1) It seems that the black/white formalism of ‘ a statement can be only true or false ‘ causes issues. Have people tried introducing additional options for verifiability, e.g. ‘true / false / maybe?’ or something that points to uncertainty à la Heisenberg?
"Everyone when faced with the dilemma of having either an unsound or incomplete formal system chooses incompleteness. What happens when we allow for unsoundness and treat this notion as first class?"
There has been a slow burn on paraconsistent logics going back to the 80s or so now.
Two thoughts:
1) It seems that the black/white formalism of ‘ a statement can be only true or false ‘ causes issues. Have people tried introducing additional options for verifiability, e.g. ‘true / false / maybe?’ or something that points to uncertainty à la Heisenberg?
2) It would be really interesting for the author to continue the line of reasoning to help add insight to Gödel’s ontological proof. ( https://en.m.wikipedia.org/wiki/Gödel%27s_ontological_proof )