Further, the detour doesn't seem structurally well-conceived. Greer gives two different accounts of what he is trying to do in this digression, and why he thinks it is worthwhile. The first is that the strength of arguments for monotheism (discussed in Chapter Three) and for atheism (discussed in Chapter Four) is relevant to building a case for the intellectual merits of polytheism:
If traditional arguments produce a strong case for for the god of monotheism, or for no gods at all, an exploration of polytheism will have to take that case into account. If those arguments turn up evidence bearing on the relative merits of monotheism and polytheism, similarly, that evidence deserves a place in our discussion. For these reasons, a review of the standard arguments need not be a waste of time. (p. 39)
This suggests one possible strategy for situating polytheism within a field largely dominated by monotheistic and atheistic arguments: identify the strongest case for each that one can and, from a polytheistic perspective, meet them head on. If polytheism even manages to build a strong and distinctive counter-case, both in terms of objections and positive proposals, the basic point of the book (to show that polytheism can have real philosophical merit) would be met. In fact, we don't really get this in either Chapter Three or Four. The survey of arguments is fairly cursory (less than thirty short pages to cover four families of theistic arguments and three families of atheistic arguments), the objections raised against them are mostly the standard generic ones, and while there are some insightful points made, the discussions here are the weakest discussions in the book.
There is another justification Greer gives for the detour; the previous one was given before embarking on it, but this one comes after he has finished it:
That detour was unavoidable, since so much previous argument about gods has focused on topics such as the origins of the universe or the reasons for human suffering. Nor must a detour of this sort be entirely a waste of time; if gods exist, after all, it's reasonable to think that there may be circumstantial evidence for their presence. (p. 66)
This suggests a second strategy that could be taken in attempting to deal with the philosophical issues arising a field currently dominated by monotheism and atheism: focus on what Greer here calls "circumstantial evidence." I think we get more of this strategy in Chapters Three and Four, and most of the more interesting passages in these Chapters fit this strategy quite well: Greer will identify an argument usually assumed to lead to monotheism, e.g., cosmological arguments, and argue that you can have polytheistic versions as well. This is certainly true; certain kinds of cosmological and teleological argument, for instance, actually have polytheistic origins, or began in forms that are clearly suggestive of polytheism (Aristotle's discussion of first movers, for instance). And there is a rich vein of serious work here waiting to be uncovered; a Hellenic Reconstructionist, just to take one example, has an entire robust philosophical heritage to draw from, and other Neo-Pagan groups have plenty of room to discuss features of the world that play a major role in their religious life and examine how these features of the world display "circumstantial evidences" of the gods they worship. Likewise, Greer makes an effort to argue that at least some standard atheistic arguments depend crucially on monotheistic assumptions. One can imagine an extensive attempt to argue for ways in which polytheism manages to avoid or overcome standard problems posed by atheists against theism.
However, in the actual form we have these discussions in this book, the "circumstantial evidences" are discussed very briefly and tentatively, while the relationship of polytheistic arguments to atheistic arguments is largely confined to some interesting but incomplete discussion of theodicy. I think there are two major problems that prevent Greer from bringing these chapters together properly: (1) the fact that there really isn't space enough to pursue both the strategies suggested by Greer's justification of the detour, and thus they interfere with each other; and (2) the fact that Greer is deliberately refraining from intensive discussion of details. The point of the book is to look at polytheism in general; particular examples of polytheistic religions -- Greer's own Druidry, Wicca, folk religions, and so forth -- come up throughout the book. But they are precisely that: brief examples for illustration. Being stuck in generalities, however, is an impediment to serious discussion of the sort of topics that will come up in the monotheistic and atheistic arguments Greer is discussing. You need to ask questions like, "Is there something necessary about the gods?" and "Are the gods the causes of the world, or causes of parts of it, or caused by it?" and "What traces of the gods do we find in the world around us, that can reasonably be attributed directly to them?" and "What role do the gods play in moral life?" and "What do the gods do in the face of evil?" Generalities don't get us far with these questions.
These two chapters are still worth reading, however; they serve as a good, albeit very elementary, introduction to any polytheists who are unfamiliar with the basic ideas and arguments commonly discussed the philosophy of religion -- they are, in fact, little more than a whirlwind tour of these ideas and arguments, with some comments here and there about how polytheism might fit into the picture. But the atheistic side of the story is shortchanged, I think, and the monotheistic arguments are too briefly handled to have much effect, and the polytheistic discussions, far and away the most interesting parts of these Chapters, often seem to be crowded out by the rest.
However, even if the reader agrees with me about these two chapters, all is not lost; the detour is soon over, and with Chapters Five and Six we finally get into the meat of the book, and its most interesting and well-developed argument: the argument that religious experience in fact provides a support for polytheism that is (1) reasonable and (2) robust in the face of possible monotheistic and atheistic objections. I'll discuss Chapters Five and Six in a future post or two.