If time is infinite does this give us any hope for life after death? After all if time is infinite, it is inevitable that all the cells in my body (my DNA etc) will be reconstructed in some far off day and age.

I don't see why since if time is indeed infinite the point at which that occurs may be infinitely in the future. Not a great deal to anticipate in that case, then!

I'm not quite ready to go along with my colleague's answer, but my answer isn't any more hopeful.

If time has the structure of the real line (as we usually think) then even if it's infinite, every moment is only a finite time away from now. (Compare: every real number is only a finite distance from 0.)

But even if time is infinite in the way the real number line is, it doesn't follow that there will be a duplicate of you somewhere off in the future. To get that conclusion woud take a lot of extra and optional premises. More important, even if there will be a duplicate of you someday, there's no good reason to think it would be you, nor is there any good reason to think that you could look forward to its experiences. (These two aren't quite the same issue, as it turns out.)

Clearly there's a lot in the background here. If you're interested in more reading on the core problem, i.e., the problem personal identity, you might have a look at Martin and Barresi's anthology, called Personal Identity.

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