It makes no sense to me that I have this indestructible, undefined,supernatural attachment called a 'soul' which gets reincarnated or goesto a vague 'afterlife'. And if that soul existed before I did, haslittle or no recollection of my life while I'm alive, does not interactwith me in any discernible way, and retains little or none of whatmakes me 'me' after I'm gone, I have news for you: The soul and havevery different agendas to say the least! It doesn't make any sense tome that I'd give a hoot what happens to it, it's an unsubstantiatedsupernatural parasite as far as I'm concerned and its future welfare isabout as important to me as an imaginary tapeworm.
I'll reproduce the comment here more or less, as it captures something I've wanted to say for a while.
Buddhism has this unusual - to a Westerner- dialectice between a "reincarnation" - or rebirth- and anatman,which means the self is insubstantial, there is no soul, it is merely aconvention by which we view our bodies and minds.( I use "convention" the sense that we use base 10 in our "head" arithmetic and binary in our computers by convention)
In DarkSyde's language, it makes no sense, and seen in the way he's it, he's 100% right, and in fact there are some Buddhists who on something like a "literal" reincarnation of personalities; itseems to be a Tibetan thing.
But there's actually a way to understand both without resort to - whatI as a Buddhist- might agree crosses over into "mumbo-jumbo." It has to with what is commonly called "karma," but perhaps as rendered one can better strip the phenomena of cause and from its New Agey connotations and consequent - negativeactions, karma, what-not, etc. arising from its consideration.("Ooooh, that's gonna give you bad karma, dude!")
Interdependence - or karma- means that a sequence of actions played outreverberates through the actions of those affected by the action (whichhas no "origin," other than the coexistence and interplay of greed,hatred, ignorance, generosity, compassion, and wisdom). You can this fairly easily, if you're mindful.
Thus "our" actions and causes are continually"reborn" as this dance of cause and effect endlessly play out; the good is that "we" when "we" are mindful have some degree of control to actually make things better.
We can't demonstrate that Aunt Emma has become a chicken in "her next but we can demonstrate that the chicken consumed by Aunt Emma been incorporated into her, has become what we know of as "her."
Now to some my view here may seem dessicated, too abstract, or an intellectual exercise that tries ot fit a "long held Buddhist belief" into the intellectually tenable, but in fact actually arises from the experience of sunyata, or emptiness or voidness (insubstantiality) of existence. If "form is no other than emptiness," then "what gets reincarnated" is like asking "who becomes enlightened," and the Mahayana answer would be an inevitable "No being is reincarnated," just as "No being becomes enlightened."Hope that clears things up; that is, there is a view of "karma" and"rebirth" that is indeed intellectually defensible to the nontheist(and at least one that is not.)
Update: Shokai's ruminations on the subject are here.