I disagree with the claim that climate change is likely to lead to the end of the world. I would rewrite your chain of events as:
1) climate change continues to worsen 2) farming becomes more difficult
3) as a species, we can’t produce enough food for everyone
4) tens or hundreds of millions of the most vulnerable people die.
To be clear—that's really bad and we should work to avoid it. But it's not the literal end of the world.
Really I feel the key factor is if fossil fuel infrastructure is taken offline in the process as we go back to the stone age.
If energy production is destroyed before the feedback loops set in then who knows, maybe emissions will go down enough to stave off the worst.
If things are stable enough that we keep pumping shit out then who knows.
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