After looking more closely at your linked post by Terence Tao, are you by chance basing your statements such as "it does not halt" in what he calls the informal platonic reasoning system (which presumably assumes ZFC as…
Well you said "if ZFC, a rather strong axiom system, cannot prove a machine halts, it does not halt.". This particular statement is what I was replying to. I agree that a non-halting Turing machine is not a very well…
I think this[0] is a good formalization of what I'm trying to say. [0] http://math.stackexchange.com/a/614017/215039
But if the machine that stops when it has proven ZFC is inconsistent does not halt, then surely it means there is no proof of the inconsistency of ZFC? Hence ZFC is consistent? Which is contradicted by Godel. I would…
After looking more closely at your linked post by Terence Tao, are you by chance basing your statements such as "it does not halt" in what he calls the informal platonic reasoning system (which presumably assumes ZFC as…
Well you said "if ZFC, a rather strong axiom system, cannot prove a machine halts, it does not halt.". This particular statement is what I was replying to. I agree that a non-halting Turing machine is not a very well…
I think this[0] is a good formalization of what I'm trying to say. [0] http://math.stackexchange.com/a/614017/215039
But if the machine that stops when it has proven ZFC is inconsistent does not halt, then surely it means there is no proof of the inconsistency of ZFC? Hence ZFC is consistent? Which is contradicted by Godel. I would…