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"humanity should be highly productive and very rich, and thus Earth is unlikely to be overcrowded. (As countries become richer, their fertility rates tend to decline.)"

Over time, people resistant to the "demographic transition"* (and they do exist) will replace those whose fertility declines. Also, the Earth is much more productive & rich now compared to the middle ages, and its population is far higher.

*An empirical observation, not a law of nature you can rely on to extrapolate from far into the future.

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