In Buddhism Where Will Souls Go if they Haven''t Reached Nirvana Before the Sun Dies?

[The Grand Nudger]

For example, if I were to suggest that anatta means that there is no underlying singular substance to self, but that the transcendent immaterial consciousness we are can be reborn with karmic responsibilities, what would the functional difference between that and having a reincarnating soul actually be, as concepts?

It seems to me that a soul is supposed to be personal.  Karma is not. 

A transcendental immaterial consciousness reborn -with- karmic responsibility seems very close to the function of soul in western mythologies.  To be expected, since it's an eastern mythology that seeks to answer the same fundamental questions and likely has at least -some- shared pedigree.  In being repackaged for a western audience the concept of anatta was rendered to be no self or no soul in some materialist sense, but it's a fair question..then, to ask what gets reborn.  The materialistic western buddhist might respond "oh, you know, circle of life".....but how does this square with the buddha (or anyone) recalling past lives?  

Ultimately, alot is made of the differences between buddhism and....say, christianity, as a marketing gimmick.... to present buddhism as a less superstitious alternative.  It isn't.  When you cut through the obfuscation they're very similar, and western buddhism is very much like western cultural christianity. As in cultural christianity, in western buddhism..inconvenient but essential dogma is simply omitted. Rebirth or reincarnation makes no more sense in the western repackaging of anatta than the title of christ does in cultural christianity. Buddhism...as practiced here, is just exotic jesusism.