We have to be careful about the term "religious experience", of course; because it can apply to many different things, Greer is careful to emphasize that he is only considering religious experience in the sense of "apparent encounters between one or more people and a god, spirit, or sacred presence, which either does not have a material body or which appears to transcend the limits of its material embodiment in ways not readily explained by a purely materialist analysis" (p. 67). This rules out, among other things:
(1) potentially ordinary material events (e.g., the appearance of omens) taken to have religious causes;
(2) experiences of oneness with all things;
(3) otherworld experiences;
(4) out-of-body experiences in this world.
Greer recognizes that these, especially the last three, have a great deal to tell us about religion, but notes that these are all things that one can find associated with monotheistic, polytheistic, and even atheistic religions and spiritualities alike -- they don't tell us much about gods, in any sense of the word, except perhaps with a measure of interpretation, or when they also fall under the definition given above.
Greer notes (although this part could surely be better argued than it is, with more up-to-date information) that religious experiences in his sense are actually very common features of the human landscape -- the number of people in most societies who have had a religious experience in Greer's sense is genuinely immense. Greer notes a study in which 23% of agnostics and 24% of atheists had had at least one religious experience; obviously they interpret them somewhat differently than theists do, but the point is that this is a standard part of human experience, and as such can be found all over the place, regardless of culture, economic status, or education.
Just as important for Greer's argument, the experiences are extremely diverse:
Even narrowing the focus to gods worshipped by existing religious and experienced by present-day worshippers, the diversity remains vast. Some gods are terrifying, others comforting, still others majestic, playful, fierce, impassive, maternal, passionately erotic -- and such a list could be extended indefinitely. (p. 69)
It's extraordinarily implausible, however, to suggest that an experience of the Risen Christ, an experience of Kali, and an experience of a buffalo spirit are just all experiences of one supernatural thing or amorphous divinity. If we just take the religious experiences at face value, then, the natural conclusion is polytheism.
Greer notes that many parties in the discussion have a vested interest in ignoring this. Atheists often discount religious experiences out of hand; monotheists often ignore those religious experiences that do not fit their own scheme of things or that would undermine their claim to possession of the truth. But people do in fact appeal to religious experiences for validation of their beliefs, and without a clear and definite argument for why they shouldn't, it's difficult to see how they could possibly be counted as irrational or unreasonable for doing so. Likewise, one temptation might be to focus on the subject having the experience -- what's going on in the brain, psychological background, and so forth -- but, again, without a clear and definite argument that the whole experience can be reduced to blips in the brain or neuroses, there's no good reason to ignore the object of the experience.
And it's clearly the object of the experience that's the real battleground. Traditional monotheists claim that God is one, eternal, etc.; more liberal monotheists are more creatively diverse; atheists and agnostics, Greer drily notes, more creatively diverse still:
Gods have been redefined by these latter as seasonal phenomena, neurotic projections, diseases of language, prehistoric political figures, prescientific explanatory strategies, bugs in human neurological programming, alien space travelers from other worlds, and more. (p. 75)
But Greer wants to insist that we focus on the key point he has already identified: the fact that, whatever gods may be, human beings encounter them in very common kinds of experience. We meet the gods, whatever they may be, and we live with the gods, whatever they may be, and this is a fundamental fact of human life. Even if the gods are blips in the brain, or projections of some kind, this does not affect the importance they have, Greer insists -- it just rules out a certain kind of theology. And this is yet another reason to pay close attention to religious experiences -- even a reductionist about the gods has to admit that they are the things about the experiences that need to be understood.
On the basis of the argument, Greer suggests that we use religious experiences to test claims about the gods, just as we use any other experiences to test claims about what they seem to be about. (And, again, if you're a reductionist about the gods, this is still the natural path to take: if you are going to disprove that what someone seems to experience is Kali, you have to test any such argument against the actual experiences people have of Kali in order to establish that your purported disproof is even relevant.)
Of course, the issue of interpretation of these experiences remains just as crucial, and perhaps even more so. Because of this, Greer will discuss the various possible interpretations of religious experience -- atheist, monotheistic, and polytheistic -- at greater length in Chapter Six.