Here’s a basic example using the statement, “This true statement is not provable.” If it were provable, it would be false, making logic inconsistent. If it’s not provable, then it’s true, but that makes any system trying to prove it incomplete. Either way, pure computation fails.

Am I the only one seing this as a misnomer? The statement is a composite of two statements: “This is a true statement” and “This is not a provable statement”.

The “This is a true statement” part asserts truth. And, given nothing else to go of, we can assume the part true. “It’s true that this is true”. There just isn’t any real statement being made. Taking the assumption is oerfectly valid, since we can disprove it at a later point.

The second statement, “This statement is not provable”, is very much provable, since it also asserts almost nothing, just like the previous one. Its assertion is “I’m not provable”, which is provably false.

Since the two sentences form a composite, we must compose the results of the previous two. We have a “true” and a “false”. From the composite sentence we can infer the logical operation used to connect them: AND.

Thus we have a TRUE AND FALSE boolean expression, which has a resounding answer of FALSE.

I have to say, my system didn’t prove it, but it evaluated it - unlike the authors, which claim to have proven the universe is forever ununderstandable to anyone and thus unable to be simulated.

That being said, my system seems to be perfectly consistent with itself, and, dare I say, quite grounded in reality.