Clearly there is a wide range of meaning for "the gods". It ranges from the very numinous
to the humorous, the metaphorical or the ironical. We must distinguish between public and
private speech where, strangely enough, Homer seems to employ a lot of private, sympotic
speech in his public poems. No other poet could do this.
Aristocrats were probably used to this. Towards the "common people" they would project a shepherd-sheep kind of relation, the gods as beings to be obeyed without argument who would be kind to you if you payed them their due respect and sacrifices. More or less like the leaders of society themselves, only more so. Plato shows this aristocratic attitude clearly - religion as a tool for rulers. Privately (in symposia for instance), as Homer and Hesiod show, they had no problems with ironical and humorous references to the gods(1).
This does not at all mean that they were irreligious or atheist. They had a much less naive view which still took the gods very seriously. This "intellectual" perspective was developed into the well-known philosophical theories by Plato and Aristotle and their predecessors but I hope to demonstrate from the texts that its roots were already there in the time of Homer and Hesiod.
There are two kinds of things that we may obey: rules and desires. I would suggest that female gods are "desire" gods, while male gods "rule". Neither Homer nor Hesiod ever hints at a difference like this but the picture fits. Gods like Zeus, Ares and Apollo in Homer impose a rule or duty on us. Goddesses like the three beauties Hera, Athena and Aphrodite represent desires. Athena in a way is both: a woman in a man's armour, an armed maiden. More on Athena below.
In Homer, the gods are what we obey(2). The classical formulation of this is that we are moved by the gods. We may obey humans: they ironically can be said to become (like) gods to us. We may obey nature: night, storms, the sea; all these make their special demands on us. We are eager to obey, to emulate, heroes (as Patroclus does), so much so that they can be described as halfgods(3). And there are major gods all of whom may tell us to do different things. Because of their superior power, these are high up in the Olympic hierarchy. We obey them, although it is still we who make the decision. The gods proper are a major subject of the Iliad. Without the gods we are "mere bellies" (Hesiod Th 26), nothing noteworthy will come out of our hands. But when we make an important decision, fight a brave battle, create something new and interesting, we are obeying gods.
Let me try to explain this by an analogy: the gods are forces, not individuals. They are like Newton's gravity. All bodies obey this force, its laws are universal. Yet it makes one body go this way, the other that way. It makes one go up, the other down. Gravity itself does not move but it moves all of us. What we see as psychological traits, the Greeks saw as forces of nature. This makes sense because they saw the world, the cosmos, as being about human beings. We were not just another animal, we were the centre of it all. For instance, the Ionian philosophers theorized about what is fundamental to the world, like water or atoms. These theories are just as much about human beings, our psychology and sociology and politics, as they are about the physical world. Plato is the supreme example of this.
So these forces rule all of us. This makes them universal and everlasting, immortal gods. At the same time they are our essential characteristics: they are human - but each only a part of us. So we have immortal humans ruling us all, the picture makes complete sense. Unfortunately, the picture is too often taken for the literal meaning.
The difference with gravity is that we can choose. The gods drive us but they do not determine us. There is complete free will. Because of this, there ought to be proper hierarchy among our gods. We can, if we recognize them, choose for ourselves how to act. This means that Zeus should make the decision. Whether he does or not, we are responsible for our actions. In other words: saying that Zeus rules and is just means that we have to be just and should know and rule ourselves. That at least seems to be not only Homer's but also Delphi's and Socrates' opinion.
To be sure, the "cosmic forces" picture stems mainly from Plato.
See also here. He calls it "soul" (psyche). Homer's
gods are less well-defined. I am only saying that Homer stands at the root of these
developments. In Homer, the most precise thing you can say is that the gods are
"what we obey". For instance:
Martin West, in his "Theogony", says the following about the gods representing abstractions like Sleep and Strife:
“In Hesiod's time it was not understood what abstractions are [...]. They must be something; they are invisible, imperishable and have great influence over humans; they must be gods.”
I am not so sure about what they did or did not understand, but these are not abstractions: Sleep and Strife are among the things that "come over you" and you may or may not give in to them. We "obey Sleep" and go to bed, we "obey Strife" and start a quarrel. But these are not simple personifications of abstractions. As indicated above and here, these are real "psychic" forces that rule us.
It should be clear that this intellectual view of the gods is not that of popular religion. If anyone did subscribe to this view, they would not have been able to express this in public anyway. There was indeed freedom of speech in their city-states, but there was also the freedom of other people to get very angry with you. Homer could get away with much, but only because of his use of the images of the gods as an allegory whose ground is private (to a class of people) and whose figure is public. Even Plato is ever reluctant to use straightforward language.
Sometimes people complain about the "amoral" character of most Greek
gods. This is a misunderstanding and betrays a naive view of the gods as
"larger people". They may be depicted as such but we must not confuse the
picture with what it depicts. The gods are what we obey, they represent
only one rule or desire each.
They rule only their own
domain so they are amoral - morality is a separate domain. Our behaviour is a result of the conflicts
and coöperations between these gods.
