Basically just that. It seems pretty clear from the dialogues that Plato didn't put any stock behind the Pantheon as an actual thing, but he does refer often to "God." So what did he mean by "God?" How did this apparent monotheistic concept grow out of the Greek pantheistic religion? Who was "God" to the ancient Greek philosophers?
This is a tough one to answer definitively, so I'll give you my reading. The term 'God' is used to translate θεός (theos). As Simon Price observed, the Greek word for god (theos) is not a name, unlike the modern ‘God’ (the capitalisation marks it as a proper noun).[1] Theos is a predicate noun, highlighting a quality of something; it is not a clear and direct reference, but a sort of description of a vague category, capturing a sense of divinity in general. There were appropriate applications of theos in the singular referring to a specific god, for instance, for Zeus, or more typically Apollo. The latter is the case in Hdt 1.87, when Croesus blamed the ‘God of Delphi’ for his fate:
“The god of the Hellenes is responsible for these things, inciting me to wage war. No one is so foolish as to choose war over peace. In peace sons bury their fathers, in war fathers bury their sons. But I suppose it was dear to the divinity that this be so.”
In the context, the referent of 'god' is quite clearly Apollo. But this type of usage is really only the case a small percentage of the time. There were no institutional controls over appropriate usage of theos and no clear boundaries of definition, which made it hard to exclude particular beings. The semantic range of the term theos is ultimately unclear because no ancient source offered any systematic semantic analysis of it. Some sources get close-ish. Carneades in Cic. De Nat. Deo. 3.43-52 offers an extended discussion of the nature and meaning of god, and distinguishing between other figures like satyrs and the Olympians. Pl. Ap. 27b-28a has Plato’s Socrates discussing the children of the gods, and the spirits and heroes, and concluding they are all ‘divine stuff’. This is basically partly due to difference between the ideas of gods and the term theos; they don't match up perfectly. Anyway, it seems likely that theos had a broad and unfixed range, as Emily Kearns has argued.[2] She observes that it can refer to ‘a particular god, some god unknown or unspecified, or a more impersonal concept of deity’, and that the only consistent connotations of theos are very broad: of ‘power, deathlessness and unpredictability’.[3] There is no genre or type of literature in which references to the anonymous abstract collective of gods does not appear, with theos conveying a sort of vague sense of ‘godkind’.[4] So when the Greeks talked about gods, they did so with language that presumed uncertainty over the form and nature of their referents: theos is semantically undefinable because the gods were ultimately undefinable.
The vagueness about individual and specific deities built into the language of belief reflects the belief itself: one of the central ‘problems’ for scholars of Greek religion is in trying to work out individual divine identities. There was a hugely complex system of gods and epithets in the Greek world, as the two pioneering scholars of religion, Jean-Pierre Vernant and Walter Burkert, unusually agreed. Vernant stressed the inseparability of the individual gods, and Burkert the variability of characteristics depending on time and place.[5] Gods could be generalised, like ‘Zeus’, but they were also localised and specialised: ‘the Zeus of Olympia’ or ‘Zeus of Guests’. In some contexts, the Greeks clearly divided local and generalised gods from one another, while in others, they were treated as unified. For instance, in Xenophon's Anabasis, (7.8.1-6), the writer's problems were caused by his neglect of Zeus Melichios even though he was a regular worshipper of Zeus Basileus. (This should be compared with the assertion of Xenophon’s Socrates in Sym. 8.9 that, ‘Zeus, though he has many epithets, is nonetheless believed to be the same god’; the need to articulate this as an argument shows the difficulty inherent in clearly making the statement.) Parker has articulated the problem neatly: ‘Is there such a thing as Zeus, or are there just a huge host of Zeuses?’[6] There is no answer to this question - as there is no answer to the true meaning of theos - because the difficulty in resolving divine identity is not a problem with, but a feature of, Greek theology: the Greek conception of their gods depended on the vagueness of divine identity.
[1] Price, S. Rituals and Power: The Roman Imperial Cult in Asia Minor (Cambridge, 1984), at 79-81.
[2] Kearns, E. ‘Order, interaction, authority: ways of looking at Greek religion’, in A. Powell (ed.), The Greek World (London, 1995), 511-29, at 512ff.
