> We can of course plug any holes we find by adding more rules but full coverage will always evade us.
So if we assume that clever software can automate the process of plugging this holes. Is it then like the human mind? Are their still holes that can not be plugged not due to lack of cleverness in the software but due to limitations of the hardware sometimes called the substrate?
> The argument is that computers are subject to this same limitation. I.e. no matter how we attempt to formalize human thinking using a computer - i.e. as a system of symbols and rules, there will be truths that the computer can simply never reach.
If computers are limited by their substrate though it seems like humans might be limited by their substrate too, though the limits might be different.
Yes I think this is one way to attack the argument but you have to break the circularity somehow. Many of the dismissals of the Hofstadter/Penrose argument I’ve read here, I think, do not appreciate the actual argument.
Without Penrose giving solid evidence people making counter arguments tend to get dismissive then sloppy. Why put in the time to make well tuned arguments filled with evidence when the other side does not bother after all.
So if we assume that clever software can automate the process of plugging this holes. Is it then like the human mind? Are their still holes that can not be plugged not due to lack of cleverness in the software but due to limitations of the hardware sometimes called the substrate?
> The argument is that computers are subject to this same limitation. I.e. no matter how we attempt to formalize human thinking using a computer - i.e. as a system of symbols and rules, there will be truths that the computer can simply never reach.
If computers are limited by their substrate though it seems like humans might be limited by their substrate too, though the limits might be different.