I just want to take some issue with your characterization of "with mathematical certainty".
You're completely right that given fertility rates are under replacement rate—from memory: 2.1 children per woman—populations will decrease with mathematical certainty. But there is no universal law that developed countries must remain below replacement fertility levels; that's just what has always happened so far—given the cultures and policies which exist today.
It's not completely absurd to imagine scenarios like:
- a rich society getting serious about the fertility problem and putting it's money where it's mouth is: free childcare, free fertility clinics, generous subsidies for having a third kid, etc
- a culture shift amongst the patriotic, or the religious, or whatever subgroup, to believe it's their responsibility to have more children.
You're completely right that given fertility rates are under replacement rate—from memory: 2.1 children per woman—populations will decrease with mathematical certainty. But there is no universal law that developed countries must remain below replacement fertility levels; that's just what has always happened so far—given the cultures and policies which exist today.
It's not completely absurd to imagine scenarios like:
- a rich society getting serious about the fertility problem and putting it's money where it's mouth is: free childcare, free fertility clinics, generous subsidies for having a third kid, etc
- a culture shift amongst the patriotic, or the religious, or whatever subgroup, to believe it's their responsibility to have more children.