= 27d567bc2d48d9f40e9ccc20ea370b15)
cousin_it comments on AI cooperation in practice - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (157)
What you're saying is certainly true (onlookers, see pages 5-6 of this pdf for as especially clear explanation), but I like to think that you can't actually exhibit a proof string that shows the inconsistency of PA. If you could, we'd all be screwed!
Proof in what theory, "can't" by what definition of truth? In the extension of PA with inconsistency-of-PA axiom, it's both provable and true that PA is inconsistent.
A proof in PA that 1+1=3 would suffice. Or, if you will, the Goedel number of this proof: an integer that satisfies some equations expressible in ordinary arithmetic. I agree that there's something Platonic about the belief that a system of equations either has or doesn't have an integer solution, but I'm not willing to give up that small degree of Platonism, I guess.
You would demand that particular proof, but why? PA+~Con(PA) doesn't need such eccentricities. You already believe Con(PA), so you can't start from ~Con(PA) as an axiom. Something in your mind makes that choice.