Eagleman refers to himself as a "Possibilian", a term he seems to have coined. Wikipedia defines Possibilianism as "a philosophy which rejects both the idiosyncratic claims of traditional theism and the positions of certainty in atheism in favor of a middle, exploratory ground."
At first blush, this sounds like the kind of wishy-washy misguided agnosticism that asserts that since we can't have 100% certainty either way about the existence of "god", the only tenable position is to throw up our arms in a grand existential shrug. I'm sure it is unnecessary to reiterate the fallacious reasoning in this position to readers of this blog.
But looking at some more quotes from Eagleman, it becomes clear this is not what Possibilianism is at all, and to be honest I'm having trouble understanding exactly what about atheism Eagleman is trying to distance himself from.
The Wikipedia article presents two quotes from interviews with Eagleman:
I call myself a Possibilian: I'm open to a lot of ideas that we don't have any way of testing right now.
Our ignorance of the cosmos is too vast to commit to atheism, and yet we know too much to commit to a particular religion. A third position, agnosticism, is often an uninteresting stance in which a person simply questions whether his traditional religious story (say, a man with a beard on a cloud) is true or not true. But with Possibilianism I'm hoping to define a new position -- one that emphasizes the exploration of new, unconsidered possibilities. Possibilianism is comfortable holding multiple ideas in mind; it is not interested in committing to any particular story.
The initial quote referring to "ideas that we don't have any way of testing right now" sounds suspiciously like the old theist claim that religion is an epistomology that deals with questions outside the realm of science -- which is all fine and good until one moves beyond pure deism, after which the truth claims become testable and religion is exposed for the load of bullshit that it is.
But looking at the second quote, I'm not so sure that's what Eagleman means after all. I am particular intrigued by his statement "we know too much to commit to a particular religion." This seems to imply that he accepts the proposition that science is not compatible with any currently existing religion, i.e. any "particular" religion in existence can already be rejected with knowledge we already have.
I think one might also say that "[science] is comfortable holding multiple ideas in mind; it is not interested in committing to any particular story," although I suppose it depends what one means by "commit". Certainly, when multiple mutually exclusive hypotheses fit all of the available evidence equally well, this is not a problem for science, and both/all of the hypotheses can continue to be evaluated without prejudice against any new evidence. By the same token, no theory is ever proclaimed to be 100% certain in science, since new evidence might emerge that does not fit the existing hypotheses.
All of this seems perfectly in line with Eagleman's idea of "Possibilianism." (Perhaps science ought to rebrand itself thusly, since science is indeed concerned with all plausible possibilities, and "Possibilianism" sounds more exciting!)
At this point, it seems that perhaps Eagleman's disdain for atheism seems to be a mental error which I have blogged about before, namely the idea that "atheism" is defined as "an automatic disbelief in anything to which the word 'god' is ever attached." Eagleman joins atheists in observing that the overwhelming evidence forces us to dismiss any of the current ideas in existence to which the word "god" has been attached, but still resists the label -- perhaps because he fears that someday an entity will emerge which demonstrably exists and that people choose to label with the word "god"? Please...
Reading between the lines, though, I think I might have a guess at what Eagleman really means. Given the topic of his book, perhaps the distinction he draws with atheism is that, while Eagleman dismisses the truth claims of all currently existing religions, he is agnostic as to the existence of an afterlife. By contrast, I think it is probably fair to say that most, if not all, atheists believe the overwhelming evidence contradicts the idea of some sort of supernatural afterlife. (Cryogenics, which is a bit tinfoil-hat-ish in its present form anyway, would not count.)
On a completely unrelated note, I think maybe the similarity between Eagleman and Eagleton is making me more irritated about this than is warranted.