You are probably concerned about AGI right now, with Eliezer’s pessimism and all that. Let me ease your worries! There is a 0.0% chance that AGI is dangerous!
Don’t believe me? Here is the proof. Let X= “There is a 0.0% chance that AGI is dangerous”. Let F=“F implies X”.
Suppose F is true.
Then by pure identity, ”F implies X” is true. Since F and ”F implies X” are both true, this implies that X is true as well!
We have shown that [if F is true, then X is true], thus we have shown ”F implies X”. But this is precisely F, so we have shown (without making assumptions) that F is true. As shown above, if F is true then X is true, so X is true; qed.
Aside from being a joke, this is also the rough concept behind the infamous Löb’s theorem Miri always talks about. (Of course Löb’s theorem doesn’t really use a formula to define itself, it gets around it in such a way that the resulting statement is actually true.)
You are probably concerned about AGI right now, with Eliezer’s pessimism and all that. Let me ease your worries! There is a 0.0% chance that AGI is dangerous!
Don’t believe me? Here is the proof. Let X= “There is a 0.0% chance that AGI is dangerous”. Let F=“F implies X”.
Suppose F is true.
Then by pure identity, ”F implies X” is true. Since F and ”F implies X” are both true, this implies that X is true as well!
We have shown that [if F is true, then X is true], thus we have shown ”F implies X”. But this is precisely F, so we have shown (without making assumptions) that F is true. As shown above, if F is true then X is true, so X is true; qed.
Aside from being a joke, this is also the rough concept behind the infamous Löb’s theorem Miri always talks about. (Of course Löb’s theorem doesn’t really use a formula to define itself, it gets around it in such a way that the resulting statement is actually true.)