I don’t believe you are engaging in a good faith discussion. Your previous comment is worthy of further contemplation but not this one. A computer can not emulate a person’s brain. At least not now and there isn’t sufficient evidence to believe that is even theoretically or practically possible to do in the future.
Your response here implicitly admits there’s difference in human thinking and computer “thinking”. A chess program that just searches a vast number of possibilities and chooses the best one is not thinking like a human. It’s not even close.
* > How will a computer prove such a thing?
I have no idea*
If you knew about these things you’d know that it isn’t possible to have an algorithm that halts in a finite number of steps that determines whether or not a given statement is an axiom in 2nd order PA. A computer is incapable of reasoning about such things.
> Can a computer beat Magnuson with the number of computations the computer can do limited to within one order of magnitude of what a human can do in the allotted time?
If a computer can't emulate a person's brain then how are you going to assess whether or not the number of computations it's doing is "within one order of magnitude of what a human can do"?
> A computer is incapable of reasoning about such things.
You want to bet on that? Before you answer you'd better re-read your claim very carefully. When you realize your mistake and correct it, then my answer will be that humans aren't guaranteed to be able to determine these things in a finite number of steps either. There's a reason that there are unsolved problems in mathematics.
Your response here implicitly admits there’s difference in human thinking and computer “thinking”. A chess program that just searches a vast number of possibilities and chooses the best one is not thinking like a human. It’s not even close.
* > How will a computer prove such a thing? I have no idea*
If you knew about these things you’d know that it isn’t possible to have an algorithm that halts in a finite number of steps that determines whether or not a given statement is an axiom in 2nd order PA. A computer is incapable of reasoning about such things.