Morality, justice, is a rule we may or may not obey and as such, it is a god: Zeus. The other gods are not Zeus, they must defer to him. So Zeus should rule, make the decisions. Will he? Homer presents us with a picture of a pater familias who boasts of being in charge of his family but is often seen to be slightly less so.
Hera, the eldest daughter of Kronos (in Homer, Il 4.59), is married to
Zeus, his youngest son. In popular religion, her main domain appears to be
marriage. This is fitting because in an aristocratic world marriage is
inextricably linked to status and power. Also Zeus' reign and Kronos' reign before
him must be seen as dependent on their marriage to the eldest daughter of
their respective fathers. (More about marriages of the godshere).
In the Iliad and elsewhere, Hera is always in conflict with Zeus about her status.
To name some examples: she is angry about Zeus' promise to Thetis (Il 1.541-);
Zeus is angry about Hera and Athena's disobedience (Il 8.444-); about Hera's trick (Il 15.12-).
Two other scenes are important for an understanding of the goddess: it is Hera who gets
Achilles to call an embassy (Il 1.53-) and to rise again to fight Hector (Il 18.165-, 356-).
See also the explanation page entries ad loc.
Sometimes she is seen obeying Zeus, other times, most notably Il 4.37-, 68-,before the Pandaros-shoots-Menelaos episode, Zeus is seen obeying her.
Her whole attitude towards her husband Zeus is: "I am as good as you are".
She is the goddess of thumos (spirit), of wanting to be number one.
As Zeus admits, nothing else but this sort of behaviour can be expected of her (Il 8.407-).
So, she is the goddess concerned with status and honour. The Olympic picture here tells us that this was the most important drive for a Greek man. For this reason it becomes "the Good" because status is about what is considered to be good. She is the goddess of the aristocratic elite who call themselves "the best" without qualification.
Athena and the choices that she offers is one of the the main subjects in
the Iliad and Homer has a great deal to say about her. He paints her within
the Olympic family as the
favourite daughter who always knows a way to get what she wants
She is the daughter of Zeus and Mētis (cleverness, craft, wisdom, trick). The story (not in Homer) is that there was a prophecy that a child of Metis would overthrow him(1), so he swallowed the pregnant Mētis in order to make the child his own (ref. Kronos). The child finally was born by splitting Zeus' head with an axe; a fully grown and armed maiden sprang out, his favourite daughter Athena.
A mētis is a way to attain something by cleverness. It is know-how and
know-when (boldness or caution). This dangerous and very powerful capacity
is now to be ruled by Zeus as is his daughter but, as the Iliad shows, she
is by no means fully under his command.
The domains belonging to Athena range from woman's handicraft like weaving (which can be clever) to being a full-scale war goddess and protector of the city. It is, in the Greek experience, after all not military power alone that decides wars, it is most of all cleverness and knowledge. In individual battle, Athena gives courage and fierceness (menos) because that is how to win in a battle. The λόχος (ambush) is also her domain: lying in ambush, or going on a night raid, you "know more" than the one you are ambushing - namely that you are there. Again, it is a cleverness.
Instead of cleverness, wisdom or intelligence is often mentioned as her
domain but this is too detached. She is an acquiring goddess, a
desire, amoral and single-minded. She is the goddess of victory, and the
goddess of plunder (Il 10.460). She is both a rule and a desire.
Athena can teach you how to be a hero, as she does with Diomedes. This means not only killing many enemies but also knowing when to withdraw. A hero like this is a survivor, like Diomedes and Odysseus, not a gloriously dead one like Achilles, Patroclus or Hector who give their life in defense of their people. The former can of course never be as great or beautiful as the latter, which brings us to our next goddess:
Aphrodite is the goddess of sexual desire. As such, an explanation of Paris' choice is simply that he desired her, the most beautiful woman in the world. Homer, however, has a slightly more sophisticated view of the issue: he makes his choice a choice for beauty. Beautiful is something that you desire to have or desire to be and Homer paints a picture of the situation where Paris chooses to be beautiful (Il 24.30). So beautiful in fact that Helen falls in love with him and willingly follows him to Troy. This is the manner in which Aphrodite delivers Helen to Paris. In Homer there is no hint of rape or abduction though he is careful to protect her from the potential hate of his public by showing that she has no choice against such a powerful goddess (the poet of the Iliad and Odyssey always seems to love the women more than the men). For Homer's wonderful picture of their relationship, see the part 'Paris in the bedroom', Il 3.383-449.
Paris is rebuked by Helen and by Hector for "not fighting", being a coward (Il 3.38, 3.426, 6.325). This diminishes his beauty (and Helen proceeds to invite the hero Hector to sit next to her, Il 6.354) and he is persuaded by those two to go to battle after all. When he goes, he goes "ἀγλαΐηφι πεποιθὼς", literally "persuaded by the force of beauty" (Il 6.510)(3).
In an eyebrow-raising scene in book 5 (Il 5.330-430) Diomedes goes after the goddess, wounds her and chases her from the battlefield. More on this, and the relation Ares-Aphrodite here.