The Final Anthropic Principle follows naturally from the Weak/Strong Anthropic Principle. Once intelligence has evolved and observed the Universe with a single first thought, why didn't it then die out? Of course the definition of Intelligence is arguable, anything from a vaguely self-aware rodent to a literature-reading human, and beyond. If we take some person called Ubuntu who discovered how to control fire 130,000 years ago at age 23 years and 7 months in southern Mozambique as having the very first aware thought, then straight afterwards there'd be no more anthropic principle at work causing intelligence to exist in the Universe. The fact we're still here, our small tribe of sole humans not eaten by hyenas or our planet not extinguished by nukes, suggests there could be a Final Anthropic Principle at work.
"Once intelligence has evolved and observed the Universe with a single first thought, why didn't it then die out?"
What proof, line of reasoning, logical principle, or evidence do you have to believe that a single first thought would lead to anything dying out? What makes you think there is some underlying Anthropic Principle at work in the universe?
Saying something could be at work is more or less saying "God did it". It doesn't explain or illuminate anything.
It only takes a single first thought by an intelligence to observe the Universe. Everything occurring up to then (e.g. nucleii, carbon, brains) is highly unlikely and therefore many people suggest an Anthropic Principle to explain it.
Once that single first thought by an intelligence has occurred, the Weak or Strong Anthropic Principle is no longer required to explain the existence of intelligence, and so its continuance has the same unlikeliness as other life forms, i.e. ultimate extinction. The fact humans became the opposite of extinct (e.g. fire, scrolls, nukes) suggests that if the Anthropic Principle applies to the emergence of intelligence, something even "stronger" such as the Final Anthropic Principle could apply to the continuance of intelligence.
I'm not saying there's an underlying Anthropic Principle in the Universe. I'm answering the question to show that the Final Anthropic Principle is as scientific a proposal as anything else.
That's not a scientific proposal. There is absolutely no reason to think that anything should cease existing simply because the first thought occurred.
