I am not a mathematician and have not read Godel's Proof. My knowledge about Godel's theorem is limited to this. So my question is this (please correct me if I have misinterpreted or misunderstood the meaning):
According to Godel's theorem, every statement is either true or false. And there are statements which cannot be proven true or false with the axioms of that mathematical system. Godel's Theorem assumes that all statements can only be true or false. Now as obvious as this statement might be but does this not bound Godel's theorem to mathematical systems which have statements which are either true or false. I mean there might be a system of mathematics where statements might either be false or true or something else all together (like undeterministic statements).
Now I am not a physicist either, but (according to my understanding) a mathematical system which has statements which can either be true or false only should not be able to classify statements like 'This electron is placed at a distance 10 nano meter.' because it is undeterministic ( Heisenberg's Uncertainity Principle).
Please share your thoughts on this. Also do let me know if my understanding of this problem is correct or not?
Thanks!