bascule said
But if you have a stable (nonzero) birth rate and eliminate aging/natural death, the population will continue to increase exponentially.
No. If, for example, every couple makes a fixed number of children and then stops, long-term population growth will be linear, not exponential.
When people are living 500+ years, what's to stop them from having, say, 8 families and raising 8 sets of children?
When people are living to be 80 years old in wealthy countries, what's to stop them from having ten kids like short-lived people in poor countries? Answer: They have the knowledge and resources to choose otherwise, and most do choose otherwise.
Why assume that just because something is possible, everbody will do it? Asking why immortality wouldn't result in exponential population growth and Malthusian disaster is like considering modern automobiles and asking, "What's to stop everybody from just turning the steering wheel and crashing into everybody else?" Answer: Because people choose not to.
Debates about exponential growth are ultimately academic because the universe by its nature will not permit it. The universe cannot sustain long-term population growth at a rate higher than time cubed, so that is probably what the growth rate of immortals (humans or posthumans) will end up being. Either entities choose to live within their means, or reality forces them to. That's equally true for mortals, immortals, posthumans, pre-humans, whatever. Immortality has *nothing* to do with it. Nothing at all.
---BrianW