Actually human Godel sentences are quite easy to construct.
For example, I can’t prove that I’m not an idiot.
If I’m not an idiot, then I can perhaps make an argument that I’m not an idiot that seems reasonable to me, and that may persuade that I’m not an idiot.
However, if I am an idiot, then I can still perhaps make an argument that I’m not an idiot that seems reasonable to me.
Therefore any argument that I might make on whether I’m an idiot or not does not determine which of the two above states is the case. Whether I’m an idiot or not is therefore unprovable under my system.
You can’t even help me. You might choose to inform me that I am / am not an idiot. I still have to decide whether you are a reasonable authority to decide the matter, and that question runs into the same problem—if I decide that you are, I may have decided so as an idiot, and therefore still have no definitive answer.
You cannot win, you can only say “I am what I am” and forget about it.
Actually human Godel sentences are quite easy to construct.
For example, I can’t prove that I’m not an idiot.
If I’m not an idiot, then I can perhaps make an argument that I’m not an idiot that seems reasonable to me, and that may persuade that I’m not an idiot.
However, if I am an idiot, then I can still perhaps make an argument that I’m not an idiot that seems reasonable to me.
Therefore any argument that I might make on whether I’m an idiot or not does not determine which of the two above states is the case. Whether I’m an idiot or not is therefore unprovable under my system.
You can’t even help me. You might choose to inform me that I am / am not an idiot. I still have to decide whether you are a reasonable authority to decide the matter, and that question runs into the same problem—if I decide that you are, I may have decided so as an idiot, and therefore still have no definitive answer.
You cannot win, you can only say “I am what I am” and forget about it.