Alright, that makes sense (if my reading of proofs seems uncharitable at times, it is because I know enough about logic to know when a statement doesn’t make sense, but I don’t know enough to tell what the statement wants to be).
Soundness seems like an interesting property to think about for a formal system. I am reminded of the bizarre systems you can get, e.g., by taking PA and adding the axiom “PA is inconsistent”. This, if I recall correctly, is consistent provided PA itself is consistent, but (whether or not it’s consistent) it definitely can’t be sound.
Alright, that makes sense (if my reading of proofs seems uncharitable at times, it is because I know enough about logic to know when a statement doesn’t make sense, but I don’t know enough to tell what the statement wants to be).
Soundness seems like an interesting property to think about for a formal system. I am reminded of the bizarre systems you can get, e.g., by taking PA and adding the axiom “PA is inconsistent”. This, if I recall correctly, is consistent provided PA itself is consistent, but (whether or not it’s consistent) it definitely can’t be sound.
I want people to read my math uncharitably and poke holes in it, otherwise I wouldn’t post :-)