[3] Kearns (no.2): 512; see also Alvar, J. ‘Matériaux pour l'étude de la formule sive deus, sive dea’, Numen 32:2 (1985), 236-273, on theos and unknowability.
[4] References abound to ‘godkind’: for detailed examination see Francois, G. Le Polythéisme et l'emploi au singulier des mots θεός (Paris, 1957); Parker, R. On Greek Religion (Cornell: 2011), at 65, and Polytheism and Society at Athens (Oxford, 2006), at 11-17, Mikalson, J. D. Athenian Popular Religion (London: 1983), at 66-8, and Honor Thy Gods: Popular Religion in Greek Tragedy (London: 1991), at 22-5.
[5] Complexity of the divine: Vernant, J. P. ‘Greek Religion, Ancient Religions’, in F. Zeitlin (ed.), Mortals and Immortals: Collected Essays (Princeton, 1991), 269-289, particularly at 277-8 on inseparability of gods; Burkert, W. Greek Religion (Oxford: 1985), particularly 119, on variability of time and place. Versnel, H. Coping With the Gods: Wayward Readings in Greek Theology (Leiden, 2011), at 30 has a good discussion of these.
[6] See Parker, R. ‘The Problem of the Greek Cult Epithet’, Opuscula Atheniensia 28 (2003), 173-83; Polytheism and Society at Athens (Oxford, 2006), at 11-17; and 2011 (no.4): 65 and 318ff., for his most recent and best treatment. Cf. Versnel 2011 (no.5): 60-87.
Hi, a similar question was raised a couple of weeks ago. While you're waiting for responses here, you may be interested in this post
One group, the Stoics, conceptualized "god" in terms of the rational, active principle that imbues all matter with its particular qualities. First and foremost, the Stoic god, the active principle, is a corporeal body which physically interacts with the passive principle, matter. Nature unfolds through this physical interaction.
Sometimes, the Stoic's use the singular term "god" to refer to this active principle. For example, Diogenes Laertius says, "they [The Stoics] say that god is an animal which is mortal and rational or intelligent, perfect in happiness, not admitting of any evil, provident towards the world and its occupants, but not anthropomorphic."[1] This conception of god is not like that of Plato's forms. Despite this alleged denial of an anthropomorphic god, Diogenes Laertius proceeds to analogize god's different activities in the world through the Pantheon; "They call him Zeus as the cause of all things...; Athena because his command-faculty into the aether; Hera because it stretches into the air..."[2] This seems to suggest that god is a singular entity, but his activities can be properly understood through the traditional roles played in the Pantheon.
In his hymn to Zeus, Cleanthes, the second leader of the Stoic school, makes explicit reference to the gods' prototypical appearance. Cleanthes is considered the most religious of the early Stoics [3] and he begs "bountiful Zeus of the dark clouds and gleaming thunderbolt, (to) protect to protect mankind from its pitiful incompetence." [4] In the same poem, he says, "neither men nor gods have any greater privilege than this: to sing for ever in the righteousness of the universal law." [5] Notice the simultaneous use of the plural 'gods' and reference to the 'universal law' determined by the singular active principle.
According to Cicero, Chrysippus, the third head of the Stoic school and pupil of Cleanthes, says "that divine power resides in reason and in the mind and intellect of universal nature. He says that god is the world itself...that he is the common nature of things, universal and embracing; also the force of fate and necessity of future events." [6] Chrysippus conceptualizes god in terms of a singular entity.
In sum, there is ambiguity in the early Stoic's reference to god as singular or plural. One could argue that they were monotheistic in the sense that their active principle was a single force pervading the entire world. At the same time, analogies to the Pantheon and multiple gods are frequently made. From their commentary on Stoic theology, Long and Sedley suggest "their vacillation between the singular 'god' and plural 'the gods' may to some extent reflect the deity's multiplicity of guises, but it’s probably to a larger extent indiscriminate, as often in Greek usage." [7]
[1]-[7] I. Long, A.A. II. Sedley D.N. The Hellenistic Philosophers. Vol I: Translations and Commentary. (Cambridge University Press: 1987.) 323-332.
edit: now I can actually do my homework about the early Stoics!!