Actually, the general dismissal of the original poster's "stupid" logic of "I cannot conceptualize non-existence, therefore existence must persist" is itself a bit arrogant. While the idea may not be adequately explained or phrased crudely, there is I think plenty of room for some philosophical exploration.
For instance, I've observed some ponderings on the nature of consciousness (of which, in our society, there is a trend toward putting forth super-mechanistic explainations for, simply because it sounds better to the materialist - the problem is that the whole thing is filled with unpercievable factors). Some of those ponderings do in fact go in the direction of questioning the consequences of a self-aware matrix of thought. Once something becomes self-aware, can it -truly- become unaware? Comparing death to things like dreamless sleep might be extraordinarily misleading. We actually may ALWAYS be aware - we may always dream for example, to some degree. It has been observed that we simply do not remember most of what we dream, or even entire sleep periods full of dreaming.
I recall listening to a friend who's a philosophy major talking about how all the books used for classes in his course were terribly biased toward mechanical explainations of consciousness and what the mind (as opposed to merely the brain) "is". And how these biases were actually not supportable in a true, deeply logical sense, but appeared to be merely aethesthic.
My own thoughts on the subject are highly subjective and theoretical; but if "mind" is something that persists beyond the momentary skips of the quantum beat, I've pondered that to whatever degree an instance of mind is aware, that instance will result in some sort of tendency to persist. The more aware and complex that instance is, the more persistent it is.
Of course, this is looking at all of it in a "logical" sense - logic in quotes because despite how some seem to talk, logic is not the end-all of reality and merely a human system of attempting to organize information. In ways aside from the logical or scientific view, I have my own ideas and what could be called spiritual beliefs. I'm not a religous person, and can't really see how I could function within a formal religious structure. But I do believe that there are, and always will be, more things in heaven and earth than -can- be dreamt of in my, your, or anybody else's philosophy.
