By semantics I mean your notion of what’s true. All I’m saying is that if you think that you can prove everything that’s true, you probably have a an overly weak notion of truth. This isn’t necessarily a problem that needs to be “fixed” by being really smart.
Also, I’m not saying that our notion of proof is too weak! Looking back I can see how you might have got the impression that I thought we ought to switch to a system that allows infinite proofs, but I don’t. For one thing, it wouldn’t be much use, and secondly I’m not even sure if there even is such a proof system for SOL that is complete.
By semantics I mean your notion of what’s true. All I’m saying is that if you think that you can prove everything that’s true, you probably have a an overly weak notion of truth. This isn’t necessarily a problem that needs to be “fixed” by being really smart.
Also, I’m not saying that our notion of proof is too weak! Looking back I can see how you might have got the impression that I thought we ought to switch to a system that allows infinite proofs, but I don’t. For one thing, it wouldn’t be much use, and secondly I’m not even sure if there even is such a proof system for SOL that is complete.