mary). Subsequently, mainly down to the Europeans, various saints and angels have been made to put flesh on the bones of a meagre faith; every Italian and Spanish town has a venerated saint who personifies their settlement—just as Athena personified Athens…
The ancient pantheons can be taken as symbolic representations for different faculties or functions within the mind. Magic is often interpreted, especially by Chaos Magic, as a means to activate the unconscious through symbolic manipulation: magic only works indirectly, so you have to activate it with an unrelated symbol—a magic spell or chant, for example. Results are only achieved when you do not actively desire what you want; so, for example, I once thought that I would like a literary agent, then I gave up the idea and then years later—when I had completely given up—I got one out of the blue.
Magical spells and incantations are a way to formalise the process of desiring without desire by encoding the desire in an unrecognisable form, so transmuting desire. Incidentally, this is what prayer and meditation do as well; they form a void—a desireless state—that then facilitates action aided by the unconscious. This is why double-blind studies into the efficacy of prayer will never achieve any results; they look for the wrong thing altogether.
So to pray to Aphrodite or Ares means to activate those parts of your mind—possibly unconscious—connected to love or war. When the various gods appear to the Greek heroes on the battlefield they can be seen as personifications of the mental states that the heroes have experienced: their need to fight harder, or to steal a slave girl away and so on. When Odysseus angers Poseidon it could be seen as a failure to sufficiently prepare himself for the long sea voyage home; to pray to Poseidon or make offerings to him before departure is to activate those parts of the mind—especially unconscious—that make you ready to be an effective sailor and avoid self-sabotage. Looked at in this way, the purpose of prayer becomes apparent and commonsensical; and the wide pantheon provided by the ancients offers a means to reach the parts of the psyche that other more austere religions, such as Christianity, cannot